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Lesson 3.1 Adding Unlike Fractions
Fractions and Mixed Numbers
101
1. 34 � � 2. 2
5 � �
3. 56 � � 4. 1
7 � �
Express each fraction in simplest form.
5. 68 � 6. 8
20 �
7. 1015 � 8. 9
21 �
Practice 1 Adding Unlike FractionsFind two equivalent fractions for each fraction.
Example
23 � �
C
hapte
r
46
69
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08(M)MIF2015CC_WBG5A_Ch03.indd 101 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Rewrite each pair of unlike fractions as like fractions.
Example
12 � 1
4 �
9. 14 �
512 �
10. 1
10 �
25 �
11. 59 �
23 �
12. 3
8 �
916 �
Write equivalent fractions for each fraction. Then find the least common denominator of the fractions.
12 � = 13. 2
3 �
23 � 3
4 �
The least common denominator The least common denominator
is . is .
14. 14 � 15. 5
6 �
56 � 3
8 �
The least common denominator The least common denominator
is . is .
24
14
Example36
46
6
24
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08(M)MIF2015CC_WBG5A_Ch03.indd 102 29/04/13 11:34 AM
Lesson 3.1 Adding Unlike Fractions
16. 15 , 12
15 � 12 � �
�
Shade and label each model to show the fractions. Then complete the addition sentence.
Example
12 � 13 � �
�
36
26
56
Find the multiples of 2 and 3. Choose the least common multiple.Use it to rewrite 1
2 and 13 as like
fractions.
12 , 13
12
13
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08(M)MIF2015CC_WBG5A_Ch03.indd 103 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Shade and label each model to show the fractions. Then complete the addition sentence.
17. 16 , 14
16 � 14 � �
�
18. 15 , 2
3
15 � 2
3 � �
�
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08(M)MIF2015CC_WBG5A_Ch03.indd 104 29/04/13 11:34 AM
Lesson 3.1 Adding Unlike Fractions
Look at the model. Write two addition sentences.
1112
19. Addition sentence 1:
12
� 12
� 12
20. Addition sentence 2 (fractions in simplest form):
� �
Add. Express each sum in simplest form.
21. 13 � 19 � 22. 5
8 � 24 �
23. 12 � 67 � 24. 4
8 � 15 �
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08(M)MIF2015CC_WBG5A_Ch03.indd 105 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Use benchmarks to estimate each sum.
25. 23 � 29
26. 79 � 1
7 � 35
13 � 47
13 is about 1
2.
47 is about 1
2.
13 + 47
12 + 1
2 = 1
13 + 47 is about 1.
Example
13
0 112
47
0 112
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08(M)MIF2015CC_WBG5A_Ch03.indd 106 29/04/13 11:34 AM
Lesson 3.2 Subtracting Unlike Fractions
Practice 2 Subtracting Unlike FractionsRewrite the fractions as like fractions and complete the subtraction sentence.
Example
�3
�3
12 �
3
613 �
2
6
�2
�2
12 � 36
13 � 26
12 � 13 � �
�
36
26
16
What is the least common multiple of 2 and 3?
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08(M)MIF2015CC_WBG5A_Ch03.indd 107 4/30/13 7:29 AM
Chapter 3 Fractions and Mixed Numbers
Rewrite the fractions as like fractions and complete the subtraction sentence.
1.
13 � 1
4 �
13 �
14 �
13 � 14 � �
�
Subtract. Express each difference in simplest form.
2. 712 � 24 � 3. 4
5 � 13 �
4. 1 � 56 � 112 � 5. 7
9 � 16 �
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08(M)MIF2015CC_WBG5A_Ch03.indd 108 4/30/13 7:29 AM
Lesson 3.2 Subtracting Unlike Fractions
6. 910 � 16
7. 512 � 1
9
Example
Use benchmarks to estimate each difference.
0 112
45
0 112
38
45 � 38
45 is about 1.
38 is about 1
2.
45 – 3
8
1 – 12 = 1
245 – 3
8 is about 12.
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08(M)MIF2015CC_WBG5A_Ch03.indd 109 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Darren drew a model to find 45 � 12. His model is drawn incorrectly.
Explain his mistakes. Then draw the correct model and find the difference.
45
12
?
Darren’s model is wrong because:
The correct model is:
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08(M)MIF2015CC_WBG5A_Ch03.indd 110 29/04/13 11:34 AM
Lesson 3.3 Fractions, Mixed Numbers, and Division Expressions
Practice 3 Fractions, Mixed Numbers, and Division Expressions
Look at the diagram. Complete.
� �
1.
� �
Example
3
4
43
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08(M)MIF2015CC_WBG5A_Ch03.indd 111 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Write each division expression as a fraction.
2. 3.
5 � 7 �
3 � 10 �
4. 5.
4 � 9 �
2 � 11 �
Write each fraction as a division expression.
7. 110 � � 8. 6
7 � �
Look at the diagram. Complete.
Example
78 � � 6. 5
12 � �
Example
� �
�
4 3
7 8
4
3
1
31
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08(M)MIF2015CC_WBG5A_Ch03.indd 112 29/04/13 11:34 AM
Lesson 3.3 Fractions, Mixed Numbers, and Division Expressions
Look at the diagram. Complete.
9.
Complete.
10. 11.
7 � 4 �
35 � 11 �
�
�
�
�
� 1 �
� 3
�
�
�
� �
�
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08(M)MIF2015CC_WBG5A_Ch03.indd 113 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Divide. Express each quotient as a mixed number.
Example
5 � 3 � 1 2
3
13. 14.
9 � 4 � 2 18 � 5 � 3
Write each fraction in simplest form. Then divide to express each quotient as a mixed number.
15. 16.
18 � 4 �
22 � 6 �
�
�
�
�
12.
7 � 2 � 3 13 5 3 2
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08(M)MIF2015CC_WBG5A_Ch03.indd 114 29/04/13 11:34 AM
Lesson 3.4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals
Practice 4 Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals
Write each fraction as a decimal.
Example
35 � 1. 13
20 �
�
�
2. 1925 � 3. 47
50 �
�
�
Express each division expression as a mixed number in simplest form and as a decimal.
Division expressionExpress division expression as
a mixed number a decimal
4. 7 � 2
5. 9 � 4
6. 21 � 5
7. 101 � 25
610
0.6
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08(M)MIF2015CC_WBG5A_Ch03.indd 115 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Express each improper fraction as a decimal.
8. 225
9. 4720 10. 32
25
Solve. Show your work.
11. 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.
Example
32 = 2
2 + 1
2= 1 + 1
2= 1 + 0.5
= 1.5
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08(M)MIF2015CC_WBG5A_Ch03.indd 116 29/04/13 11:34 AM
Lesson 3.5 Adding Mixed Numbers
Example
Practice 5 Adding Mixed NumbersAdd. Express each sum in simplest form.
3 58 � 2
14
� 3 � 2 �
� 5
1. 123 � 2
14
� 1 � 2 �
� 3
2. 2 15 � 3 1
2
� 2 � 3 �
� 5 12
15
58
14
23
14
5
8
2
8
7
8
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08(M)MIF2015CC_WBG5A_Ch03.indd 117 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Add. Express each sum in simplest form.
3. 3 27 � 2 514 4. 5 712 � 3 14
5. 4 115 � 1 310 6. 12 19 � 9 56
Add. Express each sum in simplest form.
7. 145 � 2 13
� 1 � 2 �
� 3
� 4
45
13
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08(M)MIF2015CC_WBG5A_Ch03.indd 118 29/04/13 11:34 AM
Lesson 3.5 Adding Mixed Numbers
Add. Express each sum in simplest form.
8. 3 512 � 123
� 3 � 1
�
� 4
� 5
9. 2 34 � 3 25 10. 2 59 � 156
11. 7 89 � 9 512 12. 5 712 � 134
23
512
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08(M)MIF2015CC_WBG5A_Ch03.indd 119 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Use benchmarks to estimate each sum.
Example
6 35 � 4
56
35 is about 1
2.
So, 635 is about 6 1
2.
56 is about 1.
So, 4 56 is about 5.
6 35 + 4 56
6 12 + 5 = 11 12
6 35 + 4 56 is about 11 12.
13. 9 67 � 7
512
14. 4 712
� 10 19
0 112
35
0 112
56
120
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08(M)MIF2015CC_WBG5A_Ch03.indd 120 29/04/13 11:34 AM
Lesson 3.6 Subtracting Mixed Numbers
Example
Practice 6 Subtracting Mixed NumbersSubtract. Express each difference in simplest form.
3 23 �
512
� 3 � 512
� 3
� 3
1. 4 89 � 3
13
� 4 89 � 3
� 1
23
89
8
12
3
12
1
4
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08(M)MIF2015CC_WBG5A_Ch03.indd 121 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
2. 3 712
� 2 38
� 3 � 2
� 1
3. 3 59
� 1 12
4. 7 56
� 2 14
Subtract. Express each difference as a mixed number.
5. 3 14
� 178
� 3 � 1 78
� �
�
Subtract. Express each difference in simplest form.
14
712
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08(M)MIF2015CC_WBG5A_Ch03.indd 122 29/04/13 11:34 AM
Lesson 3.6 Subtracting Mixed Numbers
Subtract. Express each difference as a mixed number.
6. 5 13
� 3 512
� 5 � 3 512
� �
�
7. 4 15
� 1 13
8. 6 38
� 3 56
9. 7 14 � 5
1112 10. 8
13 � 4
34
13
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08(M)MIF2015CC_WBG5A_Ch03.indd 123 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
7 29 � 6
512
29
is about 0.
So, 7 29
is about 7.
512
is about 12
.
So, 6 512
is about 6 12
.
7 29
� 6 512
7 � 6 12 �
12
7 29
� 6 512
is about 12
.
Example
11. 12 25
� 8 712
12. 20 18 � 5
39
Use benchmarks to estimate each difference.
29
0 112
512
0 112
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08(M)MIF2015CC_WBG5A_Ch03.indd 124 4/30/13 11:26 AM
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
Practice 7 Real-World Problems: Fractions and Mixed Numbers
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?
Name: Date:
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08(M)MIF2015CC_WBG5A_Ch03.indd 125 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Solve. Show your work.
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
first hour, 38
quart of water collects. In the second hour, 16
quart of water collects. How much water collects in the
container in the two hours?
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08(M)MIF2015CC_WBG5A_Ch03.indd 126 4/30/13 11:27 AM
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
Solve. Show your work.
6. Arnold buys 89
pound of ground turkey. He uses 34
pound of the ground turkey to make meatballs. How many pounds of ground turkey are left?
7. A snail is at the bottom of a well. In the first 10 minutes, the snail climbs 23 7
12 inches. In the next 10 minutes, it climbs 19 5
6 inches. How far is
the snail from the bottom of the well after 20 minutes?
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08(M)MIF2015CC_WBG5A_Ch03.indd 127 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Solve. Show your work.
8. Johnny is jogging along a track. He has already jogged 1 23
miles.
He plans to jog a total of 3 14
miles. How many miles does he have left to jog?
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08(M)MIF2015CC_WBG5A_Ch03.indd 128 29/04/13 11:34 AM
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
Practice 8 Real-World Problems: Fractions and Mixed Numbers
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 3 circles from each sheet. The circles are shared equally among 6 students. How many circles does each student get?
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08(M)MIF2015CC_WBG5A_Ch03.indd 129 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Solve. Show your work.
3. Mrs. Quirk buys 1 quart of milk. Michael drinks 27
quart of it.
Joel drinks 13
quart of it. How many quarts of milk are left?
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08(M)MIF2015CC_WBG5A_Ch03.indd 130 29/04/13 11:34 AM
Solve. Show your work.
4. An organic farmer buys a piece of land. She plants tomatoes
on 59
of the land and green beans on 112
of the land.
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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08(M)MIF2015CC_WBG5A_Ch03.indd 131 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Solve. Show your work.
5. A package contains three types of bagels, plain, wheat, and sesame.
The weight of the plain bagels is 123 pounds. The weight of the wheat
bagels is 2 56 pounds. The total weight of the three types of bagels is
5 pounds. What is the weight of the sesame bagels?
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08(M)MIF2015CC_WBG5A_Ch03.indd 132 29/04/13 11:34 AM
Solve. Show your work.
6. Reggie and Jay go for a walk every morning. Reggie walks 2 14 miles.
Jay walks 138 miles less than Reggie. What is the total distance
they walk every morning?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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08(M)MIF2015CC_WBG5A_Ch03.indd 133 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Solve. Show your work.
7. Alicia uses 34
gallon of paint to paint her room. Becca uses 45
gallon
more than Alicia to paint her room. How many gallons of paint do they use altogether?
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08(M)MIF2015CC_WBG5A_Ch03.indd 134 29/04/13 11:34 AM
Solve. Show your work.
8. A monkey climbs 3 35
feet up a coconut tree that has a height
of 10 feet. It rests for a while and continues to climb another 4 2
3 feet up the tree. How many more feet must the monkey climb to
reach the top of the tree?
Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers
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08(M)MIF2015CC_WBG5A_Ch03.indd 135 29/04/13 11:34 AM
18 �
23 � ?
Draw a model, and explain the steps you can use to add 23
to 18
.
Chapter 3 Fractions and Mixed Numbers136
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08(M)MIF2015CC_WBG5A_Ch03.indd 136 29/04/13 11:34 AM
Solve. Show your work.
Tina, Troy and Nate had a total of 25 equal-sized square tiles to place over a squaregrid. Tina used 8
25 of the square tiles. Troy used 1
5 of the square tiles. Shade the
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
5 of the
square grid is not covered?
Put On Your Thinking Cap!
Challenging Practice
Chapter 3 Fractions and Mixed Numbers
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08(M)MIF2015CC_WBG5A_Ch03.indd 137 29/04/13 11:34 AM
Chapter 3 Fractions and Mixed Numbers
Put On Your Thinking Cap!
Solve. Use a model to help you.
Paul mixes cement with sand. He uses 3 34 kilograms of cement and 1
2 kilogram
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?
Problem Solving
138
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08(M)MIF2015CC_WBG5A_Ch03.indd 138 29/04/13 11:34 AM
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