c h a pte 4 r multiplying and dividing fractions …...multiplying and dividing fractions and mixed...
TRANSCRIPT
![Page 1: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/1.jpg)
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
117Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
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
![Page 2: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/2.jpg)
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 .
118
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.1
MS_Reteach 5A_Ch04_117-142.indd 118 11/12/09 1:53:29 PM
![Page 3: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/3.jpg)
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 �
119Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 119 2/28/09 3:22:04 PM
![Page 4: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/4.jpg)
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 � �
� �
120
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.1
MS_Reteach 5A_Ch04_117-142.indd 120 11/12/09 1:53:45 PM
![Page 5: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/5.jpg)
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 � �
�
�
121Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 121 2/28/09 3:22:05 PM
![Page 6: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/6.jpg)
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
122
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.1
MS_Reteach 5A_Ch04_117-142.indd 122 11/12/09 1:55:17 PM
![Page 7: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/7.jpg)
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
123Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 123 10/14/09 9:13:40 AM
![Page 8: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/8.jpg)
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.
124
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.2
MS_Reteach 5A_Ch04_117-142.indd 124 11/12/09 1:55:25 PM
![Page 9: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/9.jpg)
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.
125Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 125 2/28/09 3:22:07 PM
![Page 10: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/10.jpg)
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.
126
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.2
MS_Reteach 5A_Ch04_117-142.indd 126 11/12/09 1:55:33 PM
![Page 11: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/11.jpg)
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?
127Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 127 11/12/09 1:55:47 PM
![Page 12: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/12.jpg)
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?
128
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.2
MS_Reteach 5A_Ch04_117-142.indd 128 11/12/09 1:56:01 PM
![Page 13: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/13.jpg)
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 � �
129Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 129 2/28/09 3:22:07 PM
![Page 14: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/14.jpg)
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
130
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.3
MS_Reteach 5A_Ch04_117-142.indd 130 11/12/09 1:56:13 PM
![Page 15: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/15.jpg)
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 � �
� �
�
� �
�
131Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 131 2/28/09 3:22:09 PM
![Page 16: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/16.jpg)
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 �
132
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.4
MS_Reteach 5A_Ch04_117-142.indd 132 11/12/09 1:56:22 PM
![Page 17: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/17.jpg)
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
�
�
133Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 133 2/28/09 3:22:10 PM
![Page 18: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/18.jpg)
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
134
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.4
MS_Reteach 5A_Ch04_117-142.indd 134 11/12/09 1:56:32 PM
![Page 19: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/19.jpg)
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
135Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 135 3/2/09 5:12:59 PM
![Page 20: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/20.jpg)
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?
136
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.5
MS_Reteach 5A_Ch04_117-142.indd 136 11/12/09 1:56:41 PM
![Page 21: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/21.jpg)
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
� �
137Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 137 2/28/09 3:22:11 PM
![Page 22: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/22.jpg)
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
� �
� �
138
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.6
MS_Reteach 5A_Ch04_117-142.indd 138 11/12/09 1:56:51 PM
![Page 23: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/23.jpg)
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
� �
�
139Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 139 2/28/09 3:22:12 PM
![Page 24: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/24.jpg)
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
140
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.6
MS_Reteach 5A_Ch04_117-142.indd 140 11/12/09 1:57:05 PM
![Page 25: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/25.jpg)
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?
141Reteach 5A
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
MS_Reteach 5A_Ch04_117-142.indd 141 2/28/09 3:22:13 PM
![Page 26: C H A PTE 4 R Multiplying and Dividing Fractions …...Multiplying and Dividing Fractions and Mixed Numbers C H A P T E 4 R MS_Reteach 5A_Ch04_117-142.indd 117 2/28/09 3:22:04 PM Look](https://reader035.vdocument.in/reader035/viewer/2022081613/5fb610bdee491424bb1302d4/html5/thumbnails/26.jpg)
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?
142
© 2
009
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
riva
te L
imite
d. C
opyi
ng is
per
mitt
ed; s
ee p
age
ii.
Name: Date:
Chapter 4 Lesson 4.7
MS_Reteach 5A_Ch04_117-142.indd 142 11/18/09 10:56:23 AM