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![Page 1: Worksheet 1 Adding Unlike Fractions - · PDF fileWorksheet 1 Adding Unlike Fractions Circle the unlike fraction in each set. 1. _3 10, 2_ 5, _7 10 2. _2 9, _5 9, _1 3 Write a like](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a863a8e7f8b9a882e8cbf40/html5/thumbnails/1.jpg)
Worksheet 1 Adding Unlike FractionsCircle the unlike fraction in each set.
1. 3 _ 10 , 2 _ 5 , 7 _ 10 2. 2 _ 9 , 5 _ 9 , 1 _ 3
Write a like fraction and an unlike fraction for each fraction.
Like Fraction Unlike Fraction
3. 1 _ 5
4. 3 _ 10
5. 4 _ 7
6. 5 _ 9
Identify the like fractions. Put them into sets.
7. 1 _ 3 5 _ 9 3 _
8 2 _ 7 4 _ 5 8 _ 9 3 _ 7 3 _ 4 1 _ 2 5 _ 6 1 _ 9 7 _ 8
Set 1 Set 3Set 2
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Name: Date:
Fractions and Mixed NumbersCHAPTER
3
MS_Reteach 5A_Ch03_079-116.indd 79 2/28/09 1:30:06 PM
![Page 2: Worksheet 1 Adding Unlike Fractions - · PDF fileWorksheet 1 Adding Unlike Fractions Circle the unlike fraction in each set. 1. _3 10, 2_ 5, _7 10 2. _2 9, _5 9, _1 3 Write a like](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a863a8e7f8b9a882e8cbf40/html5/thumbnails/2.jpg)
List the fi rst six multiples of each number.
Example
Multiples of 5: 5, 10, 15, 20, 25, 30
8. Multiples of 3:
9. Multiples of 4:
Each rectangle on the right is divided into smaller equal partsby the dotted lines. Find the equivalent fractions for the shadedparts of the rectangle.
Example
1 _ 2 � 2 _ 4
1 _ 2 and 2 _ 4 are equivalent fractions.
They have the same value.
10.
2 _ 3 � _ 6
11.
4 _ 5 � _
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Chapter 3 Lesson 3.1
MS_Reteach 5A_Ch03_079-116.indd 80 11/12/09 11:57:55 AM
![Page 3: Worksheet 1 Adding Unlike Fractions - · PDF fileWorksheet 1 Adding Unlike Fractions Circle the unlike fraction in each set. 1. _3 10, 2_ 5, _7 10 2. _2 9, _5 9, _1 3 Write a like](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a863a8e7f8b9a882e8cbf40/html5/thumbnails/3.jpg)
List the equivalent fractions of the fi rst fraction. Stop when you get a fraction that has the same denominator as the second fraction. Then fi nd the least common denominator of both fractions.
Example
1 _ 2 �
1 _ 6
The least common denominator of 1 _ 2 and 1 _ 6 is .
2 _ 4 � 3 _ 6
6
The least common multiple of
2 and 6 is 6. The least common denominator of 1 _ 2 and 1 _ 6 is 6.
12. 1 _ 3 �
2 _ 9
The least common denominator of 1 _ 3 and 2 _ 9 is .
13. 3 _ 4 �
1 _ 16
The least common denominator of 3 _ 4 and 1 _ 16 is .
14. 2 _ 3 �
2 _ 15
The least common denominator of 2 _ 3 and 2 _ 15 is .
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MS_Reteach 5A_Ch03_079-116.indd 81 2/28/09 1:30:07 PM
![Page 4: Worksheet 1 Adding Unlike Fractions - · PDF fileWorksheet 1 Adding Unlike Fractions Circle the unlike fraction in each set. 1. _3 10, 2_ 5, _7 10 2. _2 9, _5 9, _1 3 Write a like](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a863a8e7f8b9a882e8cbf40/html5/thumbnails/4.jpg)
List the equivalent fractions of each fraction. Stop when you get equivalent fractions with the same denominator. Then fi nd the least common denominator of both fractions.
2 _ 4 � 3 _ 6 1 _ 2 �
1 _ 3 �
The least common denominator of 1 _ 2 and 1 _ 3 is .6
Example
2 _ 6
15. 1 _ 3 �
3 _ 4 �
The least common denominator of 1 _ 3 and 3 _ 4 is .
16. 1 _ 4 �
1 _ 6 �
The least common denominator of 1 _ 4 and 1 _ 6 is .
17. 5 _ 6 �
7 _ 8 �
The least common denominator of 5 _ 6 and 7 _ 8 is .
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Chapter 3 Lesson 3.1
MS_Reteach 5A_Ch03_079-116.indd 82 11/12/09 11:58:07 AM
![Page 5: Worksheet 1 Adding Unlike Fractions - · PDF fileWorksheet 1 Adding Unlike Fractions Circle the unlike fraction in each set. 1. _3 10, 2_ 5, _7 10 2. _2 9, _5 9, _1 3 Write a like](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a863a8e7f8b9a882e8cbf40/html5/thumbnails/5.jpg)
Shade and label each model to show the fractions. Then completethe addition sentence.
?
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1 _ 2 � 1 _ 4 � 2 _ 4 � 1 _ 4 � 3 _ 4
To add unlike fractions, change
them to fractions with the same
denominator. The least common
denominator of 1 _ 2 and 1 _ 4 is 4.
Example
18.
1 _ 3 � 2 _ 9 � � �
19.
2 _ 5 � 3 _ 10 � � �
20.
3 _ 4 � 1 _ 12 � � � �
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MS_Reteach 5A_Ch03_079-116.indd 83 2/28/09 1:30:07 PM
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Add. Express each sum in simplest form.
Example
1 _ 2 � 1 _ 8 � 4 _ 8 � 1 _ 8
� 5 _ 8
21. 1 _ 4 � 1 _ 2 � 1 _ 4 �
�
22. 1 _ 10 � 1 _ 5 23. 2 _ 3 � 1 _ 6
24. 3 _ 4 � 1 _ 8 25. 1 _ 9 � 2 _ 3
26. 1 _ 4 � 1 _ 12 27. 2 _ 3 � 1 _ 12
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Chapter 3 Lesson 3.1
MS_Reteach 5A_Ch03_079-116.indd 84 11/12/09 11:58:22 AM
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Shade and label each model to show the fractions. Then complete the addition sentence.
Example
?
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1 _ 2 � 1 _ 3 � 3 _ 6 � 2 _ 6 � 5 _ 6
28.
1 _ 3 � 1 _ 5 � � �
29.
3 _ 7 � 1 _ 2 � � �
30.
4 _ 9 � 1 _ 2 � � �
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MS_Reteach 5A_Ch03_079-116.indd 85 2/28/09 1:30:08 PM
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Add.
Example
1 _ 3 � 1 _ 4 � 4 _ 12 � 3 _ 12
� 7 _ 12
31. 1 _ 5 � 1 _ 2 � 2 _ 10 �
�
32. 1 _ 4 � 1 _ 9 33. 1 _ 7 � 1 _ 8
34. 2 _ 5 � 1 _ 4 35. 2 _ 5 � 3 _ 8
36. 2 _ 9 � 2 _ 7 37. 3 _ 11 � 2 _ 3
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Chapter 3 Lesson 3.1
MS_Reteach 5A_Ch03_079-116.indd 86 11/12/09 11:58:36 AM
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Mark the fractions on the number line.
38. 1 _ 3 10 1
2
39. 3 _ 4 10 1
2
Look at the number line. Round the fraction to 0, 1 _ 2 , or 1.
Example89
10 12
8 _ 9 1
40.
10 12
58
5 _ 8
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MS_Reteach 5A_Ch03_079-116.indd 87 2/28/09 1:30:08 PM
![Page 10: Worksheet 1 Adding Unlike Fractions - · PDF fileWorksheet 1 Adding Unlike Fractions Circle the unlike fraction in each set. 1. _3 10, 2_ 5, _7 10 2. _2 9, _5 9, _1 3 Write a like](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a863a8e7f8b9a882e8cbf40/html5/thumbnails/10.jpg)
Use benchmarks to estimate each sum.
Example
1 _ 4 � 2 _ 5
0 � 1 _ 2 � 1 _ 2
Common benchmarks for estimating fractions are 0, 1 _ 2 , and 1.
41. 3 _ 4 � 7 _ 8
� �
42. 11 _ 12 � 7 _ 12
� �
43. 5 _ 9 � 5 _ 12 � 10 _ 11
� � �
44. 6 _ 9 � 11 _ 12 45. 3 _ 8 � 5 _ 9
46. 1 _ 2 � 4 _ 5 � 8 _ 9 47. 5 _ 6 � 6 _ 7 � 7 _ 8
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Chapter 3 Lesson 3.1
MS_Reteach 5A_Ch03_079-116.indd 88 11/12/09 11:58:47 AM
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Worksheet 2 Subtracting Unlike FractionsShade and label each model to show the fractions. Then complete the subtraction sentence.
Example
?
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2 _ 4 � 1 _ 4 � 1 _ 4 1 _ 2 � 1 _ 4 �
1.
2 _ 3 � 5 _ 12 � � � �
2.
7 _ 9 � 1 _ 3 � � �
3.
5 _ 8 � 1 _ 4 � � �
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MS_Reteach 5A_Ch03_079-116.indd 89 2/28/09 1:30:09 PM
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Subtract. Express each difference in simplest form.
Example
1 _ 3 � 1 _ 9 � 3 _ 9 � 1 _ 9
� 2 _ 9
4. 1 _ 2 � 1 _ 8 � 4 _ 8 �
�
5. 1 _ 5 � 1 _ 10 6. 5 _ 6 � 2 _ 3
7. 7 _ 8 � 1 _ 4 8. 3 _ 4 � 5 _ 12
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Chapter 3 Lesson 3.2
MS_Reteach 5A_Ch03_079-116.indd 90 11/12/09 11:59:04 AM
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Shade and label each model to show the fractions. Then complete the subtraction sentence.
Example
1 _ 2 � 1 _ 3 � 3 _ 6 � 2 _ 6 � 1 _ 6
?
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13
9.
1 _ 3 � 1 _ 4 � � �
10.
5 _ 7 � 1 _ 2 � � �
11.
3 _ 5 � 1 _ 3 � � �
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MS_Reteach 5A_Ch03_079-116.indd 91 2/28/09 1:30:09 PM
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Subtract.
Example
1 _ 2 � 1 _ 5 � 5 _ 10 � 2 _ 10
� 3 _ 10
12. 1 _ 3 � 1 _ 5 � 5 _ 15 �
�
13. 1 _ 5 � 1 _ 6 14. 1 _ 7 � 1 _ 8
15. 4 _ 5 � 1 _ 4 16. 5 _ 8 � 3 _ 5
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Chapter 3 Lesson 3.2
MS_Reteach 5A_Ch03_079-116.indd 92 11/12/09 11:59:14 AM
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Look at the number line. Round the fraction to 0, 1 _ 2 , or 1.
Example
10 12
18
1 _ 8 0
17.
10 12
56
5 _ 6
18.
10 12
37
3 _ 7
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MS_Reteach 5A_Ch03_079-116.indd 93 2/28/09 1:30:09 PM
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Use benchmarks to estimate each difference.
Example
7 _ 8 � 4 _ 7
1 � 1 _ 2 � 1 _ 2
Common benchmarks for estimating fractions are 0, 1 _ 2 , and 1.
19. 1 _ 2 � 1 _ 4
� �
21. 5 _ 6 � 8 _ 9
� �
23. 4 _ 5 � 11 _ 22
25. 1 _ 2 � 6 _ 11
20. 11 _ 12 � 1 _ 2
� �
22. 10 _ 11 � 5 _ 12
� �
24. 7 _ 8 � 1 _ 9
26. 8 _ 9 � 3 _ 7
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Chapter 3 Lesson 3.2
MS_Reteach 5A_Ch03_079-116.indd 94 11/12/09 11:59:24 AM
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Worksheet 3 Fractions, Mixed Numbers, and Division Expressions
Write each improper fraction as a mixed number.
1. 4 _ 3 � 3 _ 3 � 1 _ 3 3 is the denominator. I need a 3 for a numerator. 4 � 3 � 1 � 1 �
�
2. 6 _ 5 � �
� 1 �
�
3. 7 _ 3 4. 9 _ 5
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MS_Reteach 5A_Ch03_079-116.indd 95 2/28/09 1:30:10 PM
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Look at the diagram. Complete.
Divide 3 circles into 5 equal parts each. What fraction of a whole is each part? How many parts are in each group?
� � 3
_
5
3 5
Example
5.
� � _
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Chapter 3 Lesson 3.3
MS_Reteach 5A_Ch03_079-116.indd 96 11/12/09 11:59:36 AM
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Write each division expression as a fraction.
Example
2 � 7 � 2 _
7
division expression
6. 4 � 5 � _ 7. 5 � 9 � _
8. 7 � 11 � _ 9. 5 � 8 � _
Write each fraction as a division expression.
Example
9 _ 10 � � 109 10. 3 _ 8 � �
11. 5 _ 6 � � 12. 4 _ 11 � �
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MS_Reteach 5A_Ch03_079-116.indd 97 2/28/09 1:30:11 PM
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Look at the diagram. Complete.
13.
� � 4 _
3
� 3 _
3 �
1 _
3
� 1 � _
� 1 _
Divide 4 circles into 3 equal parts each. What fraction of the whole is each part? How many parts are in each group?
4 3
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Chapter 3 Lesson 3.3
MS_Reteach 5A_Ch03_079-116.indd 98 11/12/09 11:59:48 AM
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Divide. Express your answer as a mixed number.
14. 8 � 5 � _ 15. 7 � 2 � _
� _ � _ � _ � _
� � _ � � _
� _ � _
16. 10 � 3 17. 17 � 6
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MS_Reteach 5A_Ch03_079-116.indd 99 2/28/09 1:30:12 PM
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Look at the diagram. Complete.
18.
� � _
How do you use long division to fi nd the answer?
)
_
Divide. Express your answer as a mixed number in simplest form.
19. 9 � 2 20. 14 � 4
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Chapter 3 Lesson 3.3
MS_Reteach 5A_Ch03_079-116.indd 100 11/12/09 12:00:04 PM
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Worksheet 4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals
Write each fraction shown on the number line as a decimal.
1.
10
410
610
910
2. 25100
10
55100
85100
Write each fraction as a decimal.
3. 7 _ 10 � 4. 3 _ 10 �
5. 15 _ 100 � 6. 43 _ 100 �
7. 82 _ 100 � 8. 66 _ 100 �
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MS_Reteach 5A_Ch03_079-116.indd 101 2/28/09 1:30:13 PM
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Write each fraction as a decimal.
3 _ 5 � 3
5
2
2
�
�
� 6 _ 10
�
Example
0.6
Change to a fraction with a denominator of 10 or 100.
9. 4 _ 5 � �
�
� _ 10
�
10. 3 _ 4 � �
�
� _ 100
�
11. 1 _ 2 12. 12 _ 50
13. 9 _ 20 14. 21 _ 25
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Name: Date:
Chapter 3 Lesson 3.4
MS_Reteach 5A_Ch03_079-116.indd 102 11/12/09 12:00:16 PM
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Write each division expression as a decimal.
Example
6 � 5 � 6 _ 5
� 5 _ 5 �
1 _ 5
� �
�
1
1.2
0.2
1 _ 5 � 2 _ 10 � 0.2
15. 5 � 4 � _ 4
� _ 4 � _ 4
� �
�
16. 7 � 2 � _ 2
� _ 2 � _ 2
� �
�
17. 13 � 10 18. 7 � 5
19. 10 � 8 20. 35 � 25
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MS_Reteach 5A_Ch03_079-116.indd 103 2/28/09 1:30:15 PM
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Write each mixed number as a decimal.
1 4 _ 5 � 1 � 4 _ 5
� 1 �
�
0.8
1.8
Example
4 _ 5 � _ 10 8
� 0.8
21. 3 11 _ 25 � 3 � _ 25
� �
�
22. 5 17 _ 20 � �
� �
�
23. 2 3 _ 4 24. 5 49 _ 50
11 _ 25 � _ 100 �
17 _ 20 � _ 100 �
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Name: Date:
Chapter 3 Lesson 3.4
MS_Reteach 5A_Ch03_079-116.indd 104 11/12/09 12:00:47 PM
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Worksheet 5 Adding Mixed NumbersAdd. Express each sum in simplest form.
1. 3 _ 4 � 1 _ 2 � _ 4 � _ 4
� _ 4
�
2. 2 _ 3 � 5 _ 6 � _ 6 � _ 6
� _ 6
� _ 6
�
3. 7 _ 8 � 3 _ 4 4. 2 _ 3 � 4 _ 9
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MS_Reteach 5A_Ch03_079-116.indd 105 2/28/09 1:30:18 PM
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Add. Express each sum in simplest form.
Example
2 _ 5 � 1 7 _ 10 � 4 _ 10 � 7 _ 10 � 1
� 1 11 _ 10
� 2 1 _ 10
2 _ 5 � 4 _ 10
1 7 _ 10 � 7 _ 10 � 1
1 11 _ 10 � 1 � 11 _ 10
� 1 � 1 1 _ 10
� 2 1 _ 10
5. 1 3 _ 8 � 3 _ 4 � � �
�
�
6. 5 _ 6 � 2 5 _ 12 7. 3 2 _ 3 � 5 _ 9
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Name: Date:
Chapter 3 Lesson 3.5
MS_Reteach 5A_Ch03_079-116.indd 106 11/12/09 12:01:11 PM
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Add. Express each sum in simplest form.
1 1 _ 3 � 2 1 _ 9 � 1 3 _ 9 � 2
1 _ 9
� 3 4 _ 9
Example
Add the fractions.
3 _ 9 � 1 _ 9 � 4 _ 9
Add the whole numbers.
1 � 2 � 3
8. 2 1 _ 5 � 4 1 _ 6 � 2 _ 30 � 4 _ 30 9. 3 1 _ 7 � 5 1 _ 3 � 3 _ 21 � 5 _ 21
� �
10. 2 2 _ 3 � 1 3 _ 5 11. 1 5 _ 7 � 3 1 _ 2
12. 2 3 _ 4 � 4 3 _ 5 13. 3 3 _ 7 � 2 5 _ 6
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Name: Date:
MS_Reteach 5A_Ch03_079-116.indd 107 2/28/09 1:30:19 PM
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Use benchmarks to estimate each sum.
2 4 _ 5 � 1 4 _ 9
3 � 1 1 _ 2 � 4 1 _ 2
Example
Compare the fractional part
in each mixed number to the
benchmarks 0, 1 _ 2 , and 1.
14. 2 3 _ 7 � 4 7 _ 12
15. 5 2 _ 11 � 3 5 _ 8
16. 3 5 _ 6 � 6 8 _ 9
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Name: Date:
Chapter 3 Lesson 3.5
MS_Reteach 5A_Ch03_079-116.indd 108 11/12/09 12:01:25 PM
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Worksheet 6 Subtracting Mixed NumbersSubtract. Express each difference in simplest form.
1. 3 _ 4 � 3 _ 8 � _ 8 � _ 8 2. 2 _ 3 � 4 _ 9 � _ 9 � _ 9
� _ 8 � _ 9
3. 5 _ 6 � 5 _ 12 4. 7 _ 12 � 1 _ 4
Subtract. Express each difference in simplest form.
Example
1 5 _ 6 � 2 _ 3 � 1 5 _ 6 �
4 _ 6
� 1 1 _ 6
5. 2 7 _ 8 � 1 _ 2 � 2 _ 8 � _ 8
�
6. 4 2 _ 3 � 1 _ 9 7. 3 3 _ 4 � 5 _ 12
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Name: Date:
MS_Reteach 5A_Ch03_079-116.indd 109 2/28/09 1:30:20 PM
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Subtract. Express each difference in simplest form.
Example
4 3 _ 5 � 1 1 _ 10 � 4 6 _ 10 � 1
1 _ 10
� 3 5 _ 10
� 3 1 _ 2
Subtract the fractions.
6 _ 10 � 1 _ 10 � 5 _ 10
Subtract the whole numbers.
4 � 1 � 3
8. 3 1 _ 2 � 1 1 _ 3 � 3 _ 6 � 1 _ 6 9. 4 1 _ 3 � 1 1 _ 5
�
10. 5 1 _ 5 � 2 1 _ 7 11. 6 1 _ 4 � 3 1 _ 8
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Name: Date:
Chapter 3 Lesson 3.6
MS_Reteach 5A_Ch03_079-116.indd 110 11/12/09 12:01:41 PM
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Subtract. Express each difference in simplest form.
Example
3 1 _ 4 � 1 1 _ 2 � 3 1 _ 4 � 1 2 _ 4
� 2 5 _ 4 � 1 2 _ 4
� 1 3 _ 4
We cannot subtract 1 _ 2 from 1 _ 4 .
So, we rename 3 1 _ 4 as
3 1 _ 4 � 2 � 4 _ 4 � 1 _ 4 � 2 5 _ 4 .
12. 5 1 _ 10 � 2 1 _ 5 13. 4 1 _ 3 � 1 7 _ 9
14. 3 2 _ 3 � 1 3 _ 4 15. 4 3 _ 4 � 2 4 _ 5
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MS_Reteach 5A_Ch03_079-116.indd 111 2/28/09 1:30:21 PM
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Use benchmarks to estimate each difference.
3 3 _ 4 � 1 3 _ 5
4 � 1 1 _ 2 � 2 1 _ 2
Example
3 _ 4 1
3 _ 5 1 _ 2
16. 5 1 _ 8 � 2 11 _ 12
17. 4 3 _ 4 � 2 6 _ 7
18. 7 2 _ 9 � 1 7 _ 8
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Name: Date:
Chapter 3 Lesson 3.6
MS_Reteach 5A_Ch03_079-116.indd 112 11/12/09 12:02:00 PM
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Worksheet 7 Real-World Problems: Fractions and Mixed Numbers
Solve. Show your work.
1. Lauren had 3 liters of water. She poured the water into 7 glasses equally. How much water was there in each glass?
2. Mr. Bennett bought a loaf of bread, which was cut into 20 equal slices. He gave the bread equally to 8 children. How many slices of bread did each child get?
3. Mrs. Williams had some watermelons. She gave 1 _ 4 of the watermelons to
Mrs. Lopez and 7 _ 12 of the watermelons to Mrs. Brown. What fraction of
the watermelons did Mrs. Williams give away?
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MS_Reteach 5A_Ch03_079-116.indd 113 2/28/09 1:30:22 PM
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Solve. Show your work.
4. Ellen bought 5 _ 9 pound of fl our. She used 1 _ 2 pound of fl our to make pies.
How much fl our did Ellen have left?
5. Mr. Hayes sold 7 _ 9 of a crate of grapefruit. He sold 3 _ 5 of another crate of
grapefruit. How many crates of grapefruit did Mr. Hayes sell in all?
6. Latoya had 2 3 _ 4 liters of water in a watering can. She used 1 2 _ 7 liters of
the water to water her plants. How much water did Latoya have left
in the watering can?
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Chapter 3 Lesson 3.7
MS_Reteach 5A_Ch03_079-116.indd 114 11/12/09 12:02:11 PM
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Solve. Show your work.
7. Jose went jogging with Sam. Jose jogged 5 _ 8 mile before he stopped to rest.
Sam jogged 1 _ 4 mile more than Jose before stopping. After resting, they
continued jogging. Each of them jogged a total distance of 2 1 _ 5 miles.
a. How far did Sam jog before stopping?
b. What was the distance Jose jogged after resting?
8. Sharon completed her English homework in 2 _ 3 hour. She completed her
science homework in 5 _ 6 hour.
a. How much longer did Sharon take to complete her science homework?
b. How much time did she spend on her homework altogether?
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MS_Reteach 5A_Ch03_079-116.indd 115 2/28/09 1:30:22 PM
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Solve. Show your work.
9. Jana spent 1 _ 6 of her leisure time playing games. She spent 1 _ 4 more of her
time reading than playing games. Jana spent the rest of her leisure time
exercising.
a. What fraction of Jana’s leisure time was spent reading?
b. What fraction of her leisure time was spent exercising?
10. A shopkeeper had 3 1 _ 2 kilograms of onions. He sold 1 1 _ 4 kilograms of
onions in the morning and 1 3 _ 8 kilograms in the afternoon.
a. How many kilograms of onions did the shopkeeper sell altogether?
b. How many kilograms of onions did he have left?
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Chapter 3 Lesson 3.7
MS_Reteach 5A_Ch03_079-116.indd 116 11/12/09 12:02:28 PM