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Chapt
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Date:
er
Fractions and Mixed
Numbers
Practice 1
Adding Unlike Fractions
Find two equivalent fractions for each fraction.
Example
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2
3 4
6
6
9
1.
3
4 2.
2
5 3.
5
6 4.
1
7 Express each fraction in simplest form.
5.
6
8
6.
8
20 7.
10
15 8.
9
21 Lesson 3.1 Adding Unlike Fractions
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Rewrite each pair of unlike fractions as like fractions.
Example
1
4 1
4
9.
1
4 5
12 10.
1
10 2
5 11.
5
9 2
3 12.
3
8 9
16 Write equivalent fractions for each fraction. Then find the least
common denominator of the fractions.
Example
2
1
2 4
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2
3 3
4 The least common denominator
The least common denominator
6
.
1
4 is
15.
.
5
6 5
6 3
8 The least common denominator
The least common denominator
is
94
13.
4
2
3
6
is
14.
3
= 6
.
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2
4
1
2 is
.
Chapter 3 Fractions and Mixed Numbers
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Name:
Date:
Shade and label each model to show the fractions. Then complete the
addition sentence.
Example
1, 1
2 3
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1
2
16.
Find the multiples of 2 and 3.
Choose the least common multiple.
Use it to rewrite 12 and 13 as like
fractions.
1
3
1
1
2 3 3
6
5
6
2
6
1, 1
5 2
1
1
5 2
Lesson 3.1 Adding Unlike Fractions
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Shade and label each model to show the fractions. Then complete the
addition sentence.
1, 1
6 4
1
1
6 4 © 2009 Marshall Cavendish International (Singapore) Private Limited
17.
18.
1 2
5, 3
1
2
5 3 96
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:24 PM
Name:
Date:
Look at the model. Write two addition sentences.
11
12
19.
Addition sentence 1:
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12
20.
12
12
Addition sentence 2 (fractions in simplest form):
Add. Express each sum in simplest form.
21.
1
1
3 9
22.
5
2
8 4 23.
1
6
2 7
24.
4
1
8 5 Lesson 3.1 Adding Unlike Fractions
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Use benchmarks to estimate each sum.
Example
1
4
3 7
0
2
2
3 9
26.
7
1
3
9 7 5
98
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1
4
7
0
1 + 4 is about 1.
3 7
25.
1
2
1
2
1
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1 is about 1 .
3
2
4 is about 1 .
2
7
1 +4
3 7
1 + 1 =1
2 2
1
3
Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:24 PM
Name:
Date:
Practice 2 Subtracting Unlike Fractions
Rewrite the fractions as like fractions and complete the subtraction sentence.
Example
3
1
2
2
3
1
3
6
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3
1
2
1
3
2
6
What is the least
common multiple
of 2 and 3?
2
3
6
2
6
1
1
2 3
3
6
1
6
2
6
Lesson 3.2
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Subtracting Unlike Fractions
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Rewrite the fractions as like fractions and complete the subtraction sentence.
1.
1
3
1
4
1
4
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1
3
1
1
3 4
Subtract. Express each difference in simplest form.
2.
7
2
12 4 3.
4
1
5 3 4.
1
1 56 12
5.
7
1
9 6 100
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Chapter 3 Fractions and Mixed Numbers
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Name:
Date:
Use benchmarks to estimate each difference.
Example
4
5
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4
3
5 8
4 is about 1.
5
3
is about 1 .
8
2
4– 3
5 8
1– 1 = 1
2 2
4 – 3 is about 1 .
2
5 8
6.
9
1
10 6
7.
5
1
12 9
0
1
2
1
1
2
1
3
8
0
Lesson 3.2
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Subtracting Unlike Fractions
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Darren drew a model to find 45 21 . His model is drawn incorrectly.
Explain his mistakes. Then draw the correct model and find
the difference.
4
5
?
Darren’s model is wrong because:
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1
2
The correct model is:
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Chapter 3 Fractions and Mixed Numbers
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Name:
Date:
Practice 3
Fractions, Mixed Numbers, and
Division Expressions
Look at the diagram. Complete.
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Example
3
4
3
4
1.
Lesson 3.3 Fractions, Mixed Nu
mbers, and Division Expressions
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Write each division expression as a fraction.
2.
3.
3 10 5 7 4.
5.
2 11 4 9 Write each fraction as a division expression.
7
7
8 7.
8
1
10 6.
5
12 8.
6
7 Look at the diagram. Complete.
Example
4
3
4
3
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Example
1
1
3
Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:25 PM
Name:
Date:
Look at the diagram. Complete.
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9.
Complete.
10.
11.
35 11 7 4 1
3
Lesson 3.3 Fractions, Mixed Nu
mbers, and Division Expressions
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Divide. Express each quotient as a mixed number.
Example
12.
5 3 1
2
3
1
3 5
3
2
14.
9 4 2
18 5 3
Write each fraction in simplest form. Then divide to express each
quotient as a mixed number.
15.
106
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16.
18 4 22 6 © 2009 Marshall Cavendish International (Singapore) Private Limited
13.
7 2 3
Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:26 PM
Name:
Date:
Practice 4 Expressing Fractions, Division Expressions
and Mixed Numbers as Decimals
Write each fraction as a decimal.
Example
3
5
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2.
6
10
1.
13
20 0.6
19
25 3.
47
50 Express each division expression as a mixed number in simplest form
and as a decimal.
Division expression
4.
72
5.
94
6.
21 5
7.
101 25
Express division expression as
a mixed number
a decimal
Lesson 3.4 Expressing Fractions, D
ivision Expressions and Mixed Numbers as Decimals
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Express each improper fraction as a decimal.
Example
3
2
=2+ 1
8.
22
5
10.
32
25
2
2
=1+ 1
2
= 1 + 0.5
9.
47
20
Solve. Show your work.
11.
108
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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.
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= 1.5
Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:26 PM
Name:
Date:
Practice 5
Adding Mixed Numbers
Add. Express each sum in simplest form.
Example
3
5
1
2
8
4
3
5
2
8
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5
2
8
7
5
8
8
1.
1
1
4
2
1
2
3
4
1
2
3
1
4
2
3
2.
2
1
1
3
5
2
2
5
3
1
5
1
2
Lesson 3.5
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Adding Mixed Numbers
109
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Add. Express each sum in simplest form.
5
3 27 2 14
4.
7
5 12
3 14
5.
1
3
4 15
110
6.
12 19 9 56
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3.
Add. Express each sum in simplest form.
7.
145 2 13
1
2
3
4
110
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4
5
1
3
Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:26 PM
Name:
Date:
Add. Express each sum in simplest form.
8.
5
1 23
3 12
3
1
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4
5
5
12
2
3
9.
2 34 3 25
10.
2 59 156
11.
5
7 89 9 12
12.
7
5 12
134
Lesson 3.5
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Adding Mixed Numbers
111
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Use benchmarks to estimate each sum.
Example
3
5
5
3 is about 1 .
5
2
So, 6 3 is about 6 1 .
5
2
0
5
6
5 is about 1.
6
So, 4 5 is about 5.
6
0
63 + 4 5
5
6
6 1 + 5 = 11 1
2
2
6 3 + 4 5 is about 11 1 .
5
6
6
2
5
13.
9 7 7 12
14.
4 12 10 9
112
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7
1
1
2
1
2
1
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3
65 46
1
Chapter 3 Fractions and Mixed Numbers
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Name:
Date:
Practice 6 Subtracting Mixed Numbers
Subtract. Express each difference in simplest form.
Example
2
5
3 3 12
3
8
12
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3
5
12
3
12
1
3
2
3
4
1.
8
1
49 33
8
4 9 3
1
8
9
Lesson 3.6
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Subtracting Mixed Numbers
113
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Subtract. Express each difference in simplest form.
2.
3
7
3
2
12
8
3
2
1
3
5
1
1
9
2
4.
7
5
1
2
6
4
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3.
7
12
Subtract. Express each difference as a mixed number.
5.
3
7
1
18
4
3
1
7
8
1
4
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:26 PM
Name:
Date:
Subtract. Express each difference as a mixed number.
6.
5
1
3 5
3
12
5
3 5
12
© 2009 Marshall Cavendish International (Singapore) Private Limited
1
3
1
1
1
5
3
7.
4
9.
7 4 5 12
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1
11
3
5
3
8
6
8.
6
10.
83 44
1
3
Lesson 3.6
Subtracting Mixed Numbers
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Use benchmarks to estimate each difference.
Example
2
9
5
2
is about 0.
9
So, 7 2 is about 7.
9
0
72 6 5
12
1
1
762 2
7 2 6 5 is about 1 .
9
12
2
11.
12 2 8 7
12.
20 8 5 9
116
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5
12
1
3
1
1
2
1
5
12
5
is about 1 .
12
2
5
so, 6 is about 6 1 .
12
2
9
1
2
0
© 2009 Marshall Cavendish International (Singapore) Private Limited
2
7 9 6 12
Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:27 PM
Name:
Date:
Practice 7 Real-World Problems: Fractions and
Mixed Numbers
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Solve. Show your work.
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?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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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
3
first hour, quart of water collects. In the second hour,
8
1
quart of water collects. How much water collects in the
6
container in the two hours?
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© 2009 Marshall Cavendish International (Singapore) Private Limited
Solve. Show your work.
Chapter 3 Fractions and Mixed Numbers
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Name:
Date:
Solve. Show your work.
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6.
7.
8
3
Arnold buys pound of ground turkey. He uses pound of the
9
4
ground turkey to make meatballs. How many pounds of ground turkey
are left?
A snail is at the bottom of a well. In the first 10 minutes, the snail climbs
7
5
23 inches. In the next 10 minutes, it climbs 19 inches. How far is
12
6
the snail from the bottom of the well after 20 minutes?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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Solve. Show your work.
8.
Johnny is jogging along a track. He has already jogged 1
1
2
miles.
3
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He plans to jog a total of 3 miles. How many miles does
4
he have left to jog?
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:27 PM
Name:
Date:
Practice 8
Real-World Problems: Fractions and
Mixed Numbers
© 2009 Marshall Cavendish International (Singapore) Private Limited
Solve. Show your work.
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 each sheet into 3 equal-sized
rectangles. The rectangles are shared equally among 6 students.
How many rectangles does each student get?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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Solve. Show your work.
Mrs. Quirk buys 1 quart of milk. Michael drinks 2 quart of it.
7
1
Joel drinks quart of it. How many quarts of milk are left?
3
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3.
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:27 PM
Name:
Date:
Solve. Show your work.
4.
An organic farmer buys a piece of land. She plants tomatoes
on 5 of the land and green beans on 1 of the land.
9
12
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She plants potatoes on the remaining piece of land.
What fraction of the land does she plant with potatoes?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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123
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Solve. Show your work.
5.
A package contains three types of bagels, plain, wheat and sesame.
2
3
The weight of the plain bagels is 1 pounds. The weight of the wheat
5
6
bagels is 2 pounds. The total weight of the three types of bagels is
© 2009 Marshall Cavendish International (Singapore) Private Limited
5 pounds. What is the weight of the sesame bagels?
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:27 PM
Name:
Date:
Solve. Show your work.
6.
1
4
Reggie and Jay go for a walk every morning. Reggie walks 2 miles.
3
8
Jay walks 1 miles less than Reggie. What is the total distance
© 2009 Marshall Cavendish International (Singapore) Private Limited
they walk every morning?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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125
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Solve. Show your work.
7.
Alicia uses 3 gallon of paint to paint her room. Becca uses 4 gallon
4
5
© 2009 Marshall Cavendish International (Singapore) Private Limited
more than Alicia to paint her room. How many gallons of paint do they
use altogether?
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:27 PM
Name:
Date:
Solve. Show your work.
3
A monkey climbs 3 feet up a coconut tree that has a height
5
of 10 feet. It rests for a while and continues to climb another
2
4 feet up the tree. How many more feet must the monkey climb to
3
reach the top of the tree?
© 2009 Marshall Cavendish International (Singapore) Private Limited
8.
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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1
2
8
3 ?
2
1
to .
3
8
© 2009 Marshall Cavendish International (Singapore) Private Limited
Draw a model, and explain the steps you can use to add
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Chapter 3 Fractions and Mixed Numbers
1/12/09 6:24:27 PM
Name:
Date:
Put On Your Thinking Cap!
Challenging Practice
Solve. Show your work.
Tina, Troy and Nate had a total of 25 equal-sized square tiles to place over a square
grid. Tina used 8 of the square tiles. Troy used 1 of the square tiles. Shade the
25
5
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 of the
5
© 2009 Marshall Cavendish International (Singapore) Private Limited
square grid is not covered?
Chapter 3 Fractions an
d Mixed Numbers
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Put On Your Thinking Cap!
Problem Solving
Solve. Use a model to help you.
© 2009 Marshall Cavendish International (Singapore) Private Limited
Paul mixes cement with sand. He uses 3 3 kilograms of cement and 1 kilogram
4
2
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?
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Chapter 3 Fractions and Mixed Numbers
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