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Name
LESSON
Date
Class
Practice C
5-7 Adding and Subtracting with Unlike Denominators
Evaluate. Write each answer in simplest form.
11
3
! ! !!
1. !12
5
7
5
2. !1!
" !1!
2
6
3
5
3. !6! ! !1!
0
3
3
4. !4! " !1!
4
5
1
5. !2! ! !1!
7
4
2
6. !5! " !9!
5
7
7. !8! " !1!
2
3
5
8. !1!
! !6!
6
3
5
9. !1!
! !3!
6
2
11
4
1
! " !! ! !!
10. !12
9
2
2
7
2
! ! " !!
11. !1!
!
5
25
5
3
1
4
!! ! !!
12. !1!
"
4
8
7
2
Evaluate each expression for b # !5!. Write your answers in
simplest form.
9
7
14. !1!
"b
2
11
!"b
15. !16
8
4
17. !7! " b
14
!!b
18. !15
13. b ! !1!
4
16. b ! !1!
1
6
!
19. Ben, Shaneeka, and Phil live on the same street. Ben lives !
11
1
mile north of Phil, and !3! mile north of Shaneeka. How far does
Shaneeka live from Phil?
5
20. At the frog-jumping contest, Trevor’s frog jumped !6! foot and
5
4
1
then !9! foot. Mei’s frog jumped !5! foot and then !2! foot. Whose
frog jumped the farthest in all? How much farther?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
65
Holt Middle School Math Course 1
Reteach
5-7 Adding and Subtracting with Unlike Denominators
Practice C
5-7 Adding and Subtracting with Unlike Denominators
LESSON
LESSON
Evaluate. Write each answer in simplest form.
7
5
! " !!
2. !
12
16
11
3
! ! !!
1. !
12
5
31
2
13
!!
48
1!6!
0
1!1!
5
To add or subtract unlike fractions, first find the LCD of the fractions.
3
3
4. !4! " !1!
4
5
1
!
5. !2! ! !
17
4
2
6. !5! " !9!
5
7
!
7. !8! " !12
3
5
! ! !!
8. !
16
6
3
5
! ! !!
9. !16
32
15
!!
28
27
!!
34
11
!!
24
11
4
1
1
35
!!
36
2
1
A. !3! ! !4!
26
!!
45
2
7
2
! ! ! ! " !!
11. !
15
25
5
1
!!
75
Multiples of 4: 4, 8, 12,…
Multiples of 3: 3, 6, 9, 12,…
The LCD is 12.
11
!!
32
1!48!
! " !! ! !!
10. !
12
9
2
Unlike fractions have different denominators. To add and subtract
fractions, you must have a common denominator. The least common
denominator (LCD) is the least common multiple of the
denominators.
3
5
!
3. !6! ! !
10
Next, use fraction strips to find equivalent fractions.
3
1
4
12. !1!
" !8! ! !7!
4
1
3
37
!!
56
simplest form.
9
3
7
!"b
14. !
12
11
15. !1!
"b
6
4
17. !7! " b
14
18. !1!
!b
5
11
!!
60
1!7!
0
8
16. b ! !1!
1
7
1!5!
5
Then use fraction strips to find the sum or difference.
1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12
23
!!
80
6
!!
35
1
1!3!
6
1
1
1. !4! ! !8!
5
2
2. !6! " !3!
3
1
3. !4! " !3!
3
3
!
4. !5! ! !10
3
1
5. !4! ! !6!
1
3
6. !2! ! !8!
2
1
7. !3! " !6!
1
1
8. !3! " !4!
3
!!
8
5
20. At the frog-jumping contest, Trevor’s frog jumped !6! foot and
5
4
1
then !9! foot. Mei’s frog jumped !5! foot and then !2! foot. Whose
11
!!
12
frog jumped the farthest in all? How much farther?
Trevor’s frog; !4! foot farther
45
Holt Middle School Math Course 1
Challenge
5-7 Egyptian Fractions
5
!!
12
1
!!
6
7
!!
8
1
!!
12
1
!!
2
66
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
9
!!
10
Holt Middle School Math Course 1
Problem Solving
5-7 Adding and Subtracting with Unlike Denominators
LESSON
LESSON
Use the circle graph to answer the questions. Write each
answer in simplest form.
Did you know that ancient Egyptians used fractions 5,000 years
ago? Some of their fractions were like the ones we use today.
However, the Egyptians only used unit fractions, or fractions with a
numerator of 1. All other fractions had to be written as a sum of unit
fractions. And no sum could repeat the same unit fraction! For
1. On which two continents do most
people in the world live? How much
of the total population do they make
up together?
3
1
1
example, the Egyptians would write !4! as !2! ! !4!. They would not
1
1
1
write !4! ! !4! ! !4!.
World Population, 2001
1
25
1
10
2
25
Asia and Europe; !18! of the
3
50
25
population
Ancient Egyptians did not have paper. They recorded their math
work on papyrus, or thin strips of dried plants. Study the
Egyptian fractions recorded on the papyrus scrolls below. Then
write each fraction the way we do today.
3
5
2. How much of the world’s population
live in either North America or South
America?
1.
1
1
!! ! !!
2
6
12 12 12
Use fraction strips to find each sum or difference. Write your
answer in simplest form.
7
!! of a mile
33
65
! 1 1 1
8
3
11
!! ! !! # !!
12
12
12
2
1
11
!.
So, !3! ! !4! # !
12
!
19. Ben, Shaneeka, and Phil live on the same street. Ben lives !
11
1
mile north of Phil, and !3! mile north of Shaneeka. How far does
Shaneeka live from Phil?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
1 1 1
12 12 12
1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12
2
Evaluate each expression for b # !5!. Write your answers in
13. b ! !1!
4
1
4
1
3
3
25
Africa
North America
South America
Europe
Asia
Other
7
!! of the population
50
2
!!
3
3. How much more of the world’s total
population lives in Asia than in Africa?
1
!! of the population
2
2.
1
1
1
!! ! !! ! ! !
2
4
20
4
!!
5
4. How much of Earth’s total population
do people in Asia and Africa make up
all together?
5. What is the difference between North
America’s part of the total population
and Africa’s part?
7
!! of the population
10
3.
1
1
!! ! !!
2
3
5
!!
6
50
Circle the letter of the correct answer.
6. How much more of the population
lives in Europe than in North
America?
4.
1
1
!! ! !!
4
8
Africa has !1! more.
7. How much of the world’s population
lives in North America and Europe?
1
! of the population
F !
25
1
! of the population
A !
!
25
3
!!
8
1
! of the population
G!
15
1
B !5! of the population
1
H !5! of the population
!
1
! of the population
C !
15
1
1
1
!! ! !! ! ! !
2
3
15
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
9
!!
10
67
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
1
! of the population
J !
20
1
! of the population
D !
10
5.
Holt Middle School Math Course 1
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
123
68
Holt Middle School Math Course 1
Holt Middle School Math Course 1