Write the operation (+, –, , ÷) that corresponds to each phrase. 1.divided by2.difference3.more than4.product 5.minus6.sum7.multiplied by8.quotient Find

Write the operation (+, –, , ÷) that corresponds to each phrase.

1. divided by 2. difference 3. more than 4. product

5. minus 6. sum 7. multiplied by 8. quotient

Find each amount.

9. 12 more than 9 10. 8 less than 13

11. 16 divided by 4 12. twice 25

ALGEBRA 1 LESSON 1-1ALGEBRA 1 LESSON 1-1

Using VariablesUsing Variables

1-1

1. divided by: ÷ 2. difference: –

3. more than: + 4. product: 5. minus: – 6. sum: +

7. multiplied by: 8. quotient: ÷

9. 12 more than 9: 9 + 12 = 21 10. 8 less than 13: 13 – 8 = 5

11. 16 divided by 4: 16 ÷ 4 = 4 12. twice 25: 2(25) = 50



Solutions

1-1

Write an algebraic expression for “the sum of n and 8.”

“Sum” indicates addition. Add the first number, n, and the second number, 8.

n + 8



1-1

Relate: ten more than twice a number

Write: 2 • y + 10

Define: Let y = the number.

Define a variable and write an algebraic expression for “ten

more than twice a number.”

2y + 10



1-1

Write: i = 5 • t

Define: Let t = the number of tickets sold.

Let i = the total income

Write an equation to show the total income from selling

tickets to a school play for $5 each.

Relate: The total income is 5 times the number of tickets sold.

i = 5t



1-1

Define: Let m = the number of miles traveled.Let g = the number of gallons.

Relate: Miles traveled equals 20 times the number of gallons.

Write an equation for the data in the table.

Write: m = 20 • g

m = 20g

Gallons

Miles

4 6 8 10

80 120 160 200



1-1



pages 6–8 Exercises

1. p + 4

2. y – 12

3. 12 – m

4. 15c

5.

6.

7. x – 23

8. v + 3

9–16. Choice of variable may vary.

9. 2n + 2

10. n – 11

11. 9 – n

12.

13. 5n

14. 13 + 2n

15.

16.

17. c = total cost,

n = number of cans,

c = 0.70n

18. p = perimeter,

s = length of a side,

p = 4s

19. = total length in feet,

n = number of tents,

= 60n

20. = number of slices left,

e = number of slices eaten,

= 8 – e

n817 k

1-1

n82

n611n



21–24. Choices of variables may vary. Samples are given.

21. w = number of workers,

r = number of radios,

r = 13w

22. n = number of tapes,

c = cost, c = 8.5n

23. n = number of sales,

t = total earnings,

t = 0.4n

24. n = number of hours,

p = pay,

p = 8n

34–38. Answers may vary. Samples are given.

34. 5 more than q

35. the difference of 3 and t

36. one more than the product

of 9 and n

37. the quotient of y and 5

38. the product of 7

times h and b

1-1

25. 9 + k – 17

26. 5n + 6.7

27. 37t – 9.85

28.

29. 15 +

30. 7 – 3v

31. 5m –

32. +

33. 8 – 9r

3b 4.5

60w

t 7

p14

q3



1-1


39. n = number of days,

c = change in height (m),

c = 0.165n

40. t = time in months,

= length in inches,

= 4.1t

41. a. i. yes; 6 = 3 • 2

ii. yes; 6 = 3 + 3

b. Answers may vary. Sample: i;

it makes sense that an equation relating lawns mowed and hours

worked would be a multiple of the number of lawns mowed.


42. a. Let a = the amount in dollars

and n = the number of quarters,

a = 0.25q.

b. $3.25

43. a. d = drop height (ft),

f = height of first bounce (ft), f = d

b. 10 ft

44. s = height of second bounce (ft),

s = d

12

14




45. You jog at a rate of 5 miles per hour. How far do you jog in 2 hours? Let d = distance in miles and t = time in hours.

46. Anabel is three years older than her brother Barry. How old will Anabel be when Barry is 12? Let a = Anabel’s age in years and b = Barry’s age in years.

47. The Merkurs have budgeted $40 for a baby sitter. What hourly rate can they afford to pay if they need the sitter for 5 hours? Let h = the number of hours and c the cost per hour.

48. D

49. H

50. A

51. G

52. D

53. F

54. 0.9

55. 1.04

56. 1.35

57. 1.46

58. 0.63

59. 0.09

60. 0.14

61. 0.93

62. 1

63. 0.23

64. 3

65. 0.11

66. any four of 23,

29, 31, 37, 41,

43, and 47

1-1


Write an algebraic expression for each phrase.

1. 7 less than 9

2. the product of 8 and p

3. 4 more than twice c

Define variables and write an equation to model each situation.

4. The total cost is the number of sandwiches times $3.50.

5. The perimeter of a regular hexagon is 6 times the length of one side.

9 – 7

8p

2c + 4

Let c = the total cost and s = the number of sandwiches; c = 3.5s

Let p = the perimeter and s = the length of a side; p = 6s


1-1

Find each product.

1. 4 • 4 2. 7 • 7 3. 5 • 5 4. 9 • 9

Perform the indicated operations.

5. 3 + 12 – 7 6. 6 • 1 ÷ 2

7. 4 – 2 + 9 8. 10 – 5 – 4

9. 5 • 5 + 7 10. 30 ÷ 6 • 2


Exponents and Order of OperationsExponents and Order of Operations

1-2

1. 4 • 4 = 16

2. 7 • 7 = 49

3. 5 • 5 = 25

4. 9 • 9 = 81

5. 3 + 12 – 7 = (3 + 12) – 7 = 15 – 7 = 8

6. 6 • 1 ÷ 2 = (6 • 1) ÷ 2 = 6 ÷ 2 = 3

7. 4 – 2 + 9 = (4 – 2) + 9 = 2 + 9 = 11

8. 10 – 5 – 4 = (10 – 5) – 4 = 5 – 4 = 1

9. 5 • 5 + 7 = (5 • 5) + 7 = 25 + 7 = 32

10. 30 ÷ 6 • 2 = (30 ÷ 6) • 2 = 5 • 2 = 10



Solutions

1-2

Simplify 32 + 62 – 14 • 3.

32 + 62 – 14 • 3 = 32 + 36 – 14 • 3 Simplify the power: 62 = 6 • 6 = 36.

= 32 + 36 – 42 Multiply 14 and 3.

= 68 – 42 Add and subtract in order from left to right.

= 26 Subtract.



1-2

Evaluate 5x = 32 ÷ p for x = 2 and p = 3.

5x + 32 ÷ p = 5 • 2 + 32 ÷ 3 Substitute 2 for x and 3 for p.

= 5 • 2 + 9 ÷ 3 Simplify the power.

= 10 + 3 Multiply and divide from left to right.

= 13 Add.



1-2

Find the total cost of a pair of jeans that cost $32 and have

an 8% sales tax.

total cost original price sales taxC = p + r • p

sales tax rate

C = p + r • p= 32 + 0.08 • 32 Substitute 32 for p. Change 8% to 0.08 and

substitute 0.08 for r.

= 32 + 2.56 Multiply first.

= 34.56 Then add.

The total cost of the jeans is $34.56.



1-2

Simplify 3(8 + 6) ÷ (42 – 10).

3(8 + 6) ÷ (42 – 10) = 3(8 + 6) ÷ (16 – 10) Simplify the power.

= 3(14) ÷ 6 Simplify within parentheses.

= 42 ÷ 6 Multiply and divide from left to right.

= 7 Divide.



1-2

Evaluate each expression for x = 11 and z = 16.

a. (xz)2

= (176)2 Simplify within parentheses. Multiply. = 11 • 256

= 2816= 30,976 Simplify.

(xz)2 = (11 • 16)2 Substitute 11 for x and 16 for z. xz2 = 11 • 162



1-2

b. xz2

Simplify 4[(2 • 9) + (15 ÷ 3)2].

4[(2 • 9) + (15 ÷ 3)2] = 4[18 + (5)2] First simplify (2 • 9) and (15 ÷ 3).

= 4[18 + 25] Simplify the power.

= 4[43] Add within brackets.

= 172 Multiply.



1-2

A carpenter wants to build three decks in the shape of

regular hexagons. The perimeter p of each deck will be 60 ft. The

perpendicular distance a from the center of each deck to one of the

sides will be 8.7 ft.

= 3(261) Simplify the fraction.

= 783 Multiply.

The total area of all three decks is 783 ft2.

A = 3 ( )pa2

= 3 ( ) 60 • 8.7

2Substitute 60 for p and 8.7 for a.

= 3 ( )5222

Simplify the numerator.



1-2

Use the formula A = 3 ( ) to find the total area of all three decks.pa2




1. 59

2. 22

3. 7

4. 113

5. 32

6. 29

7. 21

8. 27

9. 124

10. 15

11. 180

12. 169

13. $37.09

14. $347.10

15. 22

16. 3

17. 44

18. 5

19. 16

20. 4

21. 704

22. 7744

23. 185

24. 361

25. 57

26. 9

27. 1936

28. 3872

29. 18

30. 186

31. 0

32. 7

33. 81

34. 36

35. 8 cm3

36. 91 in.3

37. 21 ft3

38. 28 cm3

39. 15,000 ft3

40. 2596 m3

41. 15

42. 7

43. 111

44. 1

45. 51

46. 50.4

47. 242

48. 61

49. 71.6

50. 58

51.

52. 7

53. 1

54. 7

13

56

1-2

7 15

58



55. a. left side = 1 right side = 1

b. left side = 4right side = 2

c. Answers may vary. Sample: For a = 2 andb = 3, left side = 25,right side = 13

d. No; as seen in part (b), (a + b)2 = a2 + b2 is not true for all valuesof a and b.

56. 17

57. 9

58. 143

59. 135

60. 143

61. 27

62. 14

63. 308

64. a. 135 in.2

b. The frame is

2 in. wide, so

it adds 2 in.

on each side.

65. $.16

66. 407.72 cm3

67. a. 523.60 cm3

b. 381.70 cm3

c. about 73%

68. 38

69. 127

70. 9

71. 10

72. 10

73. a. 23.89 in.3

b. 2.0 in.3

c. 47.38 in.2

1-2

34

13



74. Yes; the rules for simplifying are designed to produce exactly one result.

75. (10 + 6) ÷ 2 – 3 = 5

76. 14 – (2 + 5) – 3 = 4

77. (32 + 9) ÷ 9 = 2

78. (6 – 4) ÷ 2 = 1

79. a. 22; 22

b. No; part (a) shows the value is unaffected for the given numbers.

80. a. 16, 2

b. Yes; part (a) shows that the placement of parentheses can affect the value of the expression, when both add. and subtr. are involved.

81. Answers may vary. Samples:

2(4 – 1) – 5 = 1

5 + 2 – (1 + 4) = 2

(24 – 1) ÷ 5 = 3

1 + 2 + 5 – 4 = 4

2 • 5 – (1 + 4) = 5

(52 – 1) ÷ 4 = 6

5 + 4 – 1 • 2 = 7

25 ÷ (4 • 1) = 8

25 ÷ 4 + 1 = 9

42 – (1 + 5) = 10

(42 – 5) ÷ 1 = 11

1 + 2 + 4 + 5 = 12

2(4 – 1) + 5 = 13

2 • 5 + 1 • 4 = 14

5(4 – 12) = 15

2(1 + 5) + 4 = 16

5 + 4(2 + 1) = 17

4(5 – 1) + 2 = 18

4 • 5 – 12 = 19

42 + 5 – 1 = 20

1-2

82. a. 38 ft2

b. Yes; 2h = 2 h .

No; h = 2h

since b2 = 0.

Yes; h = h =

2 h .



b1 + b2

2

b1 + b2

22b1 + b2

2/ b1 + b2

2/

2(b1 + b2)2

2(b1 + b2)2

b1 + b2

2

83. D

84. F

85. B

86. H

95. 95%

96. 145%

97. 6%

98. 43

99. 18.9

100. 1.25

101. 60.3

87. B

88. F

89. c + 2

90. 36m

91. t – 21

92.

93. 50%

94. 34%

y5


102. 8, 24, 56

103. 55, 100, 250

104. 44, 66, 121

105. 60, 150, 240

106. 26, 39, 52

1-2


Simplify each expression.1. 50 – 4 • 3 + 6

2. 3(6 + 22) – 5

3. 2[(1 + 5)2 – (18 ÷ 3)]

Evaluate each expression.4. 4x + 3y for x = 2 and y = 4

5. 2 • p2 + 3s for p = 3 and s = 11

6. xy2 + z for x = 3, y = 6 and z = 4

44

25

60

20

51

112


1-2

Write each decimal as a fraction and each fraction as a decimal.

1. 0.5 2. 0.05 3. 3.25 4. 0.325

5. 6. 7. 8. 3

(For help, go to skills handbook page 725.)


Exploring Real NumbersExploring Real Numbers

1-3

25

38

23

59



1-3

1. 0.5 = = =

2. 0.05 = = =

3. 3.25 = 3 = 3 = 3 or

4. 0.325 = = =

5. = 2 ÷ 5 = 0.4

6. = 3 ÷ 8 = 0.375

7. = 2 ÷ 3 = 0.6

8. 3 = 3 + (5 ÷ 9) = 3.5

5 10

12

5 • 15 • 2

5 100

5 • 1 5 • 20

25 100

14

134

25 • 125 • 4

325 1000

25 • 1325 • 40

1340

25

38

23

59

Solutions

1 20

Name the set(s) of numbers to which each number belongs.

a. –13 b. 3.28

integers

rational numbers

rational numbers



1-3

Which set of numbers is most reasonable for displaying

outdoor temperatures?

integers



1-3

Determine whether the statement is true or false. If it is false,

give a counterexample.

All negative numbers are integers.

The statement is false.

A negative number can be a fraction, such as – . This is not an integer.23



1-3

Write – , – , and – , in order from least to greatest.

– = –0.75 Write each fraction as a decimal.

– = –0.583

– = –0.625

34

7 12

58

From least to greatest, the fractions are – , – , and – .34

7 12

58

–0.75 < –0.625 < –0.583 Order the decimals from least to greatest.



1-3

34

7 12

58

Find each absolute value.

a. |–2.5| b. |7|

–2.5 is 2.5 units from 0 on a number line.

7 is 7 units from 0 on a number line.

|–2.5| = 2.5 |7| = 7



1-3




1. integers, rational numbers

2. rational numbers

3. rational numbers

4. natural numbers, whole numbers, integers, rational numbers

5. rational numbers

6. integers, rational numbers

7. whole numbers, integers, rational numbers

8. rational numbers

9. rational numbers

10. irrational numbers

11. Answers may vary.

Sample: –17


Sample: 53


Sample: 0.3

14. rational numbers

15. whole numbers

16. integers

17. whole numbers


19. true

20. False; answers may vary.

Sample: –


Sample: 6

22. true


Sample: –6 < | –6 |

24. >

25. <

26. >

1-3

23



1-3

27. =

28. 2.001, 2.01, 2.1

29. –9 , –9 , –9

30. – , – ,

31. –1.01, –1.001, –1.0009

32. 0.63, 0.636,

33. , 0.8888,

34. 4

35. 9

36.

37. 0.5

38.

23

34

23

12

56

2225

89

7 11

7 12

39. 0

40. 1295

41.


Sample:


Sample:


Sample:


Sample:

9 14

35


Sample:





45

15

51

21310

10341000

– 41



51. =

52. >

53. <

54. >

55. =

56. >

57. 6

58. 9

59. a

60. 28

61. 48

62. 5

63. a. irrational

b. No; has no final digit.

64. 0

65. Neg.; 0 is the point between R and S since the coordinates of Q and T are opposites,so if R is to the left of 0, then R is neg.

66. Q; 0 is the point to the right of S because the coordinates of R and T are opposites, therefore the point Q is the farthest from 0, so it has the greatest absolute value.

67. Answers may vary. Sample: 25, |25| + | –25| = 50

68. sometimes

69. sometimes

70. sometimes

71. always

72. Yes; all can be expressed as ratios of themselves to 1.

73. –6

74. 17

75. 1

76. 10

1-3



77. a. 2.75 , 19.3 ,

10.5 , 3.5

b. aluminum, diamond,

silver, gold


Samples are given.

a. –2.2

b. –2.81

c. –2d. Yes; find the average

of the two given numbers.

79. A

80. G

81. D

82. G

83. C

84. I

85. C

86. 33

87. 48

88. 315

89. 7

90. 0

91. 7

92. 25

93. 4

94. 195

95–98. Choices of variables may vary.

95. n = number of tickets, 6.25n

96. i = cost of item, i + 3.98

97. n = number of hours, d = distance traveled,d = 7n

98. c = total cost, n = number of books,c = 3.5n

18

gcm3

gcm3

gcm3

gcm3

12

1-3


Name the set(s) of numbers to which each given number belongs.

1. –2.7 2. 11 3. 16

Use <, =, or > to compare.

4. 5.

6. Find |– |.

34

58

rational numbers irrational numbers natural numbers, whole numbersintegers, rational numbers

– –

7 12

> <

7 12


1-3

34

58

(For help, go to skills handbook page 726.)


Adding Real NumbersAdding Real Numbers

1-4

Find each sum.

1. 4 + 2 2. 10 + 7 3. 9 + 5

4. 27 + 32 5. 0.4 + 0.9 6. 5.2 + 0

7. 4.1 + 6.8 8. 7.6 + 9.5 9. +

10. + 11. + 12. +

15

35

49

79

12

34

38

14



1-4

1. 4 + 2 = 6 2. 10 + 7 = 17

3. 9 + 5 = 14 4. 27 + 32 = 59

5. 0.4 + 0.9 = 1.3 6. 5.2 + 0 = 5.2

7. 4.1 + 6.8 = 10.9

8. 7.6 + 9.5 = 17.1

9. + = =

10. + = = = 1

11. + = + = = = 1

12. + = + = =

15

35

1 + 35

45

49

79

4 + 79

119

12

34

24

34

2 + 34

29

54

14

38

14

38

28

3 + 28

58

Solutions

Start at –3.

Move right 5 units.

Start at –3.

Move left 5 units.

Start at 3.

Use a number line to simplify each expression.

a. 3 + (–5) b. –3 + 5

c. –3 + (–5)

3 + (–5) = –2 –3 + 5 = 2

–3 + (–5) = –8

Use a number line to simplify each expression.

Move left 5 units.



1-4

Simplify each expression.

a. 12 + (–23) = –11 b. –6.4 + (–8.6) = –15.0

The difference of the absolute values is 11.

The negative addend has the greater absolute value, so the sum is negative.

Since both addends are negative, add their absolute values.

The sum is negative.



1-4

The water level in a lake rose 6 inches and then fell 11 inches.

Write an addition statement to find the total change in water level.

6 + (–11) = –5 The water level fell 5 inches.



1-4

Evaluate 3.6 + (–t) for t = –1.7.

3.6 + (–t) = 3.6 + [–(–1.7)] Substitute –1.7 for t.

= 3.6 + [1.7] –(–1.7) means the opposite of –1.7, which is 1.7.

= 5.3 Simplify.



1-4

A scuba diver who is 88 ft below sea level begins to ascend

to the surface.

Define: Let r = the number of feet the diver rises.

a. Write an expression to represent the diver’s depth below sea level after rising any number of feet.

Relate: 88 ft below sea level plus feet diver rises

Write: –88 + r

–88 + r

b. Find the new depth of the scuba diver after rising 37 ft.

–88 + r = –88 + 37 Substitute 37 for r.= – 51 Simplify.

The scuba diver is 51 ft below sea level.



1-4



1 3.2 913.4 8 –4

Simplify.=

7 –5.4 –2

11.1 3 –1

–6 8.6 11

2.3 5 –3Add +

7 –5.4 –2

11.1 3 –1

–6 8.6 11

2.3 5 –3+

–6 + 7 8.6 + (–5.4) 11 + (–2)2.3 + 11.1 5 + 3 –3 + (–1)

Add corresponding elements.=

1-4




1. 6 + (–3); 3

2. –1 + (–2); –3

3. –5 + 7; 2

4. 3 + (–4); –1

5. 15

6. –11

7. –19

8. 12.14

9. –4

10. 5

11. –8

12. –42

13. 2.2

14. –0.65

15. –7.49

16. 1.33

17.

18. –

19. 6

20. –6

21. 0

22. –

1415

89 3 16

18

1318

23. 5

24. –

25. –47 + 12 = –35, 35 ft below the surface

26. 8 + (–5) = 3, 3 yd gain

27. –6 + 13 = 7, 7°F

28. 8.7

29. –1.7

30. 1.7

31. –8.7

32. 12.6

161314

1-4



1-4

33. –5.6

34. 5.6

35. –12.6

36–37. Choices of variable may vary.

36. c = change in temp., –8 + c

a. –1°F

b. –11°F

c. 11°F

37. c = change in amount of money, 74 + c

a. $92

b. $45

c. $27

38.

39.

40.

41.

42. –2.7

43. –13

44. 6.6

–1 1.4–21 23.2

–18.211.619.1

025

–12

1.8 22

– 712

45. 11

46. 4

47. –3

48. –18.53

49. –20.83

50. –1.72

51. –

52. –5

53. 0.8

54. 4

55. –8.8

1924

2235

11 120

13

1760



1-4

56. 13.8 million people

57. 6.3 million people

58. Weaving; add the numbers in each column.

59. a. =

b. 0.23

c. about 23%

60. 0

61. –2

62. 1

63. –5

64. 7

65. 5

66. –1

67. 1

68. The sum of –227 and 319; the sum of –227 and 319 is positive, while the sum of 227 and –319 is negative.

69. Answers may vary. Sample:Although 20 and –20 are opposite numbers, there is no such thing as opposite temperatures.

70. –0.3

71. –13.7

72. –0.6

73. 8.7

74. 0.1

75. –1.9

76. +2

100442

50 221



77. Answers may vary. Sample:

78. The matrices are not the same size, so they can’t be added.

79. No; time and temperature are different quantities and can’t be added.

80. a.

2 0 1–1 3 0.5

80. (continued)b.

c. 4 employees

d. 10 employees

e. Answers may vary. Sample: Multiply the entries in each column by the appropriate hourly wage, then by 8, and then add all entries to find the total wages.

f. $3230

81. $7

8 3 5 110 2 2 1

4 1 0 1

5 2 1 18 2 0 12 1 0 1

13 5 6 218 4 2 2

6 2 0 2

82. a. 4

b. –4

1-4



1-4

83.

84.

85.

86. –

87.

88. –

89.

8 32 –27

20 6 0

1 –1

2 1

1412

12

12

12

w 10

c2

90. –

91.

92.

93.

94. Pos.; if m is neg., –m is pos. and the sum of two pos. is pos.

95. Neg.; if n is pos., –n is neg. and the sum of two neg. is neg.

96. Pos.; if m is neg., –m is pos. and the sum of two pos. is pos.

97. Zero; sum of neg. and pos. is the difference of the abs. values. |n| = |m| so |n| – |m| = 0.

98. zero; n + (–m) = n + (–n) = 0

99. B

100. F

101. D

102. F

103. C

104. H

105. <

106. =

111. 9

112. 2.2

113. 18

114. 21

107. <

108. >

109. >

110. =

x 12

t 6 –3m + 1

4m9

58a212b9

x 12


Simplify.

1. 15 + (– 10) 2. – 57 + (– 11) 3. – 42 + 19

4. – 1 + (– 3 ) 5.

6. Evaluate 25 + 4x for x = – 5.

5 –68 –23

–4 715

5


3 –5–2 0

–2 –4 8 –6+

1 – 96 – 6

1-4

15

4 15


(For help, go to Lessons 1-3 and 1-4)

Subtracting Real NumbersSubtracting Real Numbers

1-5

Find the opposite of each number.

1. 6 2. –7 3. 3.79 4. –

Simplify.

5. 3 + (–2) 6. 9.5 + (–3.5) 7. 13 + (–8) 8. + – ( )

7 19

23

16



1-5

1. opposite of 6: –6 2. opposite of –7: 7

3. opposite of 3.79: –3.79 4. opposite of – :

5. 3 + (–2) = 1 6. 9.5 + (–3.5) = 6

7. 13 + (–8) = 5

8. + – = + – = = =

7 19

23 ( ) ( )1

646

16

4 + (–1)6

36

12

Solutions

7 19

Subtract –3 – 2 using a number line.

–3 – 2 = –5

Start at –3.

Move left 2 units



1-5

Subtract 4 – (–2) using tiles.

There are 6 positive tiles left.

4 – (–2) = 6

Start with 4 positive tiles.

Add zero pairs until there are 2 negative tiles.

Remove 2 negative tiles.



1-5

Simplify –11.6 – (–14).

–11.6 – (–14) = –11.6 + 14 The opposite of –14 is 14.

= 2.4 Add.



1-5

Simplify |–13 – (–21)|.

|–13 – (–21)| = | –13 + 21| The opposite of –21 is 21.

= | 8 | Add within absolute value symbols.

= 8 Find the absolute value.



1-5

Evaluate x – (–y) for x = –3 and y = –6.

x – (–y) = –3 – [–(–6)] Substitute –3 for x and –6 for y.

= –3 – 6 The opposite of –6 is 6.

= –9 Subtract.



1-5

The temperature in Montreal, Canada, at 6:00 P.M. was –8°C.

Find the temperature at 10:00 P.M. if it fell 7°C.

Find the temperature at 10:00 P.M. by subtracting 7°C from the temperature at 6:00 P.M.

–8 – 7 = –8 + (–7) Add the opposite.

= –15 Simplify.

The temperature at 10:00 P.M. was –15°C.



1-5



1. –1

2. –2

3. –6

4. –5

5. 1

6. –11

7. 14

8. 3

9. –4

10. 11

11. –10

12. –4

13. –2.1

14. –9.2

15. 13.7

16. 3.5

17. –

18. –1

19.

20. –

21. 3

22. 8

23. 6

24. 2

25. 13

26. 2

27. 6

28. 3

29. –10

30. 7

31. 1

32. 1

33. 3

34. 0

35. –7

36. –13

37. $50.64

38. –9.5

39. –1.5

40. –2

41. 5.5


1-5

1 10

16

1112

1960



42. 1.5

43. –1

44. 16

45. –16

46. 11

47. 1

48. –2

49. 12.5

50. 650 ft

51. Answers may vary. Sample:

52. false; –1 – (–7) = 6, –1 + (–7) = –8

53. false; 2 – (–1) = 3, 3 < 2 or –1

54. true

55. a. 1992: 1997: b.

c. Answers may vary. Sample: Invest in soccer; it is the only sport that has not lost any participants.

5 12–3 7

4 6 5 10–

1 6–8 –3=

5.5 8.2 4.91.4 3.2 3.94.2 3.8 1.31.6 5.2 5.1

6.8 7.9 4.91.0 1.8 1.75.6 4.1 1.31.8 4.9 2.9

1.3 –0.3 0–0.4 –1.4 –2.21.4 0.3 00.2 –0.3 –2.2

1-5

56.

57. [– 0 –3]

58.

59. a. Yes, answers may vary. Sample: n and –n always have the same absolute value.

b. No, answers may vary. Sample:|1| + | –1| | 1 + (–1)|, 2 0

60. –

61.



2 –2–9 3

1 –

– 1

62. –4x + 9

63. –12t – m

64.

65.

66. |x| – |y|, |x – y|

and x – y, |x + y|

67. C

68. F

69. C

70. H

71. D

72. 4

73. –9

74. –0.7

75. –4.1

76.

77.

78.

4 0 0 16

1.2–2.5 5.2

1-5

14

9 20

5 12

=/ =/

3760

29r – 3516

–15w – 89

–3

6 –4

12

2–3

13

13



79–81. Choices of variables may vary.

79. t = total cost, p = pounds of pears, t = 1.19p

80. p = bouquet’s price, m = money left, m = 20 – p

81. c = check ($), s = your share, s =

1-5

c6


–5 11 –12

–1 7



1. 7 – 12 2. 3 – (–8) 3. –7 – 5

Evaluate each expression for x = 3 and y = 4.

4. x – y 5. | – y – x| 6. –– 2 x y 4

x 8 – 5 y

–5 –5 9 0

1-5


(For help, go to Lessons 1-4 and 1-5.)


1. –2 + (–2) + (–2) + (–2) 2. –5 + (–5) + (–5) + (–5) + (–5)

3. –6 – 6 – 6 – 6 4. –12 – 12 – 12 – 12 – 12 – 12

Write the next three numbers in each pattern.

5. 2, 4, 6, , , 6. 6, 4, 2, , ,

7. 12, 9, 6, , , 8. –18, –12, –6, , ,

� � � � � ��

Multiplying and Dividing Real NumbersMultiplying and Dividing Real Numbers

1-6



1-6

1. –2 + (–2) + (–2) + (–2) = 4(–2) = –8

2. –5 + (–5) + (–5) + (–5) + (–5) = 5(–5) = –25

3. –6 – 6 – 6 – 6 = 4(–6) = –24

4. –12 – 12 – 12 – 12 – 12 – 12 = 6(–12) = –72

5. 4 – 2 = 2, and 6 – 4 = 2, so the pattern is to add 2: 6 + 2 = 8, 8 + 2 = 10, and 10 + 2 = 12. 2, 4, 6, 8, 10, 12

6. 4 – 6 = –2, and 2 – 4 = –2, so the pattern is to subtract 2: 2 – 2 = 0, 0 – 2 = –2, and –2 – 2 = –4. 6, 4, 2, 0, –2, –4

7. 9 – 12 = –3, and 6 – 9 = –3, so the pattern is to subtract 3: 6 – 3 = 3, 3 – 3 = 0, and 0 – 3 = –3. 12, 9, 6, 3, 0, –3

8. –12 – (–18) = 6, and –6 – (–12) = 6, so the pattern is to add 6: –6 + 6 = 0, 0 + 6 = 6, and 6 + 6 = 12. –18, –12, –6, 0, 6, 12

Solutions


a. –3(–11)

–3(–11) = 33 The product of two negative numbers is positive.

The product of a positive number and a negative number is negative.

–6( ) = –34

184

= –412

Write – as a

mixed number.

184



1-6

b. –6( )34

Evaluate 5rs for r = –18 and s = –5.

5rs = 5(–18)(–5) Substitute –18 for r and –5 for s.

= –90(–5) 5(–18) results in a negative number, –90.

= 450 –90(–5) results in a positive number, 450.



1-6

Use the expression –5.5( ) to calculate the change in

temperature for an increase in altitude a of 7200 ft.

a 1000

–5.5( ) = –5.5 ( )72001000

a 1000

Substitute 7200 for a.

= –5.5(7.2) Divide within parentheses.

= –39.6°F Multiply.



1-6

The change in temperature is –39.6°F.

Use the order of operations to simplify each expression.

a. –0.24

= –0.0016 Simplify.

= 0.0016 Simplify.


b. (–0.2)4


1-6

Write as repeated multiplication.–(0.2 • 0.2 • 0.2 • 0.2)=

Write as repeated multiplication.(–0.2)(–0.2)(–0.2)(–0.2)=


a. 70 ÷ (–5) b. –54 ÷ (–9)


The quotient of a positive number and a negative number is negative.

= –14

The quotient of a negative number and a negative number is positive.

= 6


1-6

Evaluate – – 4z2 for x = 4, y = –2, and z = –4.

– – 4z2 = – 4(–4)2 Substitute 4 for x, –2 for y, and –4 for z.xy

–4–2

= – 4(16) Simplify the power.–4–2

= 2 – 64 Divide and multiply.

= –62 Subtract.



1-6

xy

Evaluate for p = and r = – .

= –2 Simplify.

= p ÷ r Rewrite the equation.pr

= ÷ Substitute for p and – for r.32

34

(– ) 32

34

= Multiply by – , the reciprocal of – .32

43(– ) 4

334



1-6

pr

32

34



1-6

1. –15

2. –15

3. 15

4. 15

5. –34.4

6. –2

7. –120

8. –105

9. –80

10. 80

11. –78

12. 81

13. –12

14. 12

15. –15

16. 5

17. –8

18. –13

19. 48

20. 1

21. 12

22. –8

23. –432

24. 1

25. –64

26. –87

27. 4

28. 24

29. 36

30. 12

31. a. –24°Fb. –75°Fc. –51°Fd. –31.5°F

32. –1

33. 8

34. –25

35. 81

36. –81

37. –192

38. –5

39. 675

40. –2

41. –4

42. 5

43. 6

44. –11

pages 41–44 Exercises 45. 12

46. –2

47. –8

48. –1

49. –7

50. –28

51. 0

52. 4

53. 3

54. 1

55. –15

12

45

12

231213

12



1-6

56.

57. –

58. –2

59. 18

60. –

61. –

62. –125

63. 0.75

64. –27

65. 22.32

66. 44

67. –27

1 18

6 25

12 8 15

68. –60

69. 30

70. a. i. 2

ii. –6

iii. 24

iv. –120

b. pos.

c. neg.

d. No; answers may vary. Sample: The sign of the product is not affected by the number of pos. factors, only by the number of neg. factors.

71. a. When a and b are both neg. or both pos.

b. When a is neg. and b is pos., or when a is pos. and b is neg.

72. –1

73. –

74. 1

75. –

76. –6

77. –4

78. –

79.

5 12

15

12

15

5678

1 10



80. ac + b

81. b – a + c

82. ab – c

83. –ab + c

84. –bc + a

85. 31¢

86. Yes; whatever the signs of a and b, | ab |,| a |, and | b | are pos., and | ab | = | a | • | b |.

87. a. 4, –8, 16, –329, –27, 81, –243

b. Pos.; the expression will involve an even number of neg. factors.

c. Neg.; the expression will involve an odd number of neg. factors.

88. 0.1 is the multiplicative inverse of 10 because 0.1(10) = 1. (–10 is the opposite of 10.)

89. The opposite of a nonzero number n is –n while the multiplicative inverse is . 1

n

1-6

90.

91.

92.

93. [–12 –2 ]

94.

95.

–15 21 –9

–22 10 18 –12 8 –6

23

4.7 –1.3 0.79–0.02 6.4 0

–8 –10.6 46.2 0 12

1 –

0

14

3 16

29

23




1-6

96. a. 139 ft; 91 ft

b. Less than 4 s; for t = 4, h = 155 – 16t 2 = –101, so h = 0 for some value less than 4 (about 3.1).

97. a. a = 5000 – 25t

b. 312.5 ft

c. 4687.5 ft

98. –23°C

99. –

100.

101. –

102.

103. –

104. –8

105. , or 11

106. –

107. –

108.

109. A

110. F

111. C

112. H

113. B

18

1 16

1 32

1 64

1 64

454

9 16 5 48

12

114. –2

115. –20

116. 0.8

117. 9.8

118. 2

119.

120. 4.95

121. 56

122. 4.59

123.

124. 23

125. 121

126. 196

127. $34.93

14

14

172

34


Simplify.

1. –8(–7) 2. –6(–7 + 10) – 4

Evaluate each expression for m = –3, n = 4, and p = –1.

3. + p 4. (mp)3 5. mnp

6. Evaluate 2a ÷ 4b – c for a = –2, b = – , and c = – .

56 – 22

–7 27 12

312


1-6

8mn

13

12



Use the order of operations to simplify each expression.

1. 3(4 + 7) 2. –2(5 + 6) 3. –1(–9 + 8)

4. –0.5(8 – 6) 5. t(10 – 4) 6. m(–3 – 1)

The Distributive PropertyThe Distributive Property

1-7

12



1-7

( )

1. 3(4 + 7) = 3(11) = 33

2. –2(5 + 6) = –2(11) = –22

3. –1(–9 + 8) = –1(–1) = 1

4. –0.5(8 – 6) = –0.5(2) = –1

5. t(10 – 4) = t(6) = (6)t = • 6 t = 3t

6. m(–3 – 1) = m(–4) = –4m

12

12

12

12

Solutions

Use the Distributive Property to simplify 26(98).


26(98) = 26(100 – 2) Rewrite 98 as 100 – 2.

= 26(100) – 26(2) Use the Distributive Property.

= 2600 – 52 Simplify.

= 2548


1-7

Find the total cost of 4 CDs that cost $12.99 each.

4(12.99) = 4(13 – 0.01) Rewrite 12.99 as 13 – 0.01.

= 4(13) – 4(0.01) Use the Distributive Property.

= 52 – 0.04 Simplify.

= 51.96

The total cost of 4 CDs is $51.96.



1-7

Simplify 3(4m – 7).

3(4m – 7) = 3(4m) – 3(7) Use the Distributive Property.

= 12m – 21 Simplify.



1-7

Simplify –(5q – 6).

–(5q – 6) = –1(5q – 6) Rewrite the expression using –1.

= –1(5q) – 1(–6) Use the Distributive Property.

= –5q + 6 Simplify.



1-7

Simplify –2w2 + w2.

–2w2 + w2 = (–2 + 1)w2 Use the Distributive Property.

= –w2 Simplify.



1-7

Relate: –6 times the quantity 7 minus m

Write: –6 • (7 – m)

Write an expression for the product of –6 and the quantity 7

minus m.

–6(7 – m)



1-7



1-7


1. 2412

2. 663

3. 5489

4. 2448

5. 686

6. 2997

7. 20,582

8. 24,480

9. $3.96

10. $11.82

11. $29.55

12. $209.51

13. $98.97

14. $2.76

15. 7t – 28

16. –2n + 12

17. 3m + 12

18. b –

19. –2x – 6

20. 4y + 6

21. 1.5q + 8

22. 18n – 42

23. – r

24. –4.5b + 13.5

25. 2w + 4

26. –36 + 16n

27. –x – 3

28. –x + 3

29. –3 – x

30. –3 + x

31. –6k – 5

32. –7x + 2

33. –2 + 7x

34. –4 + z

45

52

1516 35. –3t

36. 20k2

37. 7x

38. 24w

39. 5v2

40. 6m

41. –17q

42. –45x

43. 3(m – 7)

44. –4(4 + w)

45. 2(b + 9)

46. –11(n – 8)



47. 2(3c + 9)

48. (3 + r )(r – 7)

49. 44,982

50. 2392

51. 14.021

52. 84.012

53. 11.82

54. 15.992

55. 30.1 + 7x

56. d – dh

57. 12.8 – n

58. 135b + 128

59. 18.6 + 15m

60. d – 42

61. –8.4 – 300g + 512h

62. –12k – 5m + 62

63. 6p – 14q + 30w

64. 36x + 10.8y – 72.9

65. 2 (5 – k)

66. 6 (8 + p)

67. (b – )

68.

69. 4 (x – )

407

507

58

70. 8x + 38

71. No; 2a • 2b = 4ab.

72. The student did not mult. the second number in parentheses, 10, by 4 to get the correct answer, 12x + 40.

73. Answers may vary. Sample: 2(x + 5) = 2x + 10

74. 4.78d

75. –76p2 – 20p – 9

76. –6.1t 2 + 13.7t

77. 1.5m – 12.5v

14

12

43

1120

1330

1112

1-7

17 z – 34

7 100

13

78. n + n3

79. – k + h

80. 7m2 – mz + 4

81. 19 – 7t + 6y

82. 1.4b – 5b2 + 5c

83. –4xyz + 6xy

84. terms: –7t, 6v, 7, –19y,

coefficients: –7, 6, –19,

constant: 7

85. a. (84 + 10)50 ft2

b. 4700 ft2



86. 10 pennies, 7 nickels,

4 quarters, 1 dime

87. 4(1.02) + 3(0.99) + 3(0.52)

= t ; $8.61

88. 27 + 3t

89. –6r + 37

90. –3m – 9

91. 2a + 2ab + abc

92. 14b + 42b2

93. 5y + 13z

94.

95. a. 2; 2

b. –2; –2

c. Yes; the two expressions are equal for the values of a, b, and c in parts (a) and (b).

96. a. 30; –8

b. 12, –6

c. No; parts (a) and (b) show the expressions are not equal.

1-7

7142

3 20

107120

3x – 10 3



97. D

98. G

99. A

100. F

101. D

102. H

103. C

104. I

105. –68

106. –4

107. 4

108. 7

109.

110. –

111. –

112. –3

113. –17

114. –2.386

115. 12.127

116. 45.3

117. 45.7

118. 2.57

119. 0.92

120. –9.6

121. –7.7

122. 23

123. a. 4 +

b. 7; 5; 8

1-7

16

5415

m3



1. 11(299) 2. 4(x + 8) 3. – 3(2y – 7)

4. –(6 + p) 5. 1.3a + 2b – 4c + 3.1b – 4a

6. Write an expression for the product of and the quantity b minus .

3289 4x + 32 – 6y + 21

– 6 – p –2.7a + 5.1b – 4c

47

35b –( )


1-7

47

35




1. 8 + (9 + 2) 2. 3 • (–2 • 5) 3. 7 + 16 + 3

4. –4(7)(–5) 5. –6 + 9 + (–4) 6. 0.25 • 3 • 4

7. 3 + x – 2 8. 2t – 8 + 3t 9. –5m + 2m – 4m

Properties of Real NumbersProperties of Real Numbers

1-8


1. 8 + (9 + 2) = 8 + (2 + 9) = (8 + 2) + 9 = 10 + 9 = 19

2. 3 • (–2 • 5) = 3 • (–10) = –30

3. 7 + 16 + 3 = 7 + 3 + 16 = 10 + 16 = 26

4. –4(7)(–5) = –4(–5)(7) = 20(7) = 140

5. –6 + 9 + (–4) = –6 + (–4) + 9 = –10 + 9 = –1

6. 0.25 • 3 • 4 = 0.25 • 4 • 3 = 1 • 3 = 3

7. 3 + x – 2 = 3 + (–2) + x = 1 + x

8. 2t – 8 + 3t = 2t + 3t – 8 = (2 + 3)t – 8 = 5t – 8

9. –5m + 2m – 4m = (–5 + 2 – 4)m = –7m


Solutions

1-8

Name the property each equation illustrates.

a. 3 • a = a • 3

b. p • 0 = 0

c. 6 + (–6) = 0



1-8

Commutative Property of Multiplication, because the order of the factors changes

Multiplication Property of Zero, because a factor multiplied by zero is zero

Inverse Property of Addition, because the sum of a number and its inverse is zero

Suppose you buy a shirt for $14.85, a pair of pants for

$21.95, and a pair of shoes for $25.15. Find the total amount you

spent.

14.85 + 21.95 + 25.15 = 14.85 + 25.15 + 21.95 Commutative Property of Addition

= (14.85 + 25.15) + 21.95 Associative Property of Addition

= 40.00 + 21.95 Add within parentheses first.

= 61.95 Simplify.

The total amount spent was $61.95.



1-8

Simplify 3x – 4(x – 8). Justify each step.

3x – 4(x – 8) = 3x – 4x + 32 Distributive Property

= (3 – 4)x + 32 Distributive Property

= –1x + 32 Subtraction

= –x + 32 Identity Property of Multiplication



1-8



1. Ident. Prop. of Add.; 0, the identity for addition, is added.

2. Comm. Prop. of Add.; the order of the terms changes.

3. Ident. Prop. of Mult.; 1, the identity for multiplication, is multiplied.

4. Assoc. Prop. of Add.; the grouping of the terms changes.

5. Inv. Prop. of Add.; a number and its inverse are added.

6. Comm. Prop. of Mult.; the order of the factors changes.

7. Dist. Prop.; a numberoutside parentheses is distributed to the two terms inside the parentheses.

8. Assoc. Prop. of Mult.; the grouping of the factors changes.

pages 56–57 Exercises 9. Inv. Prop. of Mult.; a number and its mult. inverse are multiplied.

10. 100

11. 7400

12. 14.95

13. 4200

14. –5

15. 13

16. $6.00

1-8



1-8

17. a. def. of subtr.

b. Dist. Prop.

c. addition

18. a. Comm. Prop. of Mult.

b. Assoc. Prop. of Mult.

c. mult.

d. mult.

19. 25 • 1.7 • 4= 25 • 4 • 1.7 Comm. Prop. of Mult.= (25 • 4) • 1.7 Assoc. Prop. of Mult.= 100 • 1.7 mult.= 170 mult.

20. –5(7y) = [–5(7)]y Assoc. Prop. of Mult.= –35y mult.

21. 8 + 9m + 7 = 9m + 8 + 7 Comm. Prop. of Add.= 9m + (8 + 7) Assoc. Prop. of Add.= 9m + 15 add.

22. 12x – 3 + 6x = 12x + (–3) + 6x def. of subtr.= 12x + 6x + (–3) Comm. Prop. of Add.= (12 + 6)x + (–3) Dist. Prop.= 18x + (–3) add.= 18x –3 def. of subtr.

23. 29c + (–29c) = [29 + (–29)]c Dist. Prop.= 0 • c Inv. Prop. of Add.= 0 Mult. Prop. of Zero

24. 43 + 1 = 1 + 1

Inv. Prop. of Mult. = 2 add.

25. 2 + g = 2 + 1

Inv. Prop. of Mult. = 3 add.

143

1g



26. 36jkm – 36mjk = 36jkm + (–36)mjk def. of subtr.= 36jkm + (–36)jmk Comm. Prop. of Mult.= 36jkm + (–36)jkm Comm. Prop. of Mult.= [36 + (–36)]jkm Dist. Prop.= (0)jkm Inv. Prop. of Add.= 0 Mult. Prop. of Zero

27. (32 – 23)(8759) = (9 – 8)(8759) mult.= [9 + (–8)](8759) def. of subtr.= 1(8759) add.= 8759 Ident. Prop. of Mult.

28. (76 – 65)(8 – 8) = (76 – 65)[8 + (–8)] def. of subtr.= (76 – 65) • 0 Inv. Prop. of Add.= 0 Mult. Prop. of Zero

29. 4 + 6(8 – 3m) = 4 + 48 – 18m Dist. Prop.= 4 + 48 + (–18m) def. of subtr.= (4 + 48) + (–18m) Assoc. Prop. of Add.= 52 + (–18m) add.= 52 – 18m def. of subtr.

1-8



1-8

15

30. 5 w – – w(9)

= 5 w – – 9w

Comm. Prop. of Mult.

= 5(w) – 5 – 9w

Dist. Prop.

= 5w – 1 – 9w

Inv. Prop. of Mult.

= 5w + (–1) + (–9w)

def. of subtr.

= 5w + (–9w) + (–1)

Comm. Prop. of Add.

= [5w + (–9w)] + (–1)

Assoc. Prop. of Add.

= [5 + (–9)]w + (–1)

Dist. Prop.

= –4w + (–1) add.

= –4w – 1

def. of subtr.

31. $52.97

32. no

33. no

34. no

35. yes

36. no

37. no

38. yes

39. yes

40. No; 3 – 5 = –2, while 5 – 3 = 2.

41. No; (5 – 3) – 1 = 2 – 1 = 1, while 5 – (3 – 1) = 5 – 2 = 3.

42. No; 1 ÷ 2 = , while 2 ÷ 1 = 2.

43. No; 16 ÷ (4 ÷ 2) = 16 ÷ 2 = 8, while (16 ÷ 4) ÷ 2 = 4 ÷ 2 = 2.

44. a. Dist. Prop.

b. Comm. Prop. of Add.

c. Assoc. Prop. of Add.

d. add.

e. Dist. Prop.

f. add.

12

15

15



1-8

45. By the Comm. Prop. of Mult., (b + c)a = a(b + c). By the Dist. Prop., a(b + c) = ab + ac. By the Comm. Prop. of Mult., ab + ac = ba + ca, so (b + c)a = ba + ca.

46. Answers may vary. Sample: The sandwich tastes the same whether the peanut butter or the jelly is on top. This is like the Comm. Prop. of Add., because you can add the peanut butter and jelly in either order.

47. both

48. both

49. both

50. not mult.; (–2)(–3) = 6

51. not add.; 1 + 3 = 4

52. both

53. A

54. I

55. D

56. G

57. B

58. F

59. 6 + 5k

60. 11 – b

61. –10p – 35

62. 28 – 4n

63. 7.4m – 0.05

64. –18v + 31.2

65. 7 + [m + (–17)]

66. 8 – (9 – t)

67. ( )

68. (x + 5.1)

69. 7

70. –18.3

71. –

72. –1

73. –135

74. 9.2

13

b4

1213

1415


Name the property that each equation illustrates.

1. 1m = m 2. (– 3 + 4) + 5 = – 3 + (4 + 5)

3. –14 • 0 = 0

4. Give a reason to justify each step.

Iden. Prop. Of Mult. Assoc. Prop. Of Add.

Mult. Prop. Of Zero

a. 3x – 2(x + 5) = 3x – 2x – 10 Distributive Property

b. = 3x + (– 2x) + (– 10) Definition of Subtraction

c. = [3 + (– 2)]x + (– 10) Distributive Property

d. = 1x + (– 10) Addition

e. = 1x – 10 Definition of Subtraction

f. = x – 10 Identity Property of Multiplication


1-8


(For help, go to Lesson 1-3.)

Graph each number on a number line.

1. 6 2. –5 3. 2.7 4. 0

Write the coordinate of each point on the number line below.

5. A 6. B 7. C 8. D

Graphing Data on the Coordinate PlaneGraphing Data on the Coordinate Plane

1-9


1.

2.

3.

4.

5. A: 1 6. B: –2.5 7. C: 3.5 8. D: –4


Solutions

1-9

Name the coordinates of point A in the graph.

Move 2 units to the left of the origin. Then move3 units up.

The coordinates of A are (–2, 3).



1-9

Graph the point B(–4, –2) on the coordinate plane.

Move 4 units to the left of the origin.


Then move 2 units down.


1-9

In which quadrant or on which axis would you find each point?

a. (2, –5)

Since the x-coordinate is positive and the y-coordinate is negative, the point is in Quadrant IV.

b. (6, 0)

Since the y-coordinate is 0, the point is on the x-axis.



1-9

The table shows thenumber of hours worked andthe amount of money eachperson earned. Make a scatterplot of the data.

Name Hours Amountworked earned

Janel 6 $25.50Roscoe 12 $51.00Victoria 11 $46.75Alex 9 $38.25Jordan 15 $63.75Jennifer 10 $42.50

For 6 hours worked and earnings of $25.50,plot (6, 25.50).

The highest amount earned is $63.75. So a reasonable scale on the vertical axis is from0 to 70 with every 10 points labeled.



1-9

Use the scatter plot in your answer for Additional Example 4

to answer the following question: Is there a positive correlation,

negative correlation, or no correlation between the number of hours

worked and the amount earned? Explain.

As the number of hours worked increases, the earnings increase. There is a positive correlation between hours worked and earnings.



1-9




1. (4, 5)

2. (2, –2)

3. (–5, 0)

4. (5, 4)

5-8.

9. II

10. x–axis

11. IV

12. y–axis

13. I

14. II

15. No; the point is on the y-axis, not in Quadrant III.

16.

17. neg. correlation

18. pos. correlation

19. no correlation

20. (–3, 4)

21. (5, 0)

22. (6, –6)

23. (–3, –2), (1, 3), (2, –4)

24. a. Answers may vary. Sample: (–1, 1), (–2, 2), (10, –10)

b. Answers may vary. Sample: (1, 1), (–2, 2), (–10, –10)

1-9



25.

square

26.

rhombus

29. Neg. correlation; the more classes you take, the more work you have, so the less free time you have.

30. Pos. correlation; the greater the number of cars, the higher the pollution levels for a city.

31. No correlation; baby’s length at birth is not related to its birthday.

27.

isosceles triangle

28.

rectangle

1-9



32. Pos. correlation; the more you exercise, the more calories you burn.

33. Answers may vary. Samples: Pos. correlation;the number of hours a person earning an hourly wage works and the size of the paycheck. Neg. correlation; the number of people working on a project and the time it takes to complete the project. No correlation; person’s height and the length of his or her hair.

34. a. Neg. correlation; rain or snow makes travel more difficult or inconvenient, so voters would be less likely to go to the polls.

b. Answers may vary. Sample: In general, the weather has the same effect on both sides, but candidates usually want as many votes as possible, so they should be concerned.

35. a. neg. correlation

b. Answers may vary. Sample: No; it is generally not reasonable to conclude that correlation between two trends implies cause.

1-9



36. a, b.

b. pos. correlation

c. In general, it appears that

the greater the number of

grams of fat in a serving

of food, the greater the

number of calories.

36. (continued)

d. Answers may vary.

Sample: about 200 cal

37. 20 units; 21 square units

38. 7.5 square units

39. Answers may vary. Sample: There is a circle with radius 5 and center (2, 3) that contains the points (–1, –1), (–2, 0), (–2, 6), (–1, 7), (5, 7), (6, 6), (6, 0), and (5, –1). (It also contains the points (–3, 3), (2, 8), (7, 3), and (2, –2).)

1-9


40. a. the distance a car traveled on the Indiana toll road and the toll charged

b. The points have the same x-coordinate; that is, they lie on the same vertical line.

c. The points have the same y-coordinate; that is, they lie on the same horizontal line.

d. Pos. correlation; in general, as distance increases, the toll increases.

41. C

42. G

43. D

44. G

45. A

46. H

47. x – 4(2x + 1) – 3 = x – 8x – 4 – 3 Dist. Prop.= 1x – 8x – 4 – 3 Ident. Prop. of Mult.= 1x + (–8x) + (–4) + (–3) def. of subtr.= [1x + (–8x)] + [(–4) + (–3)]

Assoc. Prop. of Add.= [1 + (–8)]x + (–4) + (–3) Dist. Prop.= –7x + (–4) + (–3) add.= –7x + (–7) add.= –7x –7 def. of subtr.

1-9




48. 5(8t) + 4(9 – t) – 37 = 40t + 36 – 4t – 37 Dist. Prop.= 40t + 36 + (–4t) + (–37) def. of subtr.= 40t + (–4t) + 36 + (–37) Comm. Prop. of Add.= [40t + (–4t)] + [36 + (–37)] Assoc. Prop. of Add.= [40 + (–4)]t + [36 + (–37)] Dist. Prop.= 36t + (–1) add.= 36t – 1 def. of subtr.

49. 8b + 7a – 4b – 9a = 8b + 7a + (–4b) + (–9a) def. of subtr.= 8b + (–4b) + 7a + (–9a) Comm. Prop. of Add.= [8b + (–4)b] + [7a + (–9)a] Assoc. Prop. of Add.= [8 + (–4)]b + [7 + (–9)]a Dist. Prop.= 4b + (–2)a add.= 4b – 2a def. of subtr.

1-9



50. 3m2 – (10m + 3m2) = 3m2 – 1(10m + 3m2) Mult. Prop. of –1= 3m2 – 10m – 3m2 Dist. Prop.= 3m2 + (–10m) + (–3m2) def. of subtr.= 3m2 + (–3m2) + (–10m) Comm. Prop. of Add.= [3 + (–3)]m2 + (–10m) Dist. Prop.= 0m2 + (–10m) Inv. Prop. of Add.= 0 + (–10m) Mult. Prop. of Zero= –10m Ident. Prop. of Add.

51.

52. [16.5 –29 1 –9.5]

53.

54.

55. true

56. false; 1 = 12

57. true 9 –1319 –1

3.1 –0.7 21–4.9 –4.7 –2.1

–1 –7 8

–11 –

10 –17

5 30

12

1-9

1212


Use the graph for 1 – 6.

Name the coordinates of each point.

1. A 2. D 3. F 4. G

5. In which quadrant is point E?

6. Describe the trend.

(–3, –3) (–2, 1) (2, 0) (3, 2)

II

positive correlation


1-9

ALGEBRA 1 CHAPTER 1ALGEBRA 1 CHAPTER 1

Tools of AlgebraTools of Algebra

1-A

1. n = number, c = cost, c = 2.3n

2. p = payment, c = change, c = 10 – p

3. 4

4. 0

5.

6. 12

7. 5

8. 6

9. –20

10. –10

11. 1

12. 18

13.

14.

15. False, since is a rational number but is not an integer.

16. False, since |0| = 0, which is not pos.

17. –3 + 18a

59

18. 12d – 30

19–20. Answers may vary.

19. 10x + 3( – x)

= 10x + 1 – 3x Dist. Prop.= 1 + 10x – 3x Comm. Prop. of Add.= 1 + (10 – 3)x Dist. Prop.= 1 + 7x subtr.

20. (33 – 33)(1 – 22)= (33 + (–33))(1 – 22) def. of subtr.= 0(1 – 22) Inv. Prop. of Add.= 0 Mult. Prop. of Zero

–1 15 –1113 –1 2

–10 5 –10

11 –32 5

12

13

45

Tools of AlgebraTools of AlgebraALGEBRA 1 CHAPTER 1ALGEBRA 1 CHAPTER 1

1-A

21. –10(2 – 11)

22.

23. (p – )( + p)

24. –10

25. 2.7

26. a. Sometimes; 5 – 3 = 2, but 3 – 5 = –2.

b. Never; 3 – (–2) = 5 and 8 – (–10) = 18.

c. Sometimes; –8 – (–3) = –5, but –3 – (–8) = 5.

d. Never; –3 – (8) = –11 and –7 – (10) = –17.

58

14

5 m + 6

38

34. neg. correlation

35. about 41°F

36. If a and b have

different signs,

| | is positive

and is negative.

ab

ab

27. Answers may vary. Sample:– , 1.5, 1, –

– , – , 1, 1.5

28. y-axis

29. Quadrant III

30. 28 square units

31. 2 yd lost

32. $177

33. $19.30

23

16

23

16

Documents

Write the operation (+, –, , ÷) that corresponds to each phrase. 1.divided by2.difference3.more than4.product 5.minus6.sum7.multiplied by8.quotient Find