p t h C Fractions and Mixed Numbers€¦ · Fractions and Mixed Numbers 101 1. 3 4 ˜ ˜ 2. 2 5 ˜...

$Page 1: p t h C Fractions and Mixed Numbers€¦ · Fractions and Mixed Numbers 101 1. 3 4 ˜ ˜ 2. 2 5 ˜ ˜ 3. 5 6 ˜ ˜ 4. 1 7 ˜ ˜ Express each fraction in simplest form. 5. 6 8 ˜ 6.$
Lesson 3.1 Adding Unlike Fractions

Fractions and Mixed Numbers

101

1. 34 � � 2. 2

5 � �

3. 56 � � 4. 1

7 � �

Express each fraction in simplest form.

5. 68 � 6. 8

20 �

7. 1015 � 8. 9

21 �

Practice 1 Adding Unlike FractionsFind two equivalent fractions for each fraction.

Example

23 � �

C

hapte

r

46

69

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08(M)MIF2015CC_WBG5A_Ch03.indd 101 29/04/13 11:34 AM

Chapter 3 Fractions and Mixed Numbers

Rewrite each pair of unlike fractions as like fractions.

Example

12 � 1

4 �

9. 14 �

512 �

10. 1

10 �

25 �

11. 59 �

23 �

12. 3

8 �

916 �

Write equivalent fractions for each fraction. Then find the least common denominator of the fractions.

12 � = 13. 2

3 �

23 � 3

4 �

The least common denominator The least common denominator

is . is .

14. 14 � 15. 5

6 �

56 � 3

8 �

The least common denominator The least common denominator

is . is .

24

14

Example36

46

6

24

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16. 15 , 12

15 � 12 � �

�

Shade and label each model to show the fractions. Then complete the addition sentence.

Example

12 � 13 � �

�

36

26

56

Find the multiples of 2 and 3. Choose the least common multiple.Use it to rewrite 1

2 and 13 as like

fractions.

12 , 13

12

13

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Shade and label each model to show the fractions. Then complete the addition sentence.

17. 16 , 14

16 � 14 � �

�

18. 15 , 2

3

15 � 2

3 � �

�

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Look at the model. Write two addition sentences.

1112

19. Addition sentence 1:

12

� 12

� 12

20. Addition sentence 2 (fractions in simplest form):

� �

Add. Express each sum in simplest form.

21. 13 � 19 � 22. 5

8 � 24 �

23. 12 � 67 � 24. 4

8 � 15 �

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Use benchmarks to estimate each sum.

25. 23 � 29

26. 79 � 1

7 � 35

13 � 47

13 is about 1

2.

47 is about 1

2.

13 + 47

12 + 1

2 = 1

13 + 47 is about 1.

Example

13

0 112

47

0 112

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Lesson 3.2 Subtracting Unlike Fractions

Practice 2 Subtracting Unlike FractionsRewrite the fractions as like fractions and complete the subtraction sentence.

Example

�3

�3

12 �

3

613 �

2

6

�2

�2

12 � 36

13 � 26

12 � 13 � �

�

36

26

16

What is the least common multiple of 2 and 3?

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Rewrite the fractions as like fractions and complete the subtraction sentence.

1.

13 � 1

4 �

13 �

14 �

13 � 14 � �

�

Subtract. Express each difference in simplest form.

2. 712 � 24 � 3. 4

5 � 13 �

4. 1 � 56 � 112 � 5. 7

9 � 16 �

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Lesson 3.2 Subtracting Unlike Fractions

6. 910 � 16

7. 512 � 1

9

Example

Use benchmarks to estimate each difference.

0 112

45

0 112

38

45 � 38

45 is about 1.

38 is about 1

2.

45 – 3

8

1 – 12 = 1

245 – 3

8 is about 12.

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Darren drew a model to find 45 � 12. His model is drawn incorrectly.

Explain his mistakes. Then draw the correct model and find the difference.

45

12

?

Darren’s model is wrong because:

The correct model is:

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Lesson 3.3 Fractions, Mixed Numbers, and Division Expressions

Practice 3 Fractions, Mixed Numbers, and Division Expressions

Look at the diagram. Complete.

� �

1.

� �

Example

3

4

43

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Write each division expression as a fraction.

2. 3.

5 � 7 �

3 � 10 �

4. 5.

4 � 9 �

2 � 11 �

Write each fraction as a division expression.

7. 110 � � 8. 6

7 � �


Example

78 � � 6. 5

12 � �

Example

� �

�

4 3

7 8

4

3

1

31

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Lesson 3.3 Fractions, Mixed Numbers, and Division Expressions


9.

Complete.

10. 11.

7 � 4 �

35 � 11 �

�

�

�

�

� 1 �

� 3

�

�

�

� �

�

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Divide. Express each quotient as a mixed number.

Example

5 � 3 � 1 2

3

13. 14.

9 � 4 � 2 18 � 5 � 3

Write each fraction in simplest form. Then divide to express each quotient as a mixed number.

15. 16.

18 � 4 �

22 � 6 �

�

�

�

�

12.

7 � 2 � 3 13 5 3 2

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Lesson 3.4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals

Practice 4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals

Write each fraction as a decimal.

Example

35 � 1. 13

20 �

�

�

2. 1925 � 3. 47

50 �

�

�

Express each division expression as a mixed number in simplest form and as a decimal.

Division expressionExpress division expression as

a mixed number a decimal

4. 7 � 2

5. 9 � 4

6. 21 � 5

7. 101 � 25

610

0.6

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Express each improper fraction as a decimal.

8. 225

9. 4720 10. 32

25

Solve. Show your work.

11. A coil of rope 603 feet long is cut into 25 equal pieces. What is the length of each piece? Express your answer as a mixed number and as a decimal.

Example

32 = 2

2 + 1

2= 1 + 1

2= 1 + 0.5

= 1.5

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Lesson 3.5 Adding Mixed Numbers

Example

Practice 5 Adding Mixed NumbersAdd. Express each sum in simplest form.

3 58 � 2

14

� 3 � 2 �

� 5

1. 123 � 2

14

� 1 � 2 �

� 3

2. 2 15 � 3 1

2

� 2 � 3 �

� 5 12

15

58

14

23

14

5

8

2

8

7

8

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3. 3 27 � 2 514 4. 5 712 � 3 14

5. 4 115 � 1 310 6. 12 19 � 9 56


7. 145 � 2 13

� 1 � 2 �

� 3

� 4

45

13

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Lesson 3.5 Adding Mixed Numbers


8. 3 512 � 123

� 3 � 1

�

� 4

� 5

9. 2 34 � 3 25 10. 2 59 � 156

11. 7 89 � 9 512 12. 5 712 � 134

23

512

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Use benchmarks to estimate each sum.

Example

6 35 � 4

56

35 is about 1

2.

So, 635 is about 6 1

2.

56 is about 1.

So, 4 56 is about 5.

6 35 + 4 56

6 12 + 5 = 11 12

6 35 + 4 56 is about 11 12.

13. 9 67 � 7

512

14. 4 712

� 10 19

0 112

35

0 112

56

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Lesson 3.6 Subtracting Mixed Numbers

Example

Practice 6 Subtracting Mixed NumbersSubtract. Express each difference in simplest form.

3 23 �

512

� 3 � 512

� 3

� 3

1. 4 89 � 3

13

� 4 89 � 3

� 1

23

89

8

12

3

12

1

4

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2. 3 712

� 2 38

� 3 � 2

� 1

3. 3 59

� 1 12

4. 7 56

� 2 14

Subtract. Express each difference as a mixed number.

5. 3 14

� 178

� 3 � 1 78

� �

�

Subtract. Express each difference in simplest form.

14

712

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Lesson 3.6 Subtracting Mixed Numbers

Subtract. Express each difference as a mixed number.

6. 5 13

� 3 512

� 5 � 3 512

� �

�

7. 4 15

� 1 13

8. 6 38

� 3 56

9. 7 14 � 5

1112 10. 8

13 � 4

34

13

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7 29 � 6

512

29

is about 0.

So, 7 29

is about 7.

512

is about 12

.

So, 6 512

is about 6 12

.

7 29

� 6 512

7 � 6 12 �

12

7 29

� 6 512

is about 12

.

Example

11. 12 25

� 8 712

12. 20 18 � 5

39

Use benchmarks to estimate each difference.

29

0 112

512

0 112

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Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers

Practice 7 Real-World Problems: Fractions and Mixed Numbers


1. Elena has 12 pieces of banana bread. She gives an equal amount of banana bread to 5 friends. How many pieces of banana bread does she give each friend?

2. A utility bill shows that a household used 2,001 gallons of water in a 5-day period. What was the average amount of water used by the household each day?

3. A ball of string is 50 yards long. A shipper uses 5 yards of string to tie packages. The remaining string is then cut into 7 equal pieces. What is the length of each of the 7 pieces of string?

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4. Steve picks 55 pounds of pears. He packs an equal amount of pears into 6 bags. He then has 4 pounds of pears left. What is the weight of pears in each bag?

5. Jeremy puts an empty container under a leaking faucet. In the

first hour, 38

quart of water collects. In the second hour, 16

quart of water collects. How much water collects in the

container in the two hours?

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6. Arnold buys 89

pound of ground turkey. He uses 34

pound of the ground turkey to make meatballs. How many pounds of ground turkey are left?

7. A snail is at the bottom of a well. In the first 10 minutes, the snail climbs 23 7

12 inches. In the next 10 minutes, it climbs 19 5

6 inches. How far is

the snail from the bottom of the well after 20 minutes?

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8. Johnny is jogging along a track. He has already jogged 1 23

miles.

He plans to jog a total of 3 14

miles. How many miles does he have left to jog?

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Practice 8 Real-World Problems: Fractions and Mixed Numbers


1. Susanne and Barry each buy 4 equal-sized bagels. They divide the bagels equally among themselves and 3 other friends. How many bagels does each person get?

2. Maya has 5 sheets of paper. She cuts 3 circles from each sheet. The circles are shared equally among 6 students. How many circles does each student get?

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3. Mrs. Quirk buys 1 quart of milk. Michael drinks 27

quart of it.

Joel drinks 13

quart of it. How many quarts of milk are left?

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4. An organic farmer buys a piece of land. She plants tomatoes

on 59

of the land and green beans on 112

of the land.

She plants potatoes on the remaining piece of land. What fraction of the land does she plant with potatoes?


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5. A package contains three types of bagels, plain, wheat, and sesame.

The weight of the plain bagels is 123 pounds. The weight of the wheat

bagels is 2 56 pounds. The total weight of the three types of bagels is

5 pounds. What is the weight of the sesame bagels?

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6. Reggie and Jay go for a walk every morning. Reggie walks 2 14 miles.

Jay walks 138 miles less than Reggie. What is the total distance

they walk every morning?


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7. Alicia uses 34

gallon of paint to paint her room. Becca uses 45

gallon

more than Alicia to paint her room. How many gallons of paint do they use altogether?

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8. A monkey climbs 3 35

feet up a coconut tree that has a height

of 10 feet. It rests for a while and continues to climb another 4 2

3 feet up the tree. How many more feet must the monkey climb to

reach the top of the tree?


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18 �

23 � ?

Draw a model, and explain the steps you can use to add 23

to 18

.

Chapter 3 Fractions and Mixed Numbers136

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Tina, Troy and Nate had a total of 25 equal-sized square tiles to place over a squaregrid. Tina used 8

25 of the square tiles. Troy used 1

5 of the square tiles. Shade the

square grid below to show how Tina and Troy could have placed the square tiles. What fraction of the square grid must Nate place the tiles on so that 1

5 of the

square grid is not covered?

Put On Your Thinking Cap!

Challenging Practice


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Put On Your Thinking Cap!

Solve. Use a model to help you.

Paul mixes cement with sand. He uses 3 34 kilograms of cement and 1

2 kilogram

more sand than cement. He needs 10 kilograms of the mixture. Does he have

enough mixture? If yes, how much more does he have and if no, how much

more does he need?

Problem Solving

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p t h C Fractions and Mixed Numbers€¦ · Fractions and Mixed Numbers 101 1. 3 4 ˜ ˜ 2. 2 5 ˜...

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