Date:
P
H A TE
R
C
Name:
6
Fractions and Mixed Numbers
Worksheet 1
Adding Fractions
Find the equivalent fraction. Shade the models.
Example
2
_
3
?
6
2
—
—
3
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9
1.
1
_
2
?
1 —
—
2
2.
3
—
5
?
3 —
—
5
Reteach 4A
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Date:
Find the equivalent fractions.
Example
5
1
5
5
25
To get the equivalent fraction,
multiply both the numerator and the
denominator by the same number.
5
5
4.
7
9
9
12
3
5.
6.
16
24
4
140
2
3
12
18
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3
3.
Chapter 6 Lesson 6.1
MS_Reteach 4A_Ch06_139-194.indd 140
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Name:
Date:
Find the equivalent fractions. Complete the model by shading the
correct number of parts. Then add the fractions.
Example
1
2
_
_
9
3
?
Step 1
1
Change the denominator of _
to 9.
3
3
1
_
—
3
9
3
1
3
3
9
3
Add the like fractions.
Step 2
5
9
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1
2
_
_
9
3
3
9
7.
3
2
_
—
9 9
5
_
9
2
9
3
1
_
_
4
8
1
4
1
_
4
2
3
3
1
_
_
_
4
8
8
Reteach 4A
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Name:
8.
Date:
1
1
_
_
12
3
1
3
1
_
3
1
1
_
_
12
3
Example
3
3
1
2
_
_
_
?
9
9
3
1
_
3
1
3
3
—
9
3
9
3
9
3
2
9
8
9
142
3
9
3
1
2
—
—
—
9
9
3
3
—
9
3
2
—
—
9
9
8
—
9
3
8
1
2
_
_
—
So, _
.
9
9
9
3
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Complete the models. Then add the fractions.
Chapter 6 Lesson 6.1
MS_Reteach 4A_Ch06_139-194.indd 142
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Name:
9.
Date:
3
1
1
_
_
_
2
8
8
4
1
2
1
_
2
4
1
8
3
8
3
1
1
1
—
—
—
—
2
8
8
8
3
—
8
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10.
5
1
1
_
_
_
4
12
12
1
_
4
5
1
1
—
—
—
4
12
12
Reteach 4A
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Name:
Date:
Express each fraction in simplest form.
Example
8
3
4
24
32
To simplify a fraction, divide
both the numerator and the
denominator by the same number.
8
3
24
_
—
32
11.
12
_
_
34
12.
18
_
_
42
13.
21
_
_
63
144
A fraction is in its simplest form
when the numerator and the
denominator cannot both be
divided by the same number.
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4
Chapter 6 Lesson 6.1
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Name:
Date:
Add. Express each answer in simplest form.
Example
2
1
_
_
?
5
5
To add like fractions,
add the numerators.
2
5
1
5
3
2
1
So, _
_
—.
5
5
5
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?
14.
2
7
3
2
_
_
_
7
7
3
7
?
15.
2
4
_
_
_
9
9
2
9
4
9
?
_
16.
5
7
_
_
_
12
12
Reteach 4A
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Name:
17.
Date:
3
2
1
_
_
_
5
10
10
3
_
10
1
_
10
2
5
1
4
5
1
1
_
_
_
4
6
12
146
5
_
12
1
6
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18.
Chapter 6 Lesson 6.1
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Name:
Date:
Worksheet 2
Subtracting Fractions
Find the equivalent fraction. Complete the model by shading the
correct number of parts.
Example
2
3
6
2
_
—
⫽
3
9
6
9
3
4
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1.
3
_
—
⫽
4
2
5
2.
2
—
⫽_
5
Reteach 4A
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Date:
Subtract. Express each answer in simplest form.
Example
3
5
_
_
6
6
1
—
3
2
—
6
3
6
?
5
6
3
8
3.
3
5
_
_
8
8
?
5
8
7
10
4.
9
7
_
_
10
10
?
9
10
5.
148
4
7
_
_
12
12
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To subtract like fractions,
subtract the numerators.
Chapter 6 Lesson 6.2
MS_Reteach 4A_Ch06_139-194.indd 148
11/5/09 2:51:06 PM
Name:
Date:
Complete the models by shading the correct number of parts.
Then subtract the fractions.
Example
3
7
_
_
4
8
Step 1
?
2
3
Change the denominator of _
to 8,
4
3
4
7
.
so that it has the same denominator as _
8
Step 2
2
Subtract the like fractions.
6
3
1
7
7
—
—
—
—
—
4
8
8
8
8
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1
8
6
8
3
7
1
_
—
.
So, _
4
8
8
6.
6
8
7
8
3
11
_
_
4
12
3
_
4
3
11
11
_
_
_
4
12
12
11
12
Reteach 4A
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Name:
7.
Date:
5
1_
9
1
5
1_
9
5
_
9
Find the equivalent fractions. Then subtract.
Example
?
7
2
7
_
_
_
9
9
3
3
6
9
2
3
3
1
—
9
7
2
1
_
_
So, _
.
9
9
3
10
8.
7
1_
10
7
_
10
1
1
10
150
6
9
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7
2
_
_
9
3
Chapter 6 Lesson 6.2
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Name:
9.
Date:
1
7
7
_
_
_
4
12
12
1
4
1
6
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10.
1
11
11
_
_
_
6
12
12
Reteach 4A
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Date:
Complete the models. Then subtract.
Example
2
1
_
1_
?
9
3
3
1
3
2
1
—
1—
9
3
2
9
3
9
4
9
3
9
3
2
3 —
9 —
4
—
—
9
9
9
9
9
9
2
1
4
So, 1 _
_
—
.
9
9
3
4
1
1_
_
4
12
1
4
4
1
—
1—
4
12
12.
4
—
12
3
2
_
1_
5
10
3
5
3
2
—
1—
5
10
152
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11.
Chapter 6 Lesson 6.2
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Name:
Date:
Find each difference. Express your answer in simplest form.
Example
2
1
_
1_
?
9
3
2
1
1_
_
9
3
9
—
9
2
—
9
3
3
—
9
1
3
3
9
3
4
—
9
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2
1
4
_
_
.
So, 1 _
9
9
3
13.
2
17
17
_
_
_
21
3
21
2
3
Reteach 4A
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Name:
14.
Date:
5
1
1_
_
4
12
5
_
12
1
4
1
4
15.
3
1
1_
_
4
20
154
3
_
20
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Chapter 6 Lesson 6.2
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Name:
Date:
Worksheet 3
Mixed Numbers
Shade the model to show each mixed number.
Example
1
2_
?
3
1 whole
When you add a whole number
and a fraction, you get a mixed
1
is a mixed number.
number. 2—
3
1
So, 2 _
3
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1
3
1 whole
2—1
3
.
1.
1 whole
3
8
3
1_
8
2.
1 whole
1 whole
3
_
5
3
2_
5
Reteach 4A
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Date:
Find the mixed number that describes each model.
Example
1 whole
1 whole
4 2 —
9
4 ninths
4
2—
9
3.
1 whole
1 whole
1 whole
3 fifths
1 whole
1 whole
7 twelfths
Write each mixed number on the number line.
Example
1
1_
2
0
156
1 12
1
2
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4.
Chapter 6 Lesson 6.3
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11/5/09 9:22:21 AM
Name:
Date:
1
1_
3
5.
6.
0
1
2
2_
3
2
3_
3
7.
2
3
4
Express each mixed number in simplest form.
Example
2
1_
?
4
Method 1
Draw models.
Method 2
Divide the numerator and the
denominator by the same number.
2
4
2
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2
4
1
2
2
1
2
2
1
So, 1_
1_
.
4
2
8.
3
2_
12
2
1
So, 1_
1_
.
4
2
9.
6
3_
8
Reteach 4A
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Name:
Date:
Find the number of wholes and parts that are shaded. Then write each
sum as a mixed number in simplest form.
Example
2 2 —
4
2 2—1
2—
4
2
10.
11.
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1
158
Chapter 6 Lesson 6.3
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Name:
Date:
Worksheet 4
Improper Fractions
Write each description as a fraction.
Example
1 third —1
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3
1.
3 quarters 2.
4 fifths 3.
5 sixths 4.
6 eighths 5.
7 tenths Express each mixed number as an improper fraction.
Example
2
1_
?
3
An improper
fraction is equal to
or greater than 1.
1 whole 3 thirds
There are 5
2
thirds in 1_
.
3
2
_
3
2 thirds
5
_
is an improper
3
fraction.
2
5
1 _
1 _
1 _
1 _
1 _
1_
_
3
3
3
3
3
3
3
5
2
_
.
So, 1_
3
3
Reteach 4A
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Name:
1
2_
2
2 wholes 7.
3
1_
4
1 whole 3
1_
4
3
_
4
quarters
quarters
3
quarters in 1_
.
4
There are
160
half
1
halves in 2_
.
2
There are
1
2_
2
1
_
2
halves
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6.
Date:
Chapter 6 Lesson 6.4
MS_Reteach 4A_Ch06_139-194.indd 160
11/5/09 9:23:54 AM
Name:
Date:
Express each mixed number as an improper fraction.
Use the models to help you.
Example
1
How many thirds are there in 2_
?
3
There are 7
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1
2_
7
3
8.
1
thirds in 2_
.
3
7
thirds —
3
5
How many sixths are there in 1_
?
6
There are
5
1_
6
9.
5
sixths in 1_
.
6
sixths 5
How many eighths are there in 3_
?
8
There are
5
3_
8
5
eighths in 3_
.
8
eighths Reteach 4A
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3/9/09 6:04:02 PM
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Date:
Express each improper fraction in simplest form.
Example
6
_
4
?
Method 1
Simplify the fractions shown by the shaded parts.
3
_
2
6
_
4
Method 2
Divide the numerator and the denominator by the
same number.
2
6
4
3
2
2
3
6
_
.
So, _
4
10.
12
_
8
11.
24
_
15
12.
30
_
8
13.
48
_
36
162
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2
Chapter 6 Lesson 6.4
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Name:
Date:
Write each fraction on the number line.
Example
3
_
8
3
8
0
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14.
3
_
4
15.
0
1
4
8
7
_
8
4
8
16.
1
_
2
1
3
_
—
8
4
1
—
_
8
2
Reteach 4A
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Name:
Date:
Write the missing improper fraction in each box.
Example
0
0
1 13 1 23
1
1
3
2
3
4
3
3
3
5
3
2
6
3
2 13 2 23
8
3
7
3
3
9
3
3
1 3 thirds —
3
2
2
1—
1—
3
3
3
2
—
—
3
3
17.
0
0
18.
1
2
4
5
4
2 34
2
7
4
8
4
3
10
4
1 2 3 4 5 6 7
1 18 18 18 18 18 18 18 2
0
0
164
1 24
4
8
8
8
11
8
14
8
16
8
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5
—
3
Chapter 6 Lesson 6.4
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11/5/09 9:24:33 AM
Name:
Date:
Worksheet 5
Renaming Improper Fractions
and Mixed Numbers
Complete each statement.
Example
3 thirds is
1
whole.
1.
2.
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4 quarters is
5 fifths is
whole.
3.
whole.
4.
sixths is 1 whole.
sevenths is 1 whole.
5.
eighths is 1 whole.
Reteach 4A
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Date:
Rename each improper fraction as a mixed number.
Use models to help you.
Example
7
_
?
3
7
_
3
7 thirds
6 thirds 1 third
1
6
1
—
—
3 2—
3
3
6.
14
_
5
fifths
fifths 166
7.
fifths
23
_
6
sixths
sixths sixths
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7
1
—
2
.
So, —
3
3
Chapter 6 Lesson 6.5
MS_Reteach 4A_Ch06_139-194.indd 166
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Name:
Date:
Use the division rule to rename each improper fraction as a mixed number.
Example
12
_
5
?
Division Rule:
Divide the numerator by the denominator.
12 5 2 R 2
2
5) 1
2
1
0
2
12
There are 2 wholes and 2 fifths in _
.
5
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12
So, _
5
8.
2
2_
5
.
8
_
3
9.
3) 8
37
_
7
7) 3 7
There are
wholes and
wholes and
37
sevenths in _
.
7
8
thirds in _
.
3
8
So, _
3
There are
.
37
So, _
7
.
Reteach 4A
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Name:
Date:
Rename the improper fraction as a mixed number in simplest form.
Then check your answer using the division rule.
Example
45
_
?
6
45
_
45 sixths 6
42 sixths 3 sixths
3
42 —
—
6
6
3
7 —
Check
7
7 —1 2
7—1
2
6)4
4
3
45
1
So, _
7—
.
6
2
10.
26
_
4
5
2
quarters quarters 45 6 7 R 3
45
_
6
3
7_
7—1
6
2
quarters
Check
26 4 4) 2 6
26
_
4
168
R
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6
Chapter 6 Lesson 6.5
MS_Reteach 4A_Ch06_139-194.indd 168
11/5/09 9:26:08 AM
Name:
11.
Date:
48
_
9
ninths
ninths ninths
Check
48 9 © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii.
R
9) 4 8
48
_
9
Reteach 4A
MS_Reteach 4A_Ch06_139-194.indd 169
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3/9/09 6:04:06 PM
Name:
Date:
Use the multiplication rule to rename each mixed number as an
improper fraction.
Example
1
2_
?
6
6
1
1
2_
2_
6
6
1
13
12 _
—
—
6
6
6
2
1
Multiplication Rule
12
6
6
13
1
So, 2_
—
.
6
6
1
1
4—
4_
3
3
1
_
3
3
4
1
3
13.
2
6_
6
5
170
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12.
Chapter 6 Lesson 6.5
MS_Reteach 4A_Ch06_139-194.indd 170
11/5/09 9:26:32 AM
Name:
Date:
Rename each mixed number as an improper fraction in simplest form.
Check your answer.
Example
3
2_
?
4
Check
3
3
2 —
2_
4
Step 1
4
Multiply the whole number
by the denominator.
2 4 8
3
8 —
—
4
4
Step 2
Add the product to the
numerator.
8 3 11
3
There are 11 quarters in 2_
.
4
11
—
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4
3
11
—
So, 2_
.
4
4
14.
Check
1
5—
5
2
5
There are
1
halves in 5_
.
2
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Name:
15.
Date:
5
7_
⫽
6
⫹
Check
7⫻
⫽
⫹
⫽
⫹
There are
⫽
5
sixths in 7_
.
6
⫽
8
8_
⫽
9
⫽
⫹
⫹
Check
⫻
⫽
⫹
⫽
There are
⫽
172
8
ninths in 8_
.
9
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16.
Chapter 6 Lesson 6.5
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Name:
Date:
Worksheet 6
Renaming Whole Numbers when Adding
and Subtracting Fractions
Add. Express each answer as a mixed number in simplest form.
Example
3
3
_
_
?
4
4
3
3
_
_
4
4
6
—
4
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2
4 —
—
4
4
1
2
—
2
1—
4
6
_
4
4
_
4
2
_
4
4
2
1—1
2
3
1
3
So, _
—
1—
.
4
2
4
2
4
1
2
2
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1.
Date:
3
4
_
_
5
5
2.
7
11
_
_
12
12
5
_
5
1
174
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Name:
Chapter 6 Lesson 6.6
MS_Reteach 4A_Ch06_139-194.indd 174
11/5/09 9:27:14 AM
Name:
Date:
Find the equivalent fraction. Then add. Express each answer
in simplest form.
Example
7
2
_
_
?
12
3
7
2
_
_
8 —
7
—
12
3
12
12
3
15
—
15
12
12
5
4
3
5 —
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4
1—1
4
7
1
2
_
—
So, _
1
.
4
12
3
3.
7
4
_
_
10
5
4.
8
1
_
_
9
3
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Name:
Date:
Find the sum. Express each answer in simplest form.
Example
5
4
2
_
_
_
?
9
9
3
5
4
2
_
_
_
9
9
3
6 —
9
5
—
9
4
—
9
15
—
9
2
5
1—
—
3
3
5.
7
11
2
_
_
_
12
12
3
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5
4
2
2
_
_
—
So, _
1
.
9
9
3
3
176
Chapter 6 Lesson 6.6
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11/5/09 9:27:26 AM
Name:
Date:
3
7
_
1_
4
12
6.
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Express each whole number as a mixed number.
Example
2
1
3
_
3
7.
3 2_
8
8.
4
_
12
9.
5
2 1_
10.
5
4
_
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Name:
Date:
Subtract each fraction from a whole number to get a mixed number.
Example
3
2_
?
4
Method 1
211
4
1—
4
1—1
3
—
4
4
4
1_
1_
4
4
4
4
Method 2
2
3
3
8 —
2_
—
4
8
4
4
2_
_
_
or 2 1
4
4
4
4
4
4
5
—
4
1—1
4
3
1
So, 2 _
1—
.
4
4
11.
3
1_
8
178
8
4
12.
5
3_
12
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3
2_
4
Chapter 6 Lesson 6.6
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11/5/09 2:11:40 PM
Name:
Date:
5
3_
9
13.
14.
2
4_
3
Subtract. Express your answer in simplest form.
Example
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5
2
_
_
?
9
3
3
5
2
_
_
9
3
6 —
9
—1
5
—
9
2
3
6
9
3
9
5
1
2
_
—
So, _
.
9
9
3
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Name:
15.
Date:
7
3
_
_
12
4
3
3
4
3
2
5
6
17.
3
4
_
_
10
5
180
4
5
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16.
5
5
_
_
12
6
Chapter 6 Lesson 6.6
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11/5/09 9:29:18 AM
Name:
Date:
Worksheet 7
Fraction of a Set
Find the fraction of each set.
Example
1
_
of 12 ?
3
12 pretzels are divided into 3 equal groups.
1
_
of 12 means 1 of the 3 groups of pretzels.
3
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3 groups of pretzels
1 group of pretzels
1
of 12 is
So, _
3
1.
4
12 pretzels
4 pretzels
.
1
_
of 8 4
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Date:
2.
2
_
of 24 ⫽
3
3.
3
_
of 28 ⫽
4
4.
5
_
of 27 ⫽
9
5.
3
_
of 48 ⫽
8
182
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Name:
Chapter 6 Lesson 6.7
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Name:
Date:
Answer the questions.
Example
How many toys are shaded?
9
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6.
24 toys are divided into equal groups.
There are
7.
toys are shaded.
groups of toys, and
groups are shaded.
What fraction of the set of toys are shaded?
The shaded parts ⫽ _ of the set.
8.
Write the missing numbers on the model.
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3/9/09 6:04:11 PM
Name:
Date:
Write the missing numbers.
Example
15 fruits are divided into
There are
fruits in each group.
out of the 15 fruits in the set are shaded.
10.
11.
groups.
Color the parts of the model to show the number of fruits that are shaded.
3 units ⫽ 15 fruits
1 unit
12.
1 unit
1 unit
What fraction of the fruits are shaded?
The shaded parts ⫽ _ of the set.
13.
184
From the model, 1 unit
fruits
2 units
fruits
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9.
3
Chapter 6 Lesson 6.7
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11/5/09 9:30:10 AM
Name:
Date:
Find the fractional part of each number. Use models to help you.
Example
2
_
of 12 ?
3
12
8
3
units 12
1 unit 4
2 units 4
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2
So, _
of 12 is
3
14.
8
Divide 12 into 3 equal parts.
2
of the set.
The shaded parts —
3
2
8
.
3
_
of 32
8
32
?
units 1 unit 3 units 3
So, _
of 32 8
.
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3/9/09 6:04:13 PM
Name:
Date:
Find the fractional part of each number. Show your work.
Example
3
_
of 35 ?
5
3
_
35 5
3 35
The word “of” means
to multiply.
5
105
5
21
3
So, _
of 35 21.
5
3
_
of 28
4
16.
3
—
28 4
2
—
56 7
4
_
4
17.
186
3
_
of 64
8
2
_
of 56
7
18.
7
—
of 44
11
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15.
Chapter 6 Lesson 6.7
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11/5/09 9:30:28 AM
Name:
Date:
Worksheet 8 Real-World Problems: Fractions
Solve. Show your work.
Example
1
Three friends shared a pie. Susan ate _
of the pie.
4
3
1
_
Daniel ate _
of
the
pie.
Joe
ate
of the pie.
8
8
What fraction of the pie did they eat altogether?
3
1
1
_
_
_
4
8
8
1
4
3
1
2 _
—
—
8
8
8
3
8
6 3
_
—
8
2
4
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They ate
3
_
4
1
8
of the pie.
1
4
2
8
2
1.
Lisa, Sam, and Marco each bought some dried fruit.
5
2
pound of dried fruit. Sam and Marco each bought _
pound
Lisa bought _
6
3
of dried fruit. How much dried fruit did they buy altogether?
5
5
2
_
_
_
6
6
3
They bought
5
5
_
_
6
6
pounds of dried fruit altogether.
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Name:
2.
Date:
1
Mrs. Jackson baked muffins one day. She used _
kilogram of flour to bake
4
7
kilogram of flour to bake the second
the first batch of muffins. She used _
12
11
kilogram of flour for the third batch. How much flour
batch, and another _
12
did she use altogether?
⫽
She used
3.
7
11
⫹_
⫹_
12
12
⫽
kilograms of flour altogether.
3
7
Edison made a fruit salad. He mixed _
pound of apples and _
pound of
4
12
5
pound of banana. What was the total
strawberries. He then added _
12
weight of the fruit salad?
188
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7
11
1
_
⫹_
⫹_
⫽
12
12
4
Chapter 6 Lesson 6.8
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Name:
Date:
Example
Kathy has 1 loaf of whole grain bread.
2
1
_
of
it
for
her
friend
and
for herself.
She cuts _
12
3
What fraction of the bread is left?
Method 1
Method 2
2
1
_
1_
12
3
8
2
1
1
_
_
_
_
12
12
12
3
9
_
12
3
9
12
_
_
_
12
12
12
1
_
4
_1
4
loaf of bread is left.
8
12
1
_
_
_
12
12
12
3
_
12
1
_
4
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_1
4
4.
loaf of bread is left.
1
4
Sam spent _
of his time playing soccer and _
of his time doing homework.
9
3
He spent the rest of his time playing computer games. How much of his time
did Sam spend playing computer games?
1
3
4
9
?
4
4
1
_
__
_
_
9
9
9
9
3
1
9
_
9
Sam spent
of his time playing computer games.
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Name:
5.
Date:
1
1
Latoya bought a pizza. She ate _
of the pizza and gave _
of it to her sister.
6
3
She kept the rest of the pizza for her grandmother. How much of the pizza
did Latoya keep for her grandmother?
1
6
1
3
?
1
Latoya kept
6.
of the pizza for her grandmother.
Pam made mixed juice from carrot juice and apple juice. She filled a jug
3
3
7
liter of carrot juice and _
liter of apple juice. Pam then drank _
liter
with _
4
8
8
of the mixed juice. Find the amount of mixed juice that was left in the jug.
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1
1
_
_
3
6
liters of mixed juice was left in the jug.
190
Chapter 6 Lesson 6.8
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Name:
Date:
Example
Ling bought a total of 12 apples. Of the apples she bought, 8 are
red apples and 4 are green apples.
a.
What fraction of the apples are red?
b.
What fraction of the apples are green?
a.
8 out of 12 is _.
8
12
2
2
—
3
8
_
_
12
3
b.
2
—
3
1
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1
_
3
7.
of the apples are red.
1
_
3
of the apples are green.
Elan has a bag of 10 marbles. He gives 4 marbles to his brother.
a.
What fraction of his marbles does Elan give away?
4 out of 10 is _.
__
Elan gives away
b.
of his marbles.
What fraction of the marbles are left?
1
of the marbles are left.
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Name:
8.
Date:
Bernice has a ribbon that is 12 centimeters long. She cuts 8 centimeters
off the length of the ribbon. What fraction of the ribbon is left?
Example
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5
Dianne has $72. She uses _
of it to buy a present for her father.
9
How much money does Dianne have left?
$72
5
9
?
Method 1
Method 2
9 units $72
1 unit $72 9
$8
4 units $8 4
$32
5
5
_
_
of
$72
$72
9
9
Dianne has
$32
left.
$360
9
$40
Dianne spent $40.
$72 $40 $32
Dianne has
192
$32
left.
Chapter 6 Lesson 6.8
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Name:
9.
Date:
3
Winton was given $14 to spend at his school fair. He spent _
of the money
7
playing games. How much money did Winton have left?
$14
3
7
?
Method 1
Method 2
units $
1 unit $
units $
3
_
of $14 7
$
$
$
$
$14 $
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Winton had $
He spent $
$
$14 $
left.
Winton had $
10.
.
$
left.
5
of his farm and tulips on the rest of the land.
Chris planted carrots on _
9
The total area of his farm is 621 square meters.
Find the area of the land on which he planted tulips.
621 square meters
5
Carrots: 9
Method 1
Tulips: ?
Method 2
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11/5/09 2:34:10 PM
Name:
11.
Date:
1
Of all the seats in an airplane, _
are business-class seats, and the rest are
3
economy class seats.
There are 156 seats in the airplane. Find the number of economy class seats.
156
1
3
Method 2
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Method 1
?
194
Chapter 6 Lesson 6.8
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