TM Fractions Decimals - WriteMath Enterpriseswritemath.com/wp-content/uploads/2014/11/Fractions... · Multiplying Mixed Numbers . Week 26: Fraction, Decimal, & Percentage .....119

Just Turn & Share: Fractions & Decimals www.WriteMath.com

I

WM

Volume 4

(Grades 3 – 5)

Real-World Mathematics

that students

understand ______________________________

Kathryn Robinson

WriteMath Enterprises Valrico, Florida 4

FractionsTM

Decimals&

The student pages in this publication are designed to be used with appropriate duplicating equipment to reproduce copies for permission classroom use only. WriteMath Enterprises, Inc. grants to classroom teachers only to reproduce these student sheets for students in one class per year per book purchased by the school or the teacher him/herself. Copyright © 1995, 2000, 2007, 2012 WriteMath Publications All rights reserved – Printed in the U.S.A. Published by WriteMath Enterprises 2303 Marseille Ct., Ste 104, Valrico, FL 33596


VIII

Contents Introduction .................................................................................................................. III Answer Sheet................................................................................................................ VI Contents ...................................................................................................................... VIII Fraction Information ....................................................................................................... 2 Adding & Subtracting Simple Fractions Information ..................................................... 3 Equivalent Fractions Information ................................................................................... 4 Week 1: Fraction of a Whole Group .............................................................................. 5

Equivalent Fractions Adding Fractions with Like Denominators

Factors

Week 2: Fraction of a Whole Group ................................................................................ 9 Equivalent Fractions Adding Fractions with Like Denominators

Factors Week 3: Fraction of a Whole Group .............................................................................. 13

Equivalent Fractions Adding Fractions with Like Denominators

Factors Decimal Information .................................................................................................... 17 Percentages Information ............................................................................................... 18 Greatest Common Factor Information ......................................................................... 19 Week 4: Tenths .............................................................................................................. 20

Fractions/Decimals/Percentages Subtracting Fractions with Like Denominators

Equivalent Fractions Greatest Common Factor


IX

Week 5: Tenths .............................................................................................................. 24


Equivalent Fractions Greatest Common Factor Week 6: Tenths .............................................................................................................. 28


Equivalent Fractions Greatest Common Factor Changing a Fraction to a Decimal Information ............................................................ 32 Week 7: Hundredths ...................................................................................................... 33

Fractions/Decimals/Percentages Adding & Subtracting Fractions with Like Denominators

Changing Fractions to Decimals Equivalent Fractions Greatest Common Factor for Two Numbers Week 8: Hundredths ...................................................................................................... 37


Changing Fractions to Decimals Equivalent Fractions Greatest Common Factor for Three Numbers Week 9: Hundredths ...................................................................................................... 41


Changing Fractions to Decimals Equivalent Fractions Greatest Common Factor for Three Numbers Simplifying Fractions Information ................................................................................ 45 Fraction of a Number Information ................................................................................ 46


X

Week 10: Mixed Numbers ............................................................................................. 47 Fractions/Decimals/Percentages Ordering Decimals

Fraction of a Whole Number Week 11: Mixed Numbers ............................................................................................. 51

Fractions/Decimals/Percentages Simplifying Fractions Ordering Decimals


Fractions/Decimals/Percentages Simplifying Fractions Ordering Decimals

Fraction of a Whole Number Adding & Subtraction Mixed Numbers Information .................................................... 59 Comparing Fractions Information ................................................................................. 60 Week 13: Tenths ............................................................................................................ 61

Fractions/Decimals/Percentages Adding Mixed Numbers Comparing Fractions

Fraction of a Whole Number Week 14: Tenths ............................................................................................................ 65

Fractions/Decimals/Percentages Subtracting Mixed Numbers Comparing Fractions

Fraction of a Whole Number Week 15: Tenths ............................................................................................................ 69

Fractions/Decimals/Percentages Adding & Subtracting Mixed Numbers Comparing Fractions

Fraction of a Whole Number Multiples Information ................................................................................................... 73


XI

Week 16: Mixed Numbers ............................................................................................. 74 Adding & Subtracting Mixed Numbers Least Common Multiples ‘n’

Fraction of a Whole Number Week 17: Mixed Numbers ........................................................................................... 78

Adding & Subtracting Mixed Numbers Least Common Multiples ‘n’


Adding & Subtracting Mixed Numbers Least Common Multiples ‘n’

Fraction of a Whole Number Changing Mixed Numbers to an Improper Fraction Information................................. 86 Week 19: Mixed Numbers ............................................................................................. 87

Adding & Subtracting Mixed Numbers Least Common Multiples Improper Fractions Ordering Fractions, Percentages, and Decimals





Fraction of a Whole Number Changing an Improper Fraction to a Mixed Number Information ............................... 99


XII

Adding & Subtracting Fractions with Unlike Denominators Information ............... 100 Week 22: Fraction, Decimal, & Percentage ................................................................ 101

Adding & Subtracting Mixed Numbers Adding & Subtracting Fractions with Unlike Denominators Improper Fractions Ordering Fractions, Percentages, and Decimals

Fraction of a Whole Number Week 23: Fraction, Decimal, & Percentage ................................................................ 105

Adding & Subtracting Double-Digit Mixed Numbers Adding & Subtracting Fractions with Unlike Denominators Improper Fractions Ordering Fractions, Percentages, and Decimals

Fraction of a Whole Number Week 24: Fraction, Decimal, & Percentage ................................................................ 109

Adding & Subtracting Double-Digit Mixed Numbers Adding & Subtracting Fractions with Unlike Denominators Improper Fractions Ordering Fractions, Percentages, and Decimals

Fraction of a Whole Number Multiplying Fractions .................................................................................................. 113 Multiplying Mixed Numbers ...................................................................................... 114 Week 25: Fraction, Decimal, & Percentage ................................................................ 115

Multiplying Fractions Comparing Fractions Improper Fractions & Mixed Numbers Ordering Fractions, Percentages, and Decimals Multiplying Mixed Numbers

Week 26: Fraction, Decimal, & Percentage ................................................................ 119

Multiplying Fractions Comparing Fractions Improper Fractions & Mixed Numbers Ordering Fractions, Percentages, and Decimals Multiplying Mixed Numbers


XIII

Week 27: Fraction, Decimal, & Percentage ................................................................ 123 Multiplying Fractions Comparing Fractions Improper Fractions & Mixed Numbers Ordering Fractions, Percentages, and Decimals Multiplying Mixed Numbers

Dividing Fractions ....................................................................................................... 127 Dividing Mixed Numbers ........................................................................................... 129 Week 28: Fraction, Decimal, & Percentage ................................................................ 129 Week 29: Fraction, Decimal, & Percentage ................................................................ 133 Week 30: Fraction, Decimal, & Percentage ................................................................ 137 Answer Sheet ............................................................................................................... 141

Fractions & Decimals: Week 1


2

Fractions

Fractions are written with one number (numerator) over the other number (denominator).

The numerator (top number) tells you how many parts out of the group we are talking about.

The denominator (bottom number) tells you how

many parts are in the whole group. 2 Two parts of a group of three.

3 There are three parts altogether.

2 3

e.g.: If Dan eats 6 out of 10 pieces of pie, it is written:

Fraction: 6 10



3

Adding & Subtracting Simple Fractions

1. If the denominators in both fractions are the same, write the fraction answer with the same denominator.

2. Add or subtract the numerators & write the new numerator in the answer.

1 2 ___10 10 10

1 2 3 10 10 10

+ =

+ =

+ =

Subtraction Addition

7 2 9 9

7 2 9 9 9

7 2 9 9 9

5

- = ?

- =

- =

First:

Next:

Last:

3 1 5 5

3 1 5 5 5

3 1 5 5 5

4

+ = ?

+ =

First:

Next:

Last:



4

Equivalent FractionsEquivalent fractions are two different fractions of a whole object with unlike denominators that represent the same portion of a whole object.

How can I use equivalent fractions? Suppose that your brother wants to eat ½ of a pizza and the pizza is cut into12 slices. You can figure out how many pieces to give him by computing thenumber of twelfths it will take to equal to ½ of the pizza.

Find the equivalent fraction:

Decide what number the denominator of one fraction was or to equal the other denominator.

Multiply or divide the numerator by the same number.

multiplied divided by

1 ? 2 12

1 62 12

1 ? 2 x = 12 6

1 x = 6 2 x 6 = 12

6

=

=

=

=

=

=Solution:

Equivalent Fractions:

1 ? 2 12

1 2 12

61 ? 2 = 12x 6

1 6 x = 2 x 6 = 12

6

12 ? 15 5

12 15 5

412 ? 15 = 5 3

12 4 3 = 15 3 = 5

You have not changed the value of the fraction because you are dividing by 1.

66 = 1



5

Fractions/Decimals (DAY #1)

A. What fraction of the happy faces are smiling? e.g.: _?_

i. 10

B. What fraction of the happy faces are frowning?

*** Read the information on Equivalent Fractions.

C. Give the equivalent fraction for problem “A” in fifths. *** Read the information on Adding & Subtracting Fractions.

D. Compute: 1 + 4 = ? 10 10 10

E. What are two factors for 6? ? x ? = 6 * A & D

** B, D, & E *** C, D, & E

A factor is a number that is multiplied: 3 x 4 = 12 ↑ ↑ ↑ factor factor product



6



10




D. Compute: 2 + 4 = ? 10 10 10

E. What are two factors for 8? ? x ? = 8

* B & D

** A, D, & E *** C, D, & E




7



10




D. Compute: 2 + 5 = ? 10 10 10

E. What are two factors for 10? ? x ? = 10 * A & D

** B, D, & E *** C, D, & E




8



10




D. Compute: 4 + 5 = ? 10 10 10

E. What are two factors for 12? ? x ? = 12 * B & D

** A, D, & E *** C, D, & E




73

Multiples Information

• Common multiples are products (answers) thattwo or more numbers have in common.

3 9 x 3 x 1 9 (9 is a common multiple for 3 and 9) 9

Both numbers have 9 as a product (answer)

6 9 x 3 x 2 18 (18 is a common multiple for 6 and 9) 18

Both numbers have 18 as a product (answer)

• Multiples of a number are the products (answers) whenthat number and another number are multiplied.

2 x 3 = 6 2 x 4 = 8 2 x 5 = 10

• (6, 8, and 10 are multiples of 2.)

• The Least Common Multiples (LCM) for a number is thelowest multiple (answer) that the numbers have in common.

3 3 3 3 9 9 9 9 x 3 x 6 x9 x12 x 1 x 2 x3 x4

9 18 27 36 9 18 27 36

(9 is the Least Common Multiple (LCM) for 3 and 9)



74


A. Write the fraction represented by the shaded portions of the pie graphs.

B. Compute: 14

72 + 10

75

*** Refer to the Multiples Information:

C. What is the Least Common Multiple (LCM) for 2 and 5? D. Write ½ as a percentage. E. Compute the following:

F. Beth wanted a pair of jeans that cost $9.33. She had a

coupon for 1/3 off the regular price. How much money did she save on the jeans?

G. Marvin has 2 out of a total of 5 pages illustrated in his

science report. If Alvin has an equivalent fraction of his pages illustrated, how many pages of Alvin’s 10 page-report are illustrated?

* A & B

** C, D, E, & F *** A, C, E, & G

21

= 6n

, n = What number?



75


A. Write the fraction represented by the shaded portions

of the pie graphs. B. Compute: 8

54 - 3

52

* Refer to the Multiples Information:

C. What is the Least Common Multiple (LCM) for 5 and 20? D. Write ¼ as a percentage. E. Compute the following:

F. Mark picked out a shirt that was marked $6.44. The

cashier took ¼ off the regular price. How much money did Mark save?

G. Three out of Melinda’s 12 vacation pictures did not

develop properly. Her sister, Anna, had an equivalent fraction of pictures that did not turn out. How many of Anna’s 24 pictures did not get developed?

* A & B ** A, C, E, & G

*** C, D, E, & F

51

= 10n

, n = What number?



76



B. Compute: 24112 + 8

115


C. What is the Least Common multiple (LCM) for 7 and 14? D. Write ¾ as a percentage. E. Compute the following:

F. Rosie had a dress at her garage sale for $12.24. The

lady that bought it wanted ¼ off the original price. How much money did the lady save on the dress?

G. Justin bought seven baseball cards. Three of the seven

cards had pictures of Red Sox players. If Bobby bought an equivalent fraction of Red Sox baseball cards, how many of Bobby’s 21 cards were of the Red Sox baseball team?

* A & B ** C, D, E, & F

*** A, C, E, & G

53

= 20n

, n = What number?



77



B. Compute: 19

85 - 7

83


C. What is the Least Common Multiple (LCM) for 6 and 12? D. Write 1 as a percentage. E. Compute the following: F. Patty bought a book that was marked $5.78. The store

manager took ½ off the regular price. How much money did she save?

G. Four out of Shirley’s five cousins are girls. Her best

friend, Mary, has an equivalent fraction of female cousins. How many of Mary’s ten cousins are girls?

* A & B

** A, C, E, & G *** C, D, E, & F

54

= 30n

, n = What number?



99

8 13)1

85

1

1

1

58

58

58



100

Adding & Subtracting Fractions with Unlike Denominators

1. Find the Least Common Multiple (LCM) for the denominators .

2. Write the equivalent fractions.

3. Add/subtract.

4. Simplify your answer.

3 x 2 =

6 x 1 =

6

6 multiple (6 is the lowest multiple for the denominators of both & .)3 6

2

53

6+

2356

4656+

x 2 =

x 2 =

4656+

96

96 = 1 = 13

612

4534

16201520 120

x 4 =

x 5 =

x 4 =

x 5 =

Subtraction



101

B C DA

0 1.0


A. Write the decimal, percentage, and fraction represented by the shaded portion of the graph.

B. Compute: 12

1311 - 5

134

C. Compute:

156 +

54

D. Write

814 as a mixed number.

E. Which number belongs in ‘box A’?

F. Mrs. Robinson bought ½ pound of ground beef and ¾ pound of pork for to make Swedish meatballs. How much meat did she purchase?

G. Amy’s recipe called for 1/3 dozen eggs. How many

eggs does Amy need? * A, B, & E

** A, C, D, & E *** D, E, F, & G

∗ 1.2 ∗ .5 ∗ 1/3 ∗ 80%



102

B C DA

0 1.0



B. Compute: 20

121 + 4

125

C. Compute: 127 -

245

D. Write


E. Which number belongs in ‘box B’?

F. Missy cut out 1-3/8 yard of polka-dotted fabric for a dress. She also cut out ½ yard of red fabric for the collar. How much fabric did she use?

G. Billy collected 35 worms to fish with on Saturday. He

used 3/7 of them. How many worms were left? * A, B, & D

** A, C, E, & G *** A, D, F, & G

∗ 1.2 ∗ .5 ∗ 1/3 ∗ 80%



103

B C DA

0 1.0



B. Compute: 14

158 - 8

156

C. Compute: D. Write


E. Which number belongs in ‘box C’?

F. Mr. Ramsey needed 2/3 pound of screws and 4/5 pound of nails to build a curio stand. How many pounds of screws and nails did he purchase?

G. Nancy needed 2/3 of a package of Ritz crackers for her

recipe. There were 18 crackers in the package. How many crackers did Nancy need?

* A, B, & E ** A, C, D, & E

*** D, E, F, & G

∗ 1.2 ∗ .5 ∗ 1/3 ∗ 80%

65

- 125



104

B C DA

0 1.0



B. Compute: 21

172 + 8

1715

C. Compute:

98 +

183

D. Write


E. Which number belongs in ‘box D’?

F. Joey’s tomato patch was 2¾ yards long and his onion patch was 1-3/5 yards in length. How many yards of tomatoes and onions did he plant?

G. Lauren caught 32 fish on Saturday. She threw back 3/8

of them. How many fish did she bring home? * A, B, & D

** A, C, E, & G *** A, D, F, & G

∗ 1.2 ∗ .5 ∗ 1/3 ∗ 80%

Fractions & Decimals: Answer Sheets


141

Fractions & Decimals Answer Sheet Week 1: Day #1 Page 5 A. 4/10 (2/5) B. 6/10 (3/5) C. 2/5 D. 5/10 (½) E. (2, 3) or (6, 1) Day #2 Page 6 A. 6/10 (3/5) B. 4/10 (2/5) C. 3/5 D. 6/10 (3/5) E. (2,4) or (8,1) Day #3 Page 7 A. 2/10 (1/5) B. 8/10 (4/5) C. 1/5 D. 7/10 E. (1,10) or (2,5) Day #4 Page 8 A. 8/10 (4/5) B. 2/10 (1/5) C. 4/5 D. 9/10 E. (1,12) or (2,6) or (3,4) Week 2: Day #1 Page 9 A. 4/12 (1/3) B. 8/12 (2/3) C. 2/6 D. 7/12 E. (1,15) or (3,5) Day #2 Page 10 A. 8/12 (2/3) B. 4/12 (1/3) C. 2/3 D. 7/12 E. (1,16) or (2,8) or (4,4)

Week 2 (cont’d): Day #3 Page 11 A. 2/12 (1/6) B. 10/12 (5/6) C. 4/24 (1/6) D. 9/12 (3/4) E. (1,18) or (2,9) or (3,6) Day #4 Page 12 A. 6/12 (½) B. 6/12 (½) C. ½ D. 9/12 (¾) E.(1,20) or (2,10) or (4,5) Week 3: Day #1 Page 13 A. 6/14 (3/7) B. 8/14 (4/7) C. 3/7 D. 5/15 (1/3) E. (1,21) or (3,7) Day #2 Page 14 A. 4/14 (2/7) B. 10/14 (5/7) C. 2/7 D. 11/15 E. (1,24) or (2,12) or (3,8) or (4,6) Day #3 Page 15 A. 8/14 (4/7) B. 6/14 (3/7) C. 16/28 D. 10/15 (2/5) E. (1,27) or (3,9) Day #4 Page 16 A. 2/14 (1/7) B. 12/14 (6/7) C. 1/7 D. 15/15 = 1 E. (1,30) or (2,15) or (3,10) or (5,6)

Week 4: Day #1 Page 20 A. 2/10 (1/5) B. .2 C. 20% D. 2/4 (½) E. 1/3 F. (1,7) (1,2,7,14) (7) Day #2 Page 21 A. 3/10 B. .3 C. 30% D. 1/5 E. 2/3 F. (1,2,3,6) (1,2,3,4,6,12) (6) Day #3 Page 22 A. 6/10 (3/5) B. .6 C. 60% D. 4/9 E. 4/6 F. (1,5) (1,2,5,10) (5) Day #4 Page 23 A. 4/10 (2/5) B. .4 C. 40% D. 4/8 (½) E. ¼ F. (1,2,4) (1,2,4,8,) (4) Week 5: Day #1 Page 24 A. 5/10 (½) B. .5 C. 50% D. 6/10 (3/5) E. 1/10 F. (1,2,4,8) (1,2,4,8,16) (8)

Week 5 (cont’d): Day #2 Page 25 A. 9/10 B. .9 C. 90% D. 4/12 (1/3) E. ¼ F. (1,3,9) ( 1,2,3,6,9,18, 27) (9) Day #3 Page 26 A. 7/10 B. .7 C. 70% D. 2/11 E. 1/3 F. (1,2) (1,2,3,6) (2) Day #4 Page 27 A. 1/10 B. .1 C. 10% D. 9/12 (3/4) E. 1/3 F. (1,2,4) ( 1,2,5,10) (2) Week 6: Day #1 Page 28 A. 5/10 (½) B. .5 C. 50% D. 5/15 (1/3) E. 1/9 F.(1,2,3,6) (1,2,5,10) (2) Day #2 Page 29 A. 8/10 (4/5) B. .8 C. 80% D. 7/11 E. 1/6 F.(1,2,4,8) (1,2,5,10) (2)

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TM Fractions Decimals - WriteMath Enterpriseswritemath.com/wp-content/uploads/2014/11/Fractions... · Multiplying Mixed Numbers . Week 26: Fraction, Decimal, & Percentage .....119