Date:

P H A TE

6

R

C

Name:

Fractions and Mixed Numbers

Lesson 6.1

Adding Fractions

Find the equivalent fraction. Complete the model and add the fractions. 1.

2 1 __ _ _ 3 9

3

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2 3

1 9

 3

2.

?

1 1 __ _ _ 6 2



3 1 2

1 6

 3

?

Extra Practice 4A

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3.

1 2 _ _  _ _   10 5



4.

2 2 _ __ _   12 3



5.

1 1 _ Add _ and 4 12 .

6.

1 Add _ 4 to your answer in Exercise 5.

7.

1 1 _ and Add _ 6. 3

8.

1 Add _ 6 to your answer in Exercise 7.

9.

1 _ 1 2 _ , , and What is the sum of _ 4? 8 4

10.

3 1 _ 4 _ , , and What is the sum of _ 6 18 9?

96

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Add. Write each answer in simplest form.

Chapter 6 Lesson 6.1

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Lesson 6.2

Subtracting Fractions

Find the equivalent fraction. Complete the model. Then subtract. 1.

1 5 _  _ _ _ 2 6



5 6 3 1 2

?



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3

2.

1 7 _ _  _ _  3 12



7 12 4 1 3



?

4

Extra Practice 4A

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Subtract. Write each answer in simplest form. 5 3 _ _  _ _  12  4



4.

3 4 _ _  _ _  10  5



5.

7 1 _  1_ 4  12

7.

5 1 _ from Subtract _ 6. 3

9.

3 7 _ and The difference between _ 5 is 10

10.

7 The difference between 1 and _ 8 is

98



6.

6 4 1_  _ 16 8

8.

5 11 _ Subtract _ from 6 12 .

.

.



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3.

Chapter 6 Lesson 6.2

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Lesson 6.3

Mixed Numbers

Write a mixed number for each model. 1.

5 1⫹_ 6⫽

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2.

3 3⫹_ ⫽ 8

3.

4 2⫹_ ⫽ 7

4.

7 5⫹_ 9⫽ Extra Practice 4A

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Write a mixed number for each model. 5.

wholes and

fourths is

.

wholes and

sixths is

.

wholes and

thirds is

.

7.

100

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6.

Chapter 6 Lesson 6.3

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Write a mixed number for each of the following.

2L 1L

8.

The volume of water in the container is

9.

The weight of five oranges is

liters. pounds.

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Write each answer as a mixed number. 10.

3 2_ 5

11.

5 _ 4  8

12.

4 3_ 9

13.

7 5_ 12 

14.

1 _ 62

15.

3 _ 4 10

Simplify. 16.

6 2_ 8

17.

4 1_ 10 

18.

3 4_ 9

19.

9 3_ 12 

Extra Practice 4A

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Write the correct fraction or mixed number in each box. Express each answer in simplest form. 20. 0

1 5

3 5

4 5

1

12 5

13 5

2

1 11 12 13 14 15 8 8 8 8 8

17 2 8

21 5

22 5

24 5

3

21. 5 6 8 8

22 23 24 25 8 8 8 8

27 3 8

22. 3

4

5

6

7

8

5

6

7

8

9

23. 4

102

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0 1 2 3 8 8 8

Chapter 6 Lesson 6.3

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Lesson 6.4

Improper Fractions

Write each mixed number as an improper fraction.

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1.

a.

1

b. c.

3 _ 7 3 1_ 7

d.



a.

2

eighths

b.

eighths

c.

3 _ 8 3 2_ 8

d.



sevenths sevenths sevenths

2.

eighths

Extra Practice 4A

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3.

a.

3

thirds

b.

thirds

c.

2 _ 3 2 3_ 3

d.



thirds

Write the improper fractions for the shaded parts.

3 1_ 5

5.

2 4_ 3

6.

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4.

1 6_ 2

104

Chapter 6 Lesson 6.4

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Write a mixed number and an improper fraction for each model. 7.

Mixed number:

Improper fraction:

Mixed number:

Improper fraction:

Mixed number:

Improper fraction:

Mixed number:

Improper fraction:

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8.

9.

10.

Extra Practice 4A

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11.

Mixed number:

Improper fraction:

Mixed number:

Improper fraction:

Mixed number:

Improper fraction:

Mixed number:

Improper fraction:

12.

14.

106

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13.

Chapter 6 Lesson 6.4

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Write the missing improper fraction in each box. Express each answer in simplest form. 15. 1

5 4

2

6 4

3

10 4

16. 4 3

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1

2

3

17. 9 7

1

10 7

11 7

13 7

2

15 7

16 7

18 7

19 7

20 7

3

18. 3

19 6

20 6

21 6

23 6

4

25 6

27 6

28 6

Extra Practice 4A

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19. 2

19 20 21 8 8 8

17 8

23 8

3

25 26 27 28 29 8 8 8 8 8

31 8

4

20. 4

22 5

23 5

24 5

5

27 5

28 5

6

38 10

4

44 10

46 10

5

3

32 10

34 10

22. 1

108

20 15

25 15

2

40 15

3

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21.

Chapter 6 Lesson 6.4

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Lesson 6.5

Renaming Improper Fractions and Mixed Numbers

Express each improper fraction as a mixed number. 1.

10 1 11 _ _ _ 2 2 2

2.

 5 _

6_ 3

5_ 2

 6_ 3

2

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3.

5.

20 18 2 _ _ _ 3  3 3

13 _ _ _ 4  4 4

4.

23 _ _ _ 5  5 5

3_ 4

4_ 5

3_ 4

4_ 5

27 __ _  10 10 10

 

_ 10

6.

26 __ _  7 7 7



_ 7



Extra Practice 4A

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Express each improper fraction as a mixed number in simplest form. 16 _ ⫽2⫹_ 6 6

8.

⫽

20 _ _ 8 ⫽2⫹ 8

⫽

9.

15 _ ⫽ 2

10.

18 _ 10 ⫽

11.

21 _ ⫽ 9

12.

15 _ 12 ⫽

13.

22 _ ⫽ 7

14.

36 _ 6 ⫽

15.

30 _ ⫽ 4

16.

42 _ 5 ⫽

17.

28 _ ⫽ 13

18.

48 _ 15 ⫽

110

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7.

Chapter 6 Lesson 6.5

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Express each mixed number as an improper fraction. 19.

21.

2 2 _ 3_ ⫽ 3 ⫹ 3 3

20.

2 _ ⫽_ ⫹ 3 3

1 _ ⫽_ ⫹ 4 4

⫽_ 3

⫽_ 4

3 3 _ _ 2_ 5⫽ 5 ⫹5

22.

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⫽_ 5

23.

1 1 _ 1_ ⫽ 1 ⫹ 4 4

4 _ _ 2_ 7⫽ 7 ⫹ 7

⫽_ 9

5 5 _ _ 2_ 6⫽ 6 ⫹6

⫽_ 6

24.

2 _ _ 2_ 9⫽ 9 ⫹ 9

⫽_ 9

Extra Practice 4A

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25.

1 4_ 3

26.

3 2_ 10 

27.

2 1_ 7

28.

5 1_ 9

29.

1 2_ 4

30.

5 2_ 12 

31.

3 1_ 10 

32.

2 1_ 11 

33.

4 5_ 5

34.

8 3_ 9

35.

1 6_ 5

36.

2 7_ 7

112

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Express each mixed number as an improper fraction.

Chapter 6 Lesson 6.5

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Lesson 6.6

Renaming Whole Numbers when Adding and Subtracting Fractions

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Add. Express each answer as a mixed number in simplest form. 1.

2 5 _ ⫹_ 3⫽ 9

2.

3 _ 11 _ 4 ⫹ 12 ⫽

3.

7 1 _ ⫹_ 8⫽ 2

4.

1 2 _ _ 6⫹3⫽

5.

4 7 _ _ ⫹ 5⫽ 10

6.

5 2 _ _ ⫹ 12 3⫽

7.

7 5 _ _ ⫹ 12 ⫽ 6

8.

3 6 _ _ ⫹ 4⫽ 8

9.

1 2 5 _ _ ⫹_ 2⫹3⫽ 12

10.

3 3 1 _ _ _ 2⫹8⫹4⫽

Extra Practice 4A

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11.

7 3⫺_ 12 ⫽

12.

8 4⫺_ 9⫽

13.

4 2⫺_ 5⫽

14.

2 5⫺_ 3⫽

15.

1 1 _ 3⫺_ 6⫺3⫽

16.

1 1 _ 4⫺_ 4⫺2⫽

17.

3 2 _ ⫺ 6⫺_ 5 10 ⫽

18.

5 2 _ 3⫺_ ⫺ 7 14 ⫽

19.

5 1 _ 2⫺_ 12 ⫺ 6 ⫽

20.

2 2 _ 5⫺_ 3⫺9⫽

114

Chapter 6 Lesson 6.6

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Subtract. Express each answer as a mixed number in simplest form.

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Lesson 6.7

Date:

Fraction of a Set

What fraction of each set of objects is shaded? Express your answer in simplest form. 1.

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2.

3.

4.

Extra Practice 4A

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Use a model to help you answer each question.

Example 3 What is _ 4 of 24? 24

4 units ⫽ 24 1 unit ⫽ 6 3 units ⫽ 6 ⫻ 3 ⫽ 18

?

3 So, _ 4 of 24 ⫽ 18.

4 What is _ 5 of 30?

5.

5 units ⫽

30

4 units ⫽

?

4 So, _ 5 of 30 ⫽

6.

.

5 What is _ 6 of 48?

7.

5 What is _ 12 of 60?

2 _ ⫻ 45 3 2 _ of 45 is 3

9.

4 _ 9 ⫻ 36 4 _ 9 of 36 is

Solve. 8.

10.

116

2 _ ⫻ 35 7

. 11.

3 _ ⫻ 32 8

.

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1 unit ⫽

Chapter 6 Lesson 6.7

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Lesson 6.8 Real-World Problems: Fractions

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Solve. Show your work. 1.

Arthur had $90. He spent $40 and gave $20 to his brother. What fraction of Arthur’s money is left?

2.

3 A baker has 20 pounds of sugar. He uses _ 4 of the sugar to bake muffins. How much sugar does he have left?

Extra Practice 4A

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Mya buys 6 goldfish and 4 angelfish. a. What fraction of the fish are goldfish?

b.

4.

118

Mya buys 2 more goldfish. What fraction of the fish are angelfish?

3 2 _ of her savings on a book, and Cheryl spends _ 5 of it on a pen. 10 What fraction of her savings does Cheryl spend?

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3.

Date:

Chapter 6 Lesson 6.8

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Name:

Date:

5.

1 1 Of the vehicles on the road, _ are cars and _ 8 are motorcycles. 2 What fraction of the vehicles are not cars or motorcycles?

6.

3 Allie’s plant has a height of 6 meters. Rajon’s plant grows _ 10 meter higher. How high does Rajon’s plant grow?

Extra Practice 4A

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7.

2 There are 10 packets of ham. Of the packets, _ 5 are turkey ham. Each packet 1 of turkey ham weighs _ 3 pound. What is the total weight of the turkey ham?

8.

6 1 _ hours exercising every day for 12 days. She spends Carla spends _ 4 2 of her exercise time every day lifting weights. How much time does Carla spend lifting weights during the 12 days?

120

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Name:

Chapter 6 Lesson 6.8

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Put on Your Thinking Cap! 1.

2 Justin buys a pair of pants and a shirt. He spends _ 5 of the total money on the shirt. He pays $27 for the pair of pants. How much does Justin pay for the shirt?

2.

5 Of all the peppers the chef has, _ 7 are red and the rest are green. The chef has a total of 34 green peppers. How many peppers does she have altogether?

Extra Practice 4A

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1 A basket _ 2 full of apples weighs 8 pounds. When the basket is filled with apples, it weighs 11 pounds. What is the weight of the empty basket?

4.

5 2 _ 1 _ 1 _ 7 _ 4 _ Write the fractions _ 9 , 3 , 6 , 18 , 9 , and 18 in the boxes. The three fractions on each side of the triangle should have a sum of 1. © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.

3.

122

Chapter 6 Put on Your Thinking Cap!

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