Reteaching
Name
9-4
Estimating Sums and
Differences of Fractions
To estimate the sum or difference of two fractions, replace each
fraction with the nearest half or whole. You can use a number line
to check whether each fraction is closest to 0, _​ 12  ​, or 1. Estimate
3
 ​+ ___
​ 9   ​.
the sum of ​ __
8
16
Step 1: Find ​ _38 ​ on the number line. Is _​ 38 ​ closer to 0 or _​ 12  ​? 3
8
0
1
1
2
9
9
Step 2: Find __
​ 16
  ​ on the number line. Is __
​ 16
  ​ closer to _
​ 12  ​or to 1?
9
16
0
1
1
2
Step 3: Add to find the estimate. __
​ 1 ​+ __
​ 1 ​= 1.
2
2
For 1 and 2, complete each sentence to help you replace each
fraction with the nearest half or whole. Use each number line to help.
7 ​is between
1. ​ __
8
but
. __
​ 7 ​rounds to
8
is closer to
0
and
1
2
5
2. ​ ___
  ​ is between
and
16
. ___
​ 5  ​ rounds to
is closer to
0
1
but
16
1
2
1
For 3 through 10, estimate each sum or difference by replacing
each fraction with 0, _​ 12 ​,  or 1.
3. __
​ 25 ​+ __
​ 3 ​
4
7 ​– __
4. ​ __
​ 4 ​
5. __
​ 1 ​+ __
​ 47 ​
​ 6  ​ 
7. ___
​ 7  ​ + ___
2 ​– __
8. ​ __
​ 4 ​
9. __
​ 2 ​+ __
​ 45 ​
15
10
8
3
9
2
8
9
R 9•4
7  ​ – __
6. ​ ___
​ 4 ​
12
9
10. __
​ 7 ​– __
​ 5 ​
8
6
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Practice
Name
9-4
Estimating Sums and
Differences of Fractions
In 1 through 8, tell if each fraction is closest to 0, _​ 12 ​,  or 1. You may
use a number line to help.
1 ​ 1.​ __
5
2.​ __
 ​ 6
5.​ __
 ​ 7
5
6.​ ___
  ​  
9
11  ​ 3.​ ___
9
3
7.​ __
 ​ 12
20
4
6
4.​ ___
   ​ 10
12  ​ 8.​ ___
15
In 9 through 16, estimate each sum or difference by replacing
each fraction with 0, _​ 12 ​,  or 1.
​ 45 ​
9. ___
​ 7   ​+ __
1  ​ + __
10.​ ___
​ 2 ​
4 ​– __
11.​ __
​ 1 ​
2 ​+ __
12. ​ __
​ 8 ​
1 ​– __
13.​ __
​ 1 ​
2 ​– __
14.​ __
​ 3 ​
5 7
7 ​– __
15.​ __
​ 7 ​
5
16.​ ___
  ​ + __
​ 25 ​
12
6
8
12
4
9
8
17. Which is the best estimate for the
9
  ​ – _
​ 49 ​?
 
difference of __
​ 16
A 1 – 1 = 0
C 1 – __
​ 1 ​= __
​ 1 ​
1 ​– __
B​ __
​ 1 ​= 0
2 2
D 0 – 0 = 0
2
6
9
6
9
12
18. Which fraction can NOT be
replaced with _​ 12 ​ when estimating?
10
A​ ___
  ​
2
12
__
B​ 2 ​
6
C ___
​ 4  ​ 
10
___
D ​ 13  ​
24
19.Mia estimated _​ 58  ​+ _​ 19 ​ by replacing _​ 58 ​ with 1 and _​ 19 ​ with 0. Her
estimated sum was 1 + 0 = 1. Explain why Mia’s estimate is
NOT accurate.
P 9•4
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5