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Find the fractions that make a whole.

Fractions

Cha

pter

2

5 � 35 �

55

� 1

- and - make 1whole.

Practice 1 Understanding Fractions

Lesson 14.1 Understanding Fractions

1.

6 � 16 �

66 � 1

- and

- make 1 whole.

2. 18 � 8 � 8 �

88 � 1

- , - ,

and - make 1 whole.

Example

15

15

15

15

15

0 1

This is 15

.

Two threefifths fifths

92

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Chapter 14 Fractions

Name the numerator and denominator.

3.

In this fraction, the numerator is .

In this fraction, the denominator is .

4.

In this fraction, the numerator is .

In this fraction, the denominator is .

46

of the figure is shaded.

In this fraction, the numerator is .

In this fraction, the denominator is .

4

6

16

16

16

16

16

160 1

This is 16

.

Example

of the figure is not shaded.

of the figure is shaded.

93

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Lesson 14.2 Understanding Equivalent Fractions

Practice 2 Understanding Equivalent FractionsShade the part(s) to show fractions equivalent to 1

4.

Write the fractions.

Shade the part(s) to show fractions equivalent to 15

.Write the fractions.

1.

14 �

14 �

15

� �

14

14

2

8

3

12

Example

94

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Chapter 14 Fractions

Divide the second bar into 10 equal parts.Shade the part(s) to show a fraction equivalent to 2

5.

Write the fraction.

2.

Divide the second bar into 12 equal parts.Shade the part(s) to show a fraction equivalent to 5

6.

Write the fraction.

3.

Find the missing numerator or denominator.

4.

25

� 15

15

56

� 16

16

16

16

16

34

� 6

� 12

� 12

95

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Use the number lines to find equivalent fractions.

5.

The equivalent fractions are , , and .

The equivalent fractions are , , and .

Lesson 14.2 Understanding Equivalent Fractions

13

26

39

Example

0 89

59

29

79

49

19

169

39

0 26

46

116

36

56

0 13

23

1

0 612

312

812

512

212

712

412

1112

912

1012

1112

0 28

48

118

38

58

68

78

0 14

34

124

96

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Chapter 14 Fractions

Write the missing fractions on the number lines.Then use the number lines to find the missing numerators and denominators.

6.

7. 25

� 10

8. 5

� 9

9. � 2 � 315

10. 35

� 10

�

1415

1215

1015

915

115

1415

715

215

515

0

45

10

910

710

610

310

110

1410

0

15

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Practice 3 More Equivalent FractionsComplete.

1.

Find the missing numerators and denominators.

2. 3.

� 3� 2

� 3� 2

16

�

Lesson 14.3 More Equivalent Fractions

23

is equivalent to .

Example

� 3� 2

� 3� 2

12

� 2

12

is equivalent to .

4

24

� 3� 3

� 3� 3

23

� 9

� 3� 4

� 3� 4

13

�

98

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Chapter 14 Fractions

Find the missing numerator and denominator.

4. 5.

Find the missing numerator or denominator.

6. 16

� 12

7. 17

� 2

8. 45

� 10

9. 35

� 6

10. 23

� 12

11. 34

� 12

12. 14

� 8

� 3

13. 27

� 14

� 21

14. 25

� 6

� 12

15. 3 � 612

� 24

One way to find an equivalent fraction is to multiply the numerator and denominator by the same number.

� 3� 2

� 3� 2

45

�

� 3� 3

� 3� 3

34

�

99

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Complete.

16. � 3� 2

� 3� 2

1012

� 6

1012

is equivalent to .

Find the missing numerator or denominator.

17. 612

� 1

18. 69

� 3

19. 68

� 3 20. 8 � 45

Lesson 14.3 More Equivalent Fractions

� 3� 2

� 3� 2

46

� 2

Example

3

46

is equivalent to .23

100

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Chapter 14 Fractions

Complete the equivalent fractions.Then write each fraction in simplest form.

21. 812

� 46

812

� 2

The simplest form of 812

is .

22. 612

� 612

� 612

�

The simplest form of 612

is .

Write each fraction in simplest form.

23. 412

� 24. 510

�

25. 69

� 26. 810

�

27. 68

� 28. 912

�

101

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Practice 4 Comparing FractionsCompare the fractions.

1.

is greater than .

12

57

2.

is less than .

12

49

Lesson 14.4 Comparing Fractions

Example

512

12

is greater than .

is less than .

12

12

512

512

102

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Chapter 14 Fractions

Compare the fractions.

3.

4.

5.

6.

It is easy to comparefractions with the same denominator.

It is also easy tocompare fractionswith the samenumerator.

is greater than .

23

13

is less than .

38

58

is greater than .

410

45

is less than .

37

35

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Compare the fractions.

34

and 78

34

� 8

�

7. 79

and 23

23

�

�

8. 45

and 12

45

� 12

�

�

9. 56

and 14

56

� 14

�

�

6

Lesson 14.4 Comparing Fractions

78

34

Example

Change to equivalent like fractions.

104

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Chapter 14 Fractions

Use the number lines to compare fractions.

Complete.

10.

Which is greater, 35

or 56

? Which is less, 25

or 36

?

34

14

124

0

0 13

23

1

Which is greater, 13

or 24

?

Which is less, 23

or 34

?

23

34

24

13

0 16

1

15

10

Example

105

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Compare. Choose > or

106

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Chapter 14 Fractions

Compare the fractions. Fill in the blanks.

12. 47

and 67

is greater.

13. 25

and 210

is greater.

14. 712

and 12

is greater.

15. 511

and 12

is less.

16. 712

and 511

is less.

Order the fractions from greatest to least.

37

, 38

, 35

17. 711

, 511

, 1111

18. 23

, 56

, 410

19. 13

, 12

, 34

20. 12

, 23

, 34

Compare each with 12.

12 �

6

� 10

Example

The least fraction is the one with the

greatest denominator.35

, 37

, 38

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Practice 5 Fraction as a Whole or SetWrite two fractions for the following whole numbers.

Lesson 14.5 Fraction as a Whole or Set

Example

Each shape is a whole.

1 � �

2 � �

1. 3 � ; 3 �

3. 1 � ; 1 �

3. 7 � ; 7 �

4. 10 � ; 10 �

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Chapter 14 Fractions

5. 3636

� 6. 183

�

7. 305

� 8. 9010

�

9. 162

� 10. 639

�

11. 357

� 12. 328

�

What numbers are shown by these fractions?

Solve.

Tabitha makes 9 happy-face pins.She gives away 6 of them and keeps the rest.

What fraction of the pins does she give away?

What fraction of the pins does she keep?

69 �

23

39 �

13

Tabitha gives away 69

of the pins.

She keeps 39

of the pins.

Example

109

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14. Shawn buys more trucks. He now has 20 trucks. He paints them in the same fractional parts as before. Color the trucks to help you.

a. What fraction of the trucks are green?

b. What fraction of the trucks are brown?

Solve.

13. Shawn paints 2 out of 5 model trucks green. He paints the rest brown. Color the trucks to help you.

a. What fraction of the trucks are green?

b. What fraction of the trucks are brown?

Lesson 14.5 Fraction as a Whole or Set

110

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Chapter 14 Fractions

Solve.

15. What fraction of the buttons are gray?

16. What fraction of the buttons are not gray?

17. What fraction of the buttons have 3 holes?

18. What fraction of the buttons are white with 2 holes?

19. What fraction of the buttons are white with 4 holes?

20. What fraction of the buttons are round?

21. Find 34

of 20.

14

of 20 �

24

of 20 �

So, 34

of 20 � .

111

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Solve.

22. Serena buys 24 breakfast bars. 3

4 of them are blueberry.

How many blueberry breakfast bars does Serena buy?

24 breakfast bars

?

4 units

1 unit �

�

3 units �

�

Serena buys blueberry breakfast bars.

Lesson 14.5 Fraction as a Whole or Set

112

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Chapter 14 Fractions

Put On Your Thinking Cap!

1. Write a fraction with a denominator of 9.

The fraction should be less than 12

.

Mark the number lines to help you.

2. 0 11

2

Which is greater, 37

or 23

?

�

3. 0 11

2

Which is less, 18

or 25

?

�

4. 0 11

2

Order 17

, 35

, 38

, and 89

from least to greatest.

, , ,

least

Challenging Practice

113

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Put On Your Thinking Cap!

1. Shade to show a fraction greater than 14

but less than 12

.

2. Sam wants to shade 23

of the figure.

He has already shaded 4 squares.

How many more squares must he shade?

Help him shade.

Problem Solving

Sample:

114

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Chapter 14 Fractions

3. Shade the figure to show each fraction below. Use a different color for shading each fraction.

13

, 14

, 112

What fraction of the figure is unshaded?

of the figure is unshaded.