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Simplify. 1. SOLUTION: 2. SOLUTION: eSolutions Manual - Powered by Cognero Page 1 5-3 Complex Fractions and Unit Rates

5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

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Page 1: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 1

5-3 Complex Fractions and Unit Rates

Page 2: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 2

5-3 Complex Fractions and Unit Rates

Page 3: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 3

5-3 Complex Fractions and Unit Rates

Page 4: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 4

5-3 Complex Fractions and Unit Rates

Page 5: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 5

5-3 Complex Fractions and Unit Rates

Page 6: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 6

5-3 Complex Fractions and Unit Rates

Page 7: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 7

5-3 Complex Fractions and Unit Rates

Page 8: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 8

5-3 Complex Fractions and Unit Rates

Page 9: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 9

5-3 Complex Fractions and Unit Rates

Page 10: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 10

5-3 Complex Fractions and Unit Rates

Page 11: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 11

5-3 Complex Fractions and Unit Rates

Page 12: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 12

5-3 Complex Fractions and Unit Rates

Page 13: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 13

5-3 Complex Fractions and Unit Rates

Page 14: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 14

5-3 Complex Fractions and Unit Rates

Page 15: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 15

5-3 Complex Fractions and Unit Rates

Page 16: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 16

5-3 Complex Fractions and Unit Rates

Page 17: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 17

5-3 Complex Fractions and Unit Rates

Page 18: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 18

5-3 Complex Fractions and Unit Rates

Page 19: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 19

5-3 Complex Fractions and Unit Rates

Page 20: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 20

5-3 Complex Fractions and Unit Rates

Page 21: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 21

5-3 Complex Fractions and Unit Rates

Page 22: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 22

5-3 Complex Fractions and Unit Rates

Page 23: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 23

5-3 Complex Fractions and Unit Rates

Page 24: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 24

5-3 Complex Fractions and Unit Rates

Page 25: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

eSolutions Manual - Powered by Cognero Page 25

5-3 Complex Fractions and Unit Rates

Page 26: 5-3 Complex Fractions and Unit Rates should write three complex fractions that simplify to . Students should recognize that complex fractions are fractions with a numerator, denominator,

Simplify.

1. 

SOLUTION:  

2. 

SOLUTION:  

3. 

SOLUTION:  

4. 

SOLUTION:  

5. 

SOLUTION:  

6. 

SOLUTION:  

7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute?

SOLUTION:  

To find Monica's reading rate, divide 7 by 9. Write 7 as .

 

So, Monica can read page per minute.

8. Patrick drove 220 miles to his grandmother’s house. The trip took him hours. What is his average speed in miles

per hour?

SOLUTION:  

To find his average speed in miles per hour, divide 220 by . Write as .

So, his average speed was 50 miles per hour.

Write each percent as a fraction in simplest form.

9. 

SOLUTION:  

10. 

SOLUTION:  

11. 

SOLUTION:  

12. 

SOLUTION:  

Simplify.

13. 

SOLUTION:  

14. 

SOLUTION:  

15. 

SOLUTION:  

16. 

SOLUTION:  

17. 

SOLUTION:  

18. 

SOLUTION:  

19. 

SOLUTION:  

20. 

SOLUTION:  

21. 

SOLUTION:  

22. 

SOLUTION:  

23. 

SOLUTION:  

24. 

SOLUTION:     

25. Richard rowed a canoe  miles in  hour. What is his average speed in miles per hour?

SOLUTION:  

To find Richard's average speed, divide his miles rowed by his time. Write as .

 

So, Richard rowed at a speed of 7 miles per hour.

26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour?

SOLUTION:  

To find how many gallons were used each hour, divide the number of gallons used by the time. Write as

and write as .

So, the plane used gallons of fuel each hour.

27. Sally wants to make cookies for her little sister’s tea party. Sally is cutting a roll of cookie dough into pieces that are

inch thick. If the roll is inches long, how many cookies can she make?

SOLUTION:  To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie.

Write as .

So, Sally can make 23 cookies.

28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was

the cost per yard?

SOLUTION:  

To find the cost per yard, divide $15 by 2 yards. Write 2 as .

 

So, the cost of the fabric was $6 per yard.

Write the percent as a fraction in simplest form.

29. 

SOLUTION:  

30.  %

SOLUTION:  

31.  %

SOLUTION:  

32.  %

SOLUTION:  

33.  %

SOLUTION:  

34.  %

SOLUTION:  

35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each

complete costume. She bought yards of material.

a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved.

SOLUTION:  a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom.

So, one complete costume requires yards of material.

To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material

required for each costume. Write as .

 

 

So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how

much material will be left over, multiply by the amount of material needed for one complete costume.

So, there will be yard left over.

b. To find the cost per yard, divide the total cost by the number of yards purchased.

So, the cost per yard was $3.    

36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest

form. 

SOLUTION:  

37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells.

There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can

they make?

SOLUTION:  Convert the amount of flour that the class has from pounds to cups.

So, the class has cups of flour.

To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell.

So, the class can make about 140 soft taco shells.

38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain.

SOLUTION:  Find Emma's rate by dividing the number of miles she ran by the number of minutes.

So, Emma's rate is 0.125 miles per minute.   Find Joanie's rate by dividing the number of miles she ran by the number of minutes.

So, Joanie's rate is about 0.136 miles per minute.   Joanie's speed is greater since 0.136 > 0.125.    

39. Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in

simplest form.

SOLUTION:  

So, the interest rate written as a fraction in simplest form is .

40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer.

SOLUTION:  

To determine how many times larger the moth is, divide 3 by 3 . Write 3 as and 3 as .

 

So, the moth is times larger than the butterfly.

 

Simplify.

41. 

SOLUTION:  

42. 

SOLUTION:  

43. 

SOLUTION:  

44. 

SOLUTION:  

45. 

SOLUTION:  

46. 

SOLUTION:  

47. Identify Structure Write three different complex fractions that can be simplified to .

SOLUTION:  

Students should write three complex fractions that simplify to .

Sample answer: , ,

48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one

revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object

spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.)

SOLUTION:  To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution.

So, the speed of the scooter is 220 inches per second.

49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. 

SOLUTION:  Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction.

50. Debra can run  miles in  hours. How many miles per hour can she run?

 

A   miles per hour

B   miles per hour

C   miles per hour

D   miles per hour

SOLUTION:  

To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as .

Since Debra can run 9 miles per hour, D is the answer.

51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each

bundle weigh?

 

F   lb

G  3 lb

H   lb

J  12 lb

SOLUTION:  

To determine how much each bundle weighs, divide pound by 6 bundles.

 

So, each bundle weighs pound. H is the answer.

52. LaShondra is using a model to simplify the complex fraction below.

Which statement shows how to use the model?

 

A

The figure is divided into twelfths. Count

the twelfths that fit within  of the

figure.

B

The figure is divided into twelfths.

Remove  of the twelfths, and count

those remaining.

CCount the number of thirds in the figure.  Multiply this number by 12.

DCount the number of rectangles in the figure. Divide this number by 3.

SOLUTION:  

The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer.

Write each expression using exponents.53. 3 • 3 • 3 • 3 • 3 • 3 • 3

SOLUTION:  

3 • 3 • 3 • 3 • 3 • 3 • 3 = 37

54. (–4) • (–4) • (–4) • (–4)

SOLUTION:  

(–4) • (–4) • (–4) • (–4) = (–4)4

55. 

SOLUTION:  

56. m • m • m • g • g

SOLUTION:  

m • m • m • g • g = m3g

2

57. (x + 1)(x + 1)(x + 1)

SOLUTION:  

(x + 1)(x + 1)(x + 1) = (x + 1)3

58. 5 • 5 • d • d • s • s • s • s

SOLUTION:  

5 • 5 • d • d • s • s • s • s = 52d

2s4

Express each number in scientific notation.59. 80,000

SOLUTION:  

80,000 = 8 × 104

60. 3200

SOLUTION:  

3200 = 3.2 × 103

61. 0.0054

SOLUTION:  

5.4 × 10–3

62. 2300

SOLUTION:  

2.3 × 103

63. 0.0000000098

SOLUTION:  

9.8 × 10–9

64. 47

SOLUTION:  

4.7 × 101

65. Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain.

SOLUTION:  Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces.3.48 ÷ 114 ≈ 0.03 The 114-ounce bottle costs about $0.03 per ounce.   Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces. 1.90 ÷ 44 ≈ 0.04 The 44-ounce bottle costs about $0.04 per ounce.   The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04.

Classify each polygon with the name that best describes it.

66. 

SOLUTION:  This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length.

67. 

SOLUTION:  This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal.

68. 

SOLUTION:  This polygon is a right triangle because it has three sides and one right angle.

Replace each _ with <, >, or = to make a true sentence.69. 0.925 _ 1.023

SOLUTION:  0.925 < 1.023

70. 0.15 _ 0.099

SOLUTION:  0.15 > 0.099

71. 7.3 _ 7.30

SOLUTION:  7.3 = 7.30

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5-3 Complex Fractions and Unit Rates