C H A PTE 4 R Multiplying and Dividing Fractions and Mixed ... · PDF fileWorksheet 1 Multiplying Proper Fractions Look at the models. Follow the steps and ﬁ ll in the blanks. What

Worksheet 1 Multiplying Proper FractionsLook at the models. Follow the steps and fi ll in the blanks.

What is the value of 1 _ 2 of 1 _ 3 ?

Step 1 A rectangle is divided into thirds. Shade 1 _ 3 of it.

Step 2 Draw stripes over 1 _ 2 of the shaded portion.

1 _ 6 of the rectangle has stripes drawn over the shaded portion.

1 _ 2 of 1 _ 3 is 1 _ 6 .

Example

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Multiplying and Dividing Fractions and Mixed Numbers

CHAPTER

4

MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM

Look at the models. Follow the steps and fi ll in the blanks.

1. What is the value of 1 _ 4 of 2 _ 5 ?

Step 1 A rectangle is divided into fi fths. Shade 2 _ 5 of it.


of the rectangle has stripes drawn over the shaded portion.

1 _ 4 of 2 _ 5 is .

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Chapter 4 Lesson 4.1


2. What is the value of 3 _ 4 of 2 _ 3 ?

Step 1 A rectangle is divided into thirds. Shade 2 _ 3 of it.


of the rectangle has stripes drawn over the shaded portion.

3 _ 4 of 2 _ 3 is .

Complete.

1 _ 2 of 3 _ 4 � 1 _ 2 � 3 _ 4

Example

3. 1 _ 5 of 2 _ 3 � �

4. 1 _ 3 of 7 _ 8 � 5. 1 _ 4 of 5 _ 9 �

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Complete.

1 _ 3 � 5 _ 8 � 1 _ 3 5 _ 8

Example

of 6. 3 _ 4 � 7 _ 12 � of

7. 1 _ 2 � 4 _ 9 � 1 _ 2 4 _ 9 8. 2 _ 5 � 1 _ 6 � of

Multiply. Express each product in simplest form.

Example

1 _ 2 � 1 _ 3 � 1 � 1

2 � 3

Multiply the numerators.Multiply the denominators.

� 1

6

9. 3 _ 4 � 5 _ 7 � �

� �

10. 2 _ 5 � 2 _ 9 � �

� �

11. 5 _ 6 � 1 _ 3 � �

� �

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Example

1 _ 3 � 6 _ 7 � 1 � 2

1 � 7

� 2

7

This is another way to multiply fractions.Divide a numerator and a denominator by the common factor 3.

1 _ 3 � 6 _ 7 � 1 _ 3 � 3 � 6 � 3 _ 7

� 1 _ 1 � 2 _ 7

12. 1 _ 2 � 4 _ 5 � �

�

�

13. 2 _ 5 � 3 _ 8 � �

�

�

14. 3 _ 4 � 7 _ 12 � �

�

�

15. 3 _ 4 � 8 _ 9 � �

�

�

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16. 1 _ 6 � 8 _ 9 17. 1 _ 3 � 6 _ 7

18. 4 _ 9 � 7 _ 12 19. 3 _ 5 � 11 _ 12

20. 4 _ 7 of 5 _ 12 21. 3 _ 4 of 2 _ 3

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Worksheet 2 Real-World Problems: Multiplying with Proper Fractions

Complete each model to show the statements.

Example

A bottle contains 4 _ 5 liter of juice.

Amy drinks 1 _ 4 of the juice.

drinks left

liter45

1. Mrs. Costa bought 8 _ 9 pound of beef.

She cooked 3 _ 8 of the beef.

pound

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Draw a model to show the statements.

2. Harry had 7 _ 8 meter of ribbon.

He used 2 _ 7 of the ribbon to tie a gift.

Solve. Use a model to help you.

3. Sarah poured 5 _ 7 cup of milk into a glass. She drank 1 _ 5 of it.

a. How much milk did she drink?

1 cup

drank left

cup57

From the model,

7 units cup

1 unit cup

She drank cup of milk.

b. How much milk was left?

4 units cup

cup of milk was left.

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Solve. Use a model to help you.

4. A farmer had 3 _ 4 of a bag of seeds. He planted 2 _ 3 of the seeds.

a. What fraction of the bag of seeds did the farmer plant?

Model:

From the model,

units

1 unit

units

He planted of a bag of seeds.

b. What fraction of the bag of seeds were left?

unit

of a bag of seeds was left.

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Complete each model to show the statements.

Example

Barry bought a box of fruits. Of the fruits, 3 _ 8 were apples.

Of the remainder, 2 _ 5 were oranges.

Remainder � 5 units38

of remainder25

5. Cindy collects Canadian, U.S., and British coins. Of the coins,

2 _ 9 are Canadian. Of the remainder, 3 _ 7 are British coins.

6. Jessica had some money. She spent 4 _ 9 of her money on food and

3 _ 10 of the remainder on drinks.

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Solve. Use models to help you.

7. Mike has an aquarium. Of the fi sh in his aquarium, 2 _ 5 are clownfi sh.

Of the remaining fi sh, 1 _ 3 are damselfi sh.

a. What fraction of Mike’s fi sh are damselfi sh?

b. What fraction of his fi sh are not clownfi sh or damselfi sh?

8. Lillian collects stickers. Of her collection, 5 _ 12 are animal stickers.

Of the remainder, 5 _ 14 are fl ower stickers.

a. What fraction of Lillian’s stickers are fl ower stickers?

b. What fraction of her stickers are not animal or fl ower stickers?

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Solve. Use the fraction method.

9. Zach walked his dog for 7 _ 8 hour. They spent 1 _ 2 of the time at the beach.

How much time did Zach and his dog spend at the beach?

1 _ 2 � 7 _ 8 � ?

10. Mrs. Jenkins picked some tomatoes from her garden. She used 5 _ 9 of the

tomatoes to make pasta sauce. Then she used 3 _ 4 of the remainder to

make a salad. What fraction of the tomatoes did Mrs. Jenkins use to

make the salad?

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Worksheet 3 Multiplying Improper Fractions by Fractions

Simplify each improper fraction.

1. 18 _ 8 �

18 � 2 �

8 � 2 �

9

4

2. 27 _ 6 �

27 � �

6 � �

3. 42 _ 24 �

42 � �

24 � �

4. 56 _ 32 �

56 � �

32 � �

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Complete.

Divide a numerator and a denominator by the common factor 3.

2 _ 3 � 18 _ 5 � 2 _ 3 � 3 � 18 � 3 _ 5

� 2 � 6 _ 1 � 5

Example

2 _ 3 � 18 _ 5 � �

�

2 6

51

�

12

5

� 2 2 _ 5

5. 1 _ 2 � 8 _ 7 � �

�

�

6. 5 _ 4 � 3 _ 20 � �

�

�

7. 5 _ 4 � 16 _ 3 8. 5 _ 4 � 12 _ 13

9. 7 _ 8 � 12 _ 7 10. 14 _ 9 � 18 _ 7

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Worksheet 4 Multiplying Mixed Numbersand Whole Numbers

Write each mixed number as an improper fraction.

1. 3 2 _ 5 � 2. 2 7 _ 9 �

Write the product as an improper fraction.

3. 6 _ 5 � 2 � 4. 9 _ 4 � 5 �

Write each improper fraction as a mixed number.

5. 12 _ 5 � 10 _ 5 � 2 _ 5 6. 15 _ 8 � �

� �

�

� �

�

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Divide. Find the quotient and remainder. Then write the answer as a mixed number.

7. 2 9 8

1

Quotient � Remainder �

9 _ 2 � 2

4

44

1

8. 3 1 0


10 _ 3 �

9. 4 1 3


13 _ 4 �

10. 5 2 8


28 _ 5 �

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Complete.

Example

3 1 _ 2 � 5 � 7

2 � 5

� 35

2

� 1

2 17

3 1 _ 2 � 7 _ 2

11. 4 2 _ 5 � 3 � � 3

�

�

12. 5 1 _ 3 � 4 � � 4

�

�

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Multiply. Express the product as a whole number or a mixed number in simplest form.

13. 2 8 _ 13 � 2 14. 8 � 2 4 _ 7

15. 9 � 4 3 _ 4 16. 7 2 _ 5 � 10

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Worksheet 5 Real-World Problems: Multiplying with Mixed Numbers

Solve. Show your work.

1. Juan has 8 rabbits. He wants to give 1 1 _ 4 carrots to each rabbit.

How many carrots does Juan need?

� �

Juan needs carrots.

2. Mr. Foster buys 7 boxes of cornfl akes. Each box weighs 13 1 _ 2 ounces.

Find the total weight of the cornfl akes.

1 1 _ 4 � 5 _ 4

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Solve. Show your work.

3. A rectangular envelope is 8 inches wide and 4 1 _ 3 inches long.

Find the area of the envelope.

Area of a rectangle� length � width

4. A carpenter bought 4 boxes of nails. Each box weighed 3 2 _ 5 pounds.

The price of the nails was $8 per pound. How much did the carpenter

pay for the nails?

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Worksheet 6 Dividing a Fraction by a Whole NumberEach whole is divided into parts. Each part is subdivided into smaller parts. Complete each model. Then complete the division sentence.

1 _ 3 is divided into

2 parts.

Example1 whole

13

16

1 _ 3 � 2 � 1 _ 6

1. 1 whole

� �

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Each whole is divided into parts. Each part is subdivided into smaller parts. Complete each model. Then complete the division sentence.

2. 1 whole

3. 1 whole

� �

� �

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Complete.

1 _ 3 � 1 _ 4 � 1 � 1 _ 3 � 4

� 1 _ 12

1 _ 4 � 3 � 1 _ 3 of 1 _ 4

� 1 _ 3 � 1 _ 4 � 1 _ 12

Example

4. 7 _ 8 � 5 � of 7 _ 8 5. 8 _ 9 � 4 � of

� �

�

� � 7 _ 8

�

6. 5 _ 12 � 8 � of

� �

�

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Divide. Express each quotient in simplest form.

2 _ 5 � 3 � 2 _ 5 � 1 _ 3

� 2 �1 _ 5 �3

� 2 _ 15

Example

Dividing by 3 is the same

as multiplying by 1 _ 3 .

7. 2 _ 3 � 6 8. 7 _ 8 � 9

9. 4 _ 9 � 8 10. 9 _ 11 � 3

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Worksheet 7 Real-World Problems: Multiplying and Dividing with Fractions


1. There are 144 fruits in a box. Of the fruits in the box, 1 _ 8 are red apples

and 1 _ 4 are green apples. The rest are oranges.

a. How many oranges are there altogether?

b. What fraction of the fruits are oranges?

2. A bakery had 54 buns. Of the buns that the bakery had, 1 _ 6 were sold

in the morning and 1 _ 2 were sold in the evening.

a. How many buns were sold altogether?

b. How many buns were not sold?

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3. Mr. Woods had $840. He spent 3 _ 7 of the money on a lawn mower.

He spent 1 _ 8 of the remaining money on a gift for his wife. How much

money did Mr. Woods have left?

4. Rebecca had a piece of ribbon. She used 3 _ 8 of it to tie a parcel.

She used 1 _ 5 of the remainder for a bookmark. Rebecca had

24 centimeters of ribbon left. What was the length of ribbon

Rebecca had at fi rst?

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Documents

C H A PTE 4 R Multiplying and Dividing Fractions and Mixed ... · PDF fileWorksheet 1 Multiplying Proper Fractions Look at the models. Follow the steps and ﬁ ll in the blanks. What