NAME _____________________________________________ DATE __________________ PERIOD _________ Course 2 • Chapter 4 Rational Numbers 55 Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use. Lesson 3 Reteach Add and Subtract Like Fractions Like fractions are fractions that have the same denominator. To add or subtract like fractions, add or subtract the numerators and write the result over the denominator. Simplify if necessary. Example 1 Find 3 − 4 + 1 − 4 . Write in simplest form. 3 − 4 + 1 − 4 = 3 + 1 −−−− 4 Add the numerators. = 4 − 4 Write the sum over the denominator. = 1 Simplify. Example 2 Find 2 − 3 - 1 − 3 . Write in simplest form. 2 − 3 - 1 − 3 = 2 - 1 −−−− 3 Subtract the numerators. = 1 − 3 Write the difference over the denominator. Exercises Add or subtract. Write in simplest form. 1. 5 − 8 + 1 − 8 2. 7 − 9 - 2 − 9 3. - 1 − 4 + 3 − 4 4. 7 − 8 - 5 − 8 5. 5 − 9 + 5 − 9 6. – 3 − 8 - 1 − 8 7. 3 −− 10 + 1 −− 10 8. 2 − 5 - 1 − 5 9. 7 −− 15 + 4 −− 15 10. 7 − 9 - 8 − 9 1 3 2 3 1 0 1 4 1 2 3 4 1 0
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NAME _____________________________________________ DATE __________________ PERIOD _________
Course 2 • Chapter 4 Rational Numbers 55
Copy
righ
t ©
The
McG
raw
-Hill
Com
pani
es, I
nc. P
erm
issi
on is
gra
nted
to
repr
oduc
e fo
r cl
assr
oom
use
.Lesson 3 ReteachAdd and Subtract Like Fractions
Like fractions are fractions that have the same denominator. To add or subtract like fractions, add or subtract the numerators and write the result over the denominator.
Simplify if necessary.
Example 1Find 3 −
4 + 1 −
4 . Write in simplest form.
3 −
4 + 1 −
4 = 3 + 1 −−−−
4 Add the numerators.
= 4 −
4 Write the sum over
the denominator.
= 1 Simplify.
Example 2Find 2 −
3 - 1 −
3 . Write in simplest form.
2 −
3 - 1 −
3 = 2 - 1 −−−−
3 Subtract the numerators.
= 1 −
3 Write the difference over
the denominator.
ExercisesAdd or subtract. Write in simplest form.
1. 5 −
8 + 1 −
8 2. 7 −
9 - 2 −
9
3. -
1 −
4 + 3 −
4 4. 7 −
8 - 5 −
8
5. 5 −
9 + 5 −
9 6. – 3 −
8 - 1 −
8
7. 3 −−
10 + 1 −−
10 8. 2 −
5 - 1 −
5
9. 7 −−
15 + 4 −−
15 10. 7 −
9 - 8 −
9
13
23
10
14
12
34
10
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NAME _____________________________________________ DATE __________________ PERIOD _________
56 Course 2 • Chapter 4 Rational Numbers
Copyright © The M
cGraw
-Hill Com
panies, Inc. Permission is granted to reproduce for classroom
use.Lesson 3 Skills PracticeAdd and Subtract Like Fractions
Add or subtract. Write in simplest form.
1. 3 −
8 + 3 −
8 2. 7 −−
10 -
5 −−
10 3. 9 −−
10 +
3 −−
10
4. 4 −
7 -
2 −
7 5. 2 −
3 +
2 −
3 6. 5 −
9 – 2 −
9
7. 8 −−
15 -
1 −−
15 8. 5 −−
12 + 5 −−
12 9. 7 −−
10 -
3
−−
10
10. 7 −−
16 +
5 −−
16 11. 19 −−
20 -
3 −−
20 12. -
5 −
9 +
7 −
9
13. -
4 −
9 -
1 −
9 14. 2 −
3 +
1 −
3 15. -
3 −
4 -
2 −
4
16. 7 −
8 -
5 −
8 17. 8 −
9 -
5 −
9 18. -
5 −−
12 -
(
-
3 −−
12 )
19. 7 −
9 + 2 −
9 20. 3 −
5 + 4 −
5 21. -
11 −−
12 - 5 −−
12
22. 5 −
6 +
4 −
6 23. 3 −
8 +
5 −
8 24. -
7 −−
16 -
(
-
3 −−
16 )
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Course 2 • Chapter 4 Rational Numbers 57
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righ
t ©
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McG
raw
-Hill
Com
pani
es, I
nc. P
erm
issi
on is
gra
nted
to
repr
oduc
e fo
r cl
assr
oom
use
.Lesson 4 ReteachAdd and Subtract Unlike Fractions
To add or subtract fractions with different denominators,
• Rename the fractions using the least common denominator (LCD).
• Add or subtract as with like fractions.
• If necessary, simplify the sum or difference.
Example
Find 2 −
3 + 1 −
4 .
Method 1 Use a model.
2 −
3
+
1 −
4
11 −−
12
ExercisesAdd or subtract. Write in simplest form.
1. 1 −
2 + 3 −
4 2. 3 −
8 - 1 −
2
3. 7 −−
15 +
(
-
5 −
6 )
4. 2 −
5 - 1 −
3
5. 5 −
9 +
(
-
5 −−
12 )
6. 11 −−
12 - 3 −
4
7. 7 −
8 -
(
-
1 −
3 )
8. 7 −
9 - 1 −
2
9. 3 −−
10 + 7 −−
12 10. 3 −
5 + 2 −
3
Method 2 Use the LCD.
2 −
3 + 1 −
4 = 2 −
3 · 4 −
4 + 1 −
4 · 3 −
3 Rename using the LCD, 12.
= 8 −−
12 + 3 −−
12 or 11 −−
12 Add the fractions.
13
13
14
112
112
112
112
112
112
112
112
112
112
112
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NAME _____________________________________________ DATE __________________ PERIOD _________
58 Course 2 • Chapter 4 Rational Numbers
Copyright © The M
cGraw
-Hill Com
panies, Inc. Permission is granted to reproduce for classroom
use.Lesson 4 Skills PracticeAdd and Subtract Unlike Fractions
Add or subtract. Write in simplest form.
1. 8 −−
15 - 1 −
5 2. 5 −
6 + 5 −−
12
3. 3 −
5 - 3 −−
10 4. 7 −−
16 + 3 −
8
5. 19 −−
20 - 3 −−
10 6. 4 −
9 - 1 −−
12
7. 2 −
3 + 3 −
7 8. 3 −
4 + 1 −
7
9. 7 −
8 - 2 −
3 10. 8 −
9 - 5 −
6
11. 5 −−
12 - 3 −−
10 12. 7 −
9 + 2 −
3
13. 3 −
5 + 4 −
7 14. 11 −−
12 - 1 −
2
15. 3 −
4 -
(
- 1 −
2 )
16. - 5 −
6 + 1 −
4
17. - 2 −
3 -
(
-
3 −
4 )
18. 7 −
8 + 1 −−
12
19. -
3 −−
10 + 5 −−
20 20. 7 −−
12 -
(
-
1 −
3 )
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NAME _____________________________________________ DATE __________________ PERIOD _________
Course 2 • Chapter 4 Rational Numbers 59
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righ
t ©
The
McG
raw
-Hill
Com
pani
es, I
nc. P
erm
issi
on is
gra
nted
to
repr
oduc
e fo
r cl
assr
oom
use
.Lesson 5 ReteachAdd and Subtract Mixed Numbers
Example 1
Find 6 1 −−
10 + 2 3 −−
10 . Write in simplest form.
6 1 −−
10 Add the whole numbers and the fractions separately.
+ 2 3 −−
10
8 4 −−
10 or 8 2 −
5 Simplify.
Example 2
Find 8 2 −
3 - 6 1 −
2 .
8 2 −
3 8 4 −
6 Rename the fractions using the LCD.
-6 1 −
2 6 3 −
6
2 1 −
6 Subtract.
Example 3
Find 4 1 −
4 - 2 3 −
5 .
4 1 −
4 4 5 −−
20 3 25 −−
20 Rename 4 5 −−
20 as 3 25 −−
20 .
-2 3 −
5 2 12 −−
20 2 12 −−
20
1 13 −−
20 Subtract the whole numbers and then the fractions.
ExercisesAdd or subtract. Write in simplest form.
1. 1 3 −
5 + 4 1 −
5 2. 2 5 −
6 - 1 1 −
6
3. 3 2 −
3 + 2 1 −
2 4. 5 3 −
4 - 3 1 −
6
5. 8 - 6 7 −
8 6. 1 4 −
5 + 3 −−
10
To add or subtract mixed numbers:
• Add or subtract the fractions. Rename using the LCD if necessary.
• Then, add or subtract the whole numbers.
• Simplify if necessary.
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NAME _____________________________________________ DATE __________________ PERIOD _________
60 Course 2 • Chapter 4 Rational Numbers
Copyright © The M
cGraw
-Hill Com
panies, Inc. Permission is granted to reproduce for classroom
use.Lesson 5 Skills Practice Add and Subtract Mixed Numbers
Add or subtract. Write in simplest form.
1. 3 2 −
5 + 1 1 −
5 2. 6 7 −−
10 + 12 1 −−
10
3. 5 3 −
8 - 4 1 −
8 4. 3 1 −
2 - 2 1 −
2
5. 7 1 −
4 - 5 3 −
4 6. 8 5 −
6 + 9 5 −
6
7. 2 1 −
2 - 1 1 −
4 8. 3 7 −
8 + 5 3 −
4
9. 2 5 −
6 - 7 −
8 10. 8 1 −
5 + 3 7 −−
10
11. 8 4 −
5 - 2 9 −−
10 12. 3 1 −
4 - 2 5 −
6
13. 4 3 −
5 + 5 1 −
2 14. 10 - 7 7 −
8
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NAME _____________________________________________ DATE __________________ PERIOD _________
Course 2 • Chapter 4 Rational Numbers 55
Copy
righ
t ©
The
McG
raw
-Hill
Com
pani
es, I
nc. P
erm
issi
on is
gra
nted
to
repr
oduc
e fo
r cl
assr
oom
use
.Lesson 3 ReteachAdd and Subtract Like Fractions
Like fractions are fractions that have the same denominator. To add or subtract like fractions, add or subtract the numerators and write the result over the denominator.
Simplify if necessary.
Example 1Find 3 −
4 + 1 −
4 . Write in simplest form.
3 −
4 + 1 −
4 = 3 + 1 −−−−
4 Add the numerators.
= 4 −
4 Write the sum over
the denominator.
= 1 Simplify.
Example 2Find 2 −
3 - 1 −
3 . Write in simplest form.
2 −
3 - 1 −
3 = 2 - 1 −−−−
3 Subtract the numerators.
= 1 −
3 Write the difference over
the denominator.
ExercisesAdd or subtract. Write in simplest form.
1. 5 −
8 + 1 −
8 2. 7 −
9 - 2 −
9
3. -
1 −
4 + 3 −
4 4. 7 −
8 - 5 −
8
5. 5 −
9 + 5 −
9 6. – 3 −
8 - 1 −
8
7. 3 −−
10 + 1 −−
10 8. 2 −
5 - 1 −
5
9. 7 −−
15 + 4 −−
15 10. 7 −
9 - 8 −
9
13
23
10
14
12
34
10
3 −
4
5 −
9
1 −
2
1 −
4
1 1 −
9 -
1 −
2
2 −
5
1 −
5
11
−−
15 -
1 −
9
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NAME _____________________________________________ DATE __________________ PERIOD _________
56 Course 2 • Chapter 4 Rational Numbers
Copyright © The M
cGraw
-Hill Com
panies, Inc. Permission is granted to reproduce for classroom
use.Lesson 3 Skills PracticeAdd and Subtract Like Fractions
Add or subtract. Write in simplest form.
1. 3 −
8 + 3 −
8 2. 7 −−
10 -
5 −−
10 3. 9 −−
10 +
3 −−
10
4. 4 −
7 -
2 −
7 5. 2 −
3 +
2 −
3 6. 5 −
9 – 2 −
9
7. 8 −−
15 -
1 −−
15 8. 5 −−
12 + 5 −−
12 9. 7 −−
10 -
3
−−
10
10. 7 −−
16 +
5 −−
16 11. 19 −−
20 -
3 −−
20 12. -
5 −
9 +
7 −
9
13. -
4 −
9 -
1 −
9 14. 2 −
3 +
1 −
3 15. -
3 −
4 -
2 −
4
16. 7 −
8 -
5 −
8 17. 8 −
9 -
5 −
9 18. -
5 −−
12 -
(
-
3 −−
12 )
19. 7 −
9 + 2 −
9 20. 3 −
5 + 4 −
5 21. -
11 −−
12 - 5 −−
12
22. 5 −
6 +
4 −
6 23. 3 −
8 +
5 −
8 24. -
7 −−
16 -
(
-
3 −−
16 )
2 −
7
4 −
5
5 −
6
1 −
5
1 −
3
2 −
5
2 −
9
7 −−
15
3 −
4
-
5 −
9
1 −
4
1 −
3
1
1 1 −
2 1
1 2 −
5
1 1 −
3
1 1 −
5
-1 1 −
4
-
1 −
6
-1 1 −
3
-
1 −
4
1
3 −
4
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NAME _____________________________________________ DATE __________________ PERIOD _________
Course 2 • Chapter 4 Rational Numbers 57
Copy
righ
t ©
The
McG
raw
-Hill
Com
pani
es, I
nc. P
erm
issi
on is
gra
nted
to
repr
oduc
e fo
r cl
assr
oom
use
.Lesson 4 ReteachAdd and Subtract Unlike Fractions
To add or subtract fractions with different denominators,
• Rename the fractions using the least common denominator (LCD).
• Add or subtract as with like fractions.
• If necessary, simplify the sum or difference.
Example
Find 2 −
3 + 1 −
4 .
Method 1 Use a model.
2 −
3
+
1 −
4
11 −−
12
ExercisesAdd or subtract. Write in simplest form.
1. 1 −
2 + 3 −
4 2. 3 −
8 - 1 −
2
3. 7 −−
15 +
(
-
5 −
6 )
4. 2 −
5 - 1 −
3
5. 5 −
9 +
(
-
5 −−
12 )
6. 11 −−
12 - 3 −
4
7. 7 −
8 -
(
-
1 −
3 )
8. 7 −
9 - 1 −
2
9. 3 −−
10 + 7 −−
12 10. 3 −
5 + 2 −
3
Method 2 Use the LCD.
2 −
3 + 1 −
4 = 2 −
3 · 4 −
4 + 1 −
4 · 3 −
3 Rename using the LCD, 12.
= 8 −−
12 + 3 −−
12 or 11 −−
12 Add the fractions.
13
13
14
112
112
112
112
112
112
112
112
112
112
112
1 1 −
4 -
1 −
8
- 11
−−
30
1 −−
15
5 −−
36
1 −
6
1 5 −−
24
5 −−
18
53
−−
60 1
4 −−
15
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NAME _____________________________________________ DATE __________________ PERIOD _________
58 Course 2 • Chapter 4 Rational Numbers
Copyright © The M
cGraw
-Hill Com
panies, Inc. Permission is granted to reproduce for classroom
use.Lesson 4 Skills PracticeAdd and Subtract Unlike Fractions
Add or subtract. Write in simplest form.
1. 8 −−
15 - 1 −
5 2. 5 −
6 + 5 −−
12
3. 3 −
5 - 3 −−
10 4. 7 −−
16 + 3 −
8
5. 19 −−
20 - 3 −−
10 6. 4 −
9 - 1 −−
12
7. 2 −
3 + 3 −
7 8. 3 −
4 + 1 −
7
9. 7 −
8 - 2 −
3 10. 8 −
9 - 5 −
6
11. 5 −−
12 - 3 −−
10 12. 7 −
9 + 2 −
3
13. 3 −
5 + 4 −
7 14. 11 −−
12 - 1 −
2
15. 3 −
4 -
(
- 1 −
2 )
16. - 5 −
6 + 1 −
4
17. - 2 −
3 -
(
-
3 −
4 )
18. 7 −
8 + 1 −−
12
19. -
3 −−
10 + 5 −−
20 20. 7 −−
12 -
(
-
1 −
3 )
1 −
3
3 −−
10
1 2 −−
21
13
−−
20
5 −−
24
7 −−
60
1 6 −−
35
1 1 −
4
1 −−
12
-
1 −−
20
13
−−
36
25
−−
28
13
−−
16
1 −−
18
1 4 −
9
5 −−
12
23
−−
24
11
−−
12
-
7 −−
12
1 1 −
4
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NAME _____________________________________________ DATE __________________ PERIOD _________
Course 2 • Chapter 4 Rational Numbers 59
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righ
t ©
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McG
raw
-Hill
Com
pani
es, I
nc. P
erm
issi
on is
gra
nted
to
repr
oduc
e fo
r cl
assr
oom
use
.Lesson 5 ReteachAdd and Subtract Mixed Numbers
Example 1
Find 6 1 −−
10 + 2 3 −−
10 . Write in simplest form.
6 1 −−
10 Add the whole numbers and the fractions separately.
+ 2 3 −−
10
8 4 −−
10 or 8 2 −
5 Simplify.
Example 2
Find 8 2 −
3 - 6 1 −
2 .
8 2 −
3 8 4 −
6 Rename the fractions using the LCD.
-6 1 −
2 6 3 −
6
2 1 −
6 Subtract.
Example 3
Find 4 1 −
4 - 2 3 −
5 .
4 1 −
4 4 5 −−
20 3 25 −−
20 Rename 4 5 −−
20 as 3 25 −−
20 .
-2 3 −
5 2 12 −−
20 2 12 −−
20
1 13 −−
20 Subtract the whole numbers and then the fractions.
ExercisesAdd or subtract. Write in simplest form.
1. 1 3 −
5 + 4 1 −
5 2. 2 5 −
6 - 1 1 −
6
3. 3 2 −
3 + 2 1 −
2 4. 5 3 −
4 - 3 1 −
6
5. 8 - 6 7 −
8 6. 1 4 −
5 + 3 −−
10
To add or subtract mixed numbers:
• Add or subtract the fractions. Rename using the LCD if necessary.
• Then, add or subtract the whole numbers.
• Simplify if necessary.
5 4 −
5
1 1 −
8
1 2 −
3
2 7 −−
12
2 1 −−
10
6 1 −
6
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NAME _____________________________________________ DATE __________________ PERIOD _________
60 Course 2 • Chapter 4 Rational Numbers
Copyright © The M
cGraw
-Hill Com
panies, Inc. Permission is granted to reproduce for classroom
use.Lesson 5 Skills Practice Add and Subtract Mixed Numbers
Add or subtract. Write in simplest form.
1. 3 2 −
5 + 1 1 −
5 2. 6 7 −−
10 + 12 1 −−
10
3. 5 3 −
8 - 4 1 −
8 4. 3 1 −
2 - 2 1 −
2
5. 7 1 −
4 - 5 3 −
4 6. 8 5 −
6 + 9 5 −
6
7. 2 1 −
2 - 1 1 −
4 8. 3 7 −
8 + 5 3 −
4
9. 2 5 −
6 - 7 −
8 10. 8 1 −
5 + 3 7 −−
10
11. 8 4 −
5 - 2 9 −−
10 12. 3 1 −
4 - 2 5 −
6
13. 4 3 −
5 + 5 1 −
2 14. 10 - 7 7 −
8
4 3 −
5
1 1 −
4
1 1 −
2
1 1 −
4
1 23
−−
24
5 9 −−
10
10 1 −−
10
18 4 −
5
1
18 2 −
3
9 5 −
8
11 9 −−
10
5 −−
12
2 1 −
8
051_068_CC_A_RSPC2_C04_662331.indd Page 60 30/06/11 7:28 PM s-60user051_068_CC_A_RSPC2_C04_662331.indd Page 60 30/06/11 7:28 PM s-60user Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY...Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY...
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