C H A PTE 4 R Multiplying and Dividing Fractions and Mixed ... · PDF fileWorksheet 1...
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Transcript of C H A PTE 4 R Multiplying and Dividing Fractions and Mixed ... · PDF fileWorksheet 1...
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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Name: Date:
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.
Step 2 Draw stripes over 1 _ 4 of the shaded portion.
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
MS_Reteach 5A_Ch04_117-142.indd 118 11/12/09 1:53:29 PM
2. What is the value of 3 _ 4 of 2 _ 3 ?
Step 1 A rectangle is divided into thirds. Shade 2 _ 3 of it.
Step 2 Draw stripes over 3 _ 4 of the shaded portion.
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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MS_Reteach 5A_Ch04_117-142.indd 119 2/28/09 3:22:04 PM
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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Chapter 4 Lesson 4.1
MS_Reteach 5A_Ch04_117-142.indd 120 11/12/09 1:53:45 PM
Multiply. Express each product in simplest form.
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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MS_Reteach 5A_Ch04_117-142.indd 121 2/28/09 3:22:05 PM
Multiply. Express each product in simplest form.
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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Chapter 4 Lesson 4.1
MS_Reteach 5A_Ch04_117-142.indd 122 11/12/09 1:55:17 PM
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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MS_Reteach 5A_Ch04_117-142.indd 123 10/14/09 9:13:40 AM
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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Chapter 4 Lesson 4.2
MS_Reteach 5A_Ch04_117-142.indd 124 11/12/09 1:55:25 PM
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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MS_Reteach 5A_Ch04_117-142.indd 125 2/28/09 3:22:07 PM
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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Chapter 4 Lesson 4.2
MS_Reteach 5A_Ch04_117-142.indd 126 11/12/09 1:55:33 PM
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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MS_Reteach 5A_Ch04_117-142.indd 127 11/12/09 1:55:47 PM
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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Chapter 4 Lesson 4.2
MS_Reteach 5A_Ch04_117-142.indd 128 11/12/09 1:56:01 PM
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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MS_Reteach 5A_Ch04_117-142.indd 129 2/28/09 3:22:07 PM
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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Chapter 4 Lesson 4.3
MS_Reteach 5A_Ch04_117-142.indd 130 11/12/09 1:56:13 PM
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
Quotient � Remainder �
10 _ 3 �
9. 4 1 3
Quotient � Remainder �
13 _ 4 �
10. 5 2 8
Quotient � Remainder �
28 _ 5 �
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Chapter 4 Lesson 4.4
MS_Reteach 5A_Ch04_117-142.indd 132 11/12/09 1:56:22 PM
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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Chapter 4 Lesson 4.4
MS_Reteach 5A_Ch04_117-142.indd 134 11/12/09 1:56:32 PM
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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MS_Reteach 5A_Ch04_117-142.indd 135 3/2/09 5:12:59 PM
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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Chapter 4 Lesson 4.5
MS_Reteach 5A_Ch04_117-142.indd 136 11/12/09 1:56:41 PM
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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Chapter 4 Lesson 4.6
MS_Reteach 5A_Ch04_117-142.indd 138 11/12/09 1:56:51 PM
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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Chapter 4 Lesson 4.6
MS_Reteach 5A_Ch04_117-142.indd 140 11/12/09 1:57:05 PM
Worksheet 7 Real-World Problems: Multiplying and Dividing with Fractions
Solve. Use models to help you.
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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MS_Reteach 5A_Ch04_117-142.indd 141 2/28/09 3:22:13 PM
Solve. Use models to help you.
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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Chapter 4 Lesson 4.7
MS_Reteach 5A_Ch04_117-142.indd 142 11/18/09 10:56:23 AM