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Chapt
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Date:
er
Multiplying and Dividing
Fractions and Mixed Numbers
Practice 1
Multiplying Proper Fractions
Complete.
1.
?

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3
4
1
3
2 of 4 Multiply. Express the product in simplest form.
2.
3
1
8 2 3.
5
7
12 8 Lesson 4.1 Multiplying Proper Fractions
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Multiply. Express the product in simplest form.
4.
2
7
11 12 5.
3
4
8 9 Complete. Express the product in simplest form.
7.
1
5
3 of 8 2
9
7 of 11 8.
9.
2
7
5 of 10 1
1
3
8
4 of 9 140
1
1
1
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6.
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Practice 2
Real-World Problems: Multiplying
with Proper Fractions
Solve. Draw models to help you.
1.
Lena has some eggs in the refrigerator. She takes out 35 of the eggs to make waffles
and scrambled eggs. She uses 23 of the eggs she took out to make waffles.
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What fraction of the total number of eggs does Lena use to make waffles?
2.
Dawn has 56 yard of lace. She uses 45 of it for a dress and the rest for
a jewel box. How much lace does she use for the jewel box?
Lesson 4.2 Real-World Problems: Multiplying with Proper Fractions
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3.
Tasha finished a job in 34 hour. Megan finished it in 45 of the time
Tasha took. How long did Megan take to finish the job?
4.
Lily has a bottle containing 78 quart of milk. She pours 45 of it into
a bowl. What amount of milk does she pour into the bowl?
5.
Raoul ran 34 mile in a race. Eduardo ran 27 of the distance that
Raoul ran. What distance did Eduardo run?
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Solve. Show your work.
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Name:
Date:
Solve. Draw models to help you.
6.
Jenny spends 16 of her paycheck and saves 25 of the remaining amount.
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What fraction of her total paycheck is saved?
Lesson 4.2 Real-World Problems: Multiplying with Proper Fractions
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Solve. Draw models to help you.
7.
In Rod’s family, 34 of the members wear glasses. Of those who do not
wear glasses, 13 are male. What fraction of the family are males who
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do not wear glasses?
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Name:
Date:
Solve. Draw models to help you.
8.
Ned folded a set of origami figures. Of this set, 58 are cranes
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and 16 of the remainder are frogs. The rest are grasshoppers.
What fraction of the origami figures are grasshoppers?
Lesson 4.2 Real-World Problems: Multiplying with Proper Fractions
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9.
5
are
In a garden, 23 of the flowers are roses. Of the roses in the garden, 12
yellow and the rest are red. What fraction of the flowers are red roses?
10.
Karen collects local and foreign coins. Of the coins in her collection,
1
2
4 are foreign coins. Of the foreign coins, 5 are from Mexico.
What fraction of the collection are foreign coins that are not from Mexico?
146
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Solve. Show your work.
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Date:
Practice 3
Multiplying Improper Fractions
by Fractions
Complete.
1.
3
1
2 2 © Marshall Cavendish International (Singapore) Private Limited.
2.
8
1
3 4 Find the product.
3.
11 1 3
2
Lesson 4.3 Multiplying Improper Fractions by Fractions
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Multiply. Express the product in simplest form.
Example
4
7
5 6
Method 1
Method 2
4 × 7 = 4÷2 × 7
5 6
5
6÷2
4 × 7 = 4×7
5 6 5×6
= 2 × 7
= 28
= 2×7
= 28 ÷ 2
30
3
30 ÷ 2
= 14
15
5×3
= 14
15
4.
7
1
4 3 5.
9
2
8 7 6.
8
3
3 10 7.
15 3 9
20
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5
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Name:
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Multiply. Express the product as a whole number or a mixed number
in simplest form.
Example
2
15
5 4
Method 1
Method 2
2 × 15 = 2 ÷ 2 × 15
5
4
5
4÷2
2 × 15 = 2 × 15
5
4
5×4
=
= 30
1 × 15 ÷ 5
5÷5
2
20
= 1×3
=3
=3
=11
2
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1×2
2
2
=11
2
8.
3
8
46
9.
16 21 7
2
10.
15
8
12 5 11.
32 36 9
8
Lesson 4.3 Multiplying Improper Fractions by Fractions
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12.
7
6
8 5 13.
11 28 12
3
14.
21
15
5 6 15.
25 18 4
10
16.
30
7
9 2 17.
14 5 3
8
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Multiply. Express the product as a whole number or a mixed number
in simplest form.
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Practice 4
Multiplying Mixed Numbers and
Whole Numbers
Complete.
1.
1
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12 2
1
12
2 2.
1
23 6
1
23
6 Lesson 4.4 Multiplying Mixed Numbers and Whole Numbers
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Multiply. Express the product as a whole number or a
mixed number in simplest form.
Example
9 2 13
9×2 1 =9× 7
3
3
= 9×7
3
= 63
3
3.
4 15 15 4.
2 37 28 5.
24 1 56 6.
4 12 18 152
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= 21
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Name:
Date:
Multiply. Express the product as a whole number or a
mixed number in simplest form.
7.
2 34 16 8.
32 3 18 Multiply. Express the product as a whole number or a
mixed number in simplest form.
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Example
6 2 15
6 × 2 1 = 6 × 11
5
5
= 66
5
= 65 + 1
5
5
= 13 + 1
5
= 13 1
5
9.
4 2 79 10.
5 2 37 Lesson 4.4 Multiplying Mixed Numbers and Whole Numbers
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Multiply. Express the product as a whole number or a mixed number
in simplest form.
2 14 7 12.
1 45 12 13.
12 2 38 14.
26 1 16 © Marshall Cavendish International (Singapore) Private Limited.
11.
Answer each question.
15.
Is the product of 6 and 10 greater than or less than each of its factors?
Explain your reasoning.
16.
Is the product of 25 and 5 greater than or less than 25 ? Is it greater than or less
than 5? Explain your reasoning.
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Practice 5
Real-World Problems: Multiplying
Mixed Numbers
Solve. Show your work.
1.
At a party, there are 8 guests. Each guest eats 2 14 oranges.
How many oranges do the 8 guests eat?
1 guest → 2 14 oranges
8 guests →
oranges
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The 8 guests eat a total of
2.
oranges.
One pound of chicken costs $3. Jim buys 8 23 pounds of chicken.
How much does Jim pay for the chicken?
3.
Nolan practices the piano for 1 25 hours every Saturday and Sunday.
How long does he practice each weekend? Express your answer in hours and
minutes.
Lesson 4.5 Real-World Problems: Multiplying Mixed Numbers
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Solve. Show your work.
4.
7
yards long.
Sue buys 5 pieces of fabric. Each piece of fabric is 1 10
a. What is the total length of the fabric she buys?
5.
Angela works 1 12 hours a day and is paid $7 per hour. She works
5 days a week. How much does Angela earn in 7 weeks?
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b. One yard of the fabric costs $5. How much does she pay for all
5 pieces of fabric?
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Name:
Date:
Practice 6
Dividing Fractions and
Whole Numbers
Shade parts of the model to show the division expression.
Then complete.
Example
1
3 2
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1
3
1
is shaded.
6
1 2
3
1.
1
6
1
6 3
is shaded.
1 3 6
Lesson 4.6 Dividing Fractions and Whole Numbers
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2.
4
5 2 3.
6
7 3 4.
3
4 2 5.
2
5 3 Divide. Express each quotient in simplest form.
6.
4
5 7 7.
5
8 9 8.
8
9 4 9.
10
11 5 158
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Divide. Draw models to help you.
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Name:
Date:
Divide. Draw models to help you.
Example
3 15
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
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So, 3 ÷ 1 = 3 × 5
5
= 15
10.
1 14 12.
5 18 13.
9 16 11.
3 13 Lesson 4.6 Dividing Fractions and Whole Numbers
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14.
Mr. Chagall’s garden covers 25 of an acre of land. He divides the land into
4 equal sections. What fraction of an acre is each section of the garden?
15.
Gordon pours 49 quart of milk from a pitcher equally into 4 mugs.
a. Find the amount of milk in each mug.
b. Find the amount of milk in 3 mugs.
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Solve. Show your work.
umbers
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Name:
Date:
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Solve. Show your work.
16.
Calvin buys 3 pound of ground beef. He divides the beef into
5
6 equal portions.
a. Find the weight of 1 portion of beef.
b. Find the weight of 4 portions of beef.
17.
Devon buys a plot of land with an area of 5 square kilometer.
6
He divides the land equally into 4 smaller plots. What is the
total area of 3 of the smaller plots of land?
Lesson 4.6 Dividing Fractions and Whole Numbers
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18.
Sandra has a 5-foot length of canvas. She cuts the canvas into pieces that are
1 feet long. How many pieces will she have?
4
19.
Aidan uses 14 of the water in a bucket to water 1 potted plant. How many potted
plants can Aidan water with 3 full buckets of water?
20.
Mrs. Carter needs 12 meter of cloth to make a pillowcase. How many pillowcases
can she make with 5 meters of cloth?
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Solve. Show your work.
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Name:
Date:
Practice 7
Real-World Problems: Multiplying
and Dividing with Fractions
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Solve. Draw models to help you.
1.
Evan typed 72 pages of notes one day. He typed 12 of the pages
in the morning and 13 of the pages in the afternoon. He typed the rest
of the pages in the evening. How many pages of notes did he type
in the morning and afternoon?
2.
Last Saturday, Jay spent 6 hours playing games, studying and talking
with his friends. He spent 25 of the time playing games and 12 of
the time studying. How many minutes did he spend talking with his friends?
Lesson 4.7 Real-World Problems: Multiplying and
Dividing with Fractions
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Solve. Draw models to help you.
Joanne earns $720 a week. She spends 1 of her money on groceries
3
and household goods and 3 of the remaining money on rent. How much
4
money does she spend on rent, groceries and household goods?
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3.
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Name:
Date:
Solve. Draw models to help you.
4.
During a triathlon, Sharon swims 1 of the total route and cycles
4
3 of the remaining route. She runs the rest of the route. If she runs
5
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3,600 meters, find the total distance of the triathlon route.
Lesson 4.7 Real-World Problems: Multiplying and
Dividing with Fractions
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Solve. Show your work.
Victoria has a 2-pound package of flour. She uses 2 of the flour to
5
make a pizza. She then uses 3 of the remaining flour to make bread.
10
Find the weight of the package of flour that she has left.
Express your answer as a decimal.
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5.
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Name:
Date:
Solve. Show your work.
6.
Karen collects 6 quart of rainwater. She uses 1 of the water to
7
2
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clean her bicycle and uses the remaining water equally for 3 houseplants.
What volume of water does she use for each houseplant?
7.
Ricardo spends 8 hour reading the newspaper. He spends 1 of the
9
4
time reading the world news and splits the remaining time equally
between the sports news and the comics. How much time does he
spend reading the comics?
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Dividing with Fractions
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8.
A square foot of wall space needs 18 quart of paint. Terrence has 7 quarts
of paint, but uses 2 quarts to paint a pipe. How many square feet of wall
can he paint with the rest of the paint?
9.
Mary spends 16 hour to make a friendship bracelet. She spends 3 hours
before lunch and 2 hours after lunch making the bracelets. How many
bracelets does she make in all?
10.
Clayton wants to be a musician. After school one afternoon, he spends half his
time practicing his drums and 34 of the remaining time on homework and dinner.
He spends the remaining 34 hour talking with and texting his friends. How long did
he practice the drums?
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Solve. Show your work.
umbers
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Name:
Julia spends 59 of her vacation at summer camp. She spends 34 of the
remaining time at her grandparent's home. The remaining 7 days she spends at
the seashore with her family. How many days of summer vacation does she get
each summer.
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11.
Date:
Lesson 4.7 Real-World Problems: Multiplying and
Dividing with Fractions
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Rachel drew a model to solve this problem:
Earl pours 1 of a bottle of juice into his glass. Roberto pours 1 of the
3
3
remainder into his glass. What fraction of the bottle of juice is left?
Roberto
1 13 13 13
1
3 of the bottle of juice is left.
Did Rachel solve the problem correctly? Explain.
170
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Earl
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Date:
Put On Your Thinking Cap!
Challenging Practice
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An art teacher has a box of markers. She keeps half of the markers in the
box and gives 1 of the other half to group A. The remaining markers
3
were shared equally among the 8 students in group B. What fraction of
the whole box does each of the students in group B get?
Chapter 4 Multiplying and Dividing Fractions and Mixed Numbers
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Put On Your Thinking Cap!
Problem Solving
Mimi’s Market sold 24 heads of lettuce one morning. That afternoon
2
of the remaining heads of lettuce were sold. The number of heads
7
left was now 1 of the number the market had at the beginning of
2
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the day. How many heads of lettuce were there at the beginning of the day?
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