Solved Examples and Worksheet for Estimating Addition and Subtraction of Fractions

Q1Estimate: 32 - 817
A. 1
B. 17
C. 2
D. 3

Solutions
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Step: 1
32 ≈ 1
  [Round to the nearest half.]
Step: 2
817 ≈ 0
  [Round to the nearest half.]
Step: 3
32 - 817 ≈ 1 - 0
  [Subtract the fractions.]
Step: 4
≈ 1
  
Correct Answer is :   1
Q2Estimate: 2372 + 663

A. 0
B. 6
C. 23
D. 72

Solutions
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Step: 1
2372 + 663 ≈ 0 + 0
  [Round to the nearest half.]
Step: 2
= 0
  [Add.]
Step: 3
2372 + 663 ≈ 0
  
Correct Answer is :   0
Q3Estimate the sum of 1626 and 3262.

A. 112
B. 12
C. 2
D. 1

Solutions
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Step: 1
1626 ≈ 12 and 3262 ≈ 12
  [Round the fractions to 12 as the denominators are nearly twice the numerators.]
Step: 2
1626 + 3262 ≈ 12 + 12 = 1
  [Add the fractions.]
Correct Answer is :   1
Q4Estimate.
35 - 14
A. 0
B. 2
C. 3
D. 1

Solutions
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Step: 1
35 ≈ 1
  [Round to 1, if the numerator almost equals the denominator.]
Step: 2
14 ≈ 0
  [Round to 0, if the numerator is close to 0.]
Step: 3
35 - 14 ≈ 1 - 0 = 1
  [Round the fractions and subtract.]
Step: 4
Therefore, 35 - 14 ≈ 1.
Correct Answer is :   1
Q5Estimate.
27 - 19
A. 1
B. 2
C. 0
D. 3

Solutions
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Step: 1
27 ≈ 0
  [Round to 0, if the numerator is close to 0.]
Step: 2
19 ≈ 0
  [Round to 0, if the numerator is close to 0.]
Step: 3
27 - 19 ≈ 0 - 0 = 0
  [Round the fractions and subtract.]
Step: 4
Therefore, 27 - 19 ≈ 0.
Correct Answer is :   0
Q6Alice buys a sack of potatoes that weighs 118 lb and a sack of tomatoes that weighs 127 lb. Estimate the total weight of the vegetables.

A. 2 lb
B. 138 lb
C. 312 lb
D. 4 lb

Solutions
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Step: 1
Weight of potatoes = 118 lb
Step: 2
118 ≈ 1
  [18 is close to 0.]
Step: 3
Weight of tomatoes = 127 lb
Step: 4
127 ≈ 1
  [27 is close to 0.]
Step: 5
Total weight of vegetables = Weight of potatoes + Weight of tomatoes
Step: 6
= 1 + 1 = 2
  [Substitute the values and add.]
Step: 7
So, the weight of the vegetables is about 2 lb.
Correct Answer is :   2 lb
Q7Estimate the sum of 511 and 1011.
A. 112
B. 10111
C. 11011
D. 2111

Solutions
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Step: 1
511 ≈ 12
  [Round to the nearest half.]
Step: 2
1011 ≈ 1
  [Round to the nearest half.]
Step: 3
511 + 1011
  [Sum of the fractions.]
Step: 4
≈ 12 + 1
  
Step: 5
≈ 112
  [Add the rounded fractions.]
Correct Answer is :   112
Q8Estimate the sum of 78 and 56.

A. 4
B. 3
C. 2
D. 1

Solutions
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Step: 1
78 ≈ 1
  [Round to 1, if the numerator almost equals the denominator.]
Step: 2
56 ≈ 1
  [Round to 1, if the numerator almost equals the denominator.]
Step: 3
1 + 1 = 2
  [Round the fractions and add.]
Step: 4
78 + 56 ≈ 1 + 1 = 2
  [Round the fractions and add.]
Step: 5
Therefore, 78 + 56 ≈ 2.
Correct Answer is :   2
Q9Mary has two sewing needles. The length of one needle is 1112 in. and the length of another needle is 178 in. Estimate the sum of the lengths of the two needles.
A. 113 in.
B. 1 in.
C. 3 in.
D. 2 in.

Solutions
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Step: 1
Length of the first needle = 1112 in. ≈ 1 in.
Step: 2
Length of the second needle = 178 in. ≈ 2 in.
Step: 3
The sum of the two needles = 1 + 2 = 3 in.
Step: 4
So, the total length of the two needles is about 3 in.
Correct Answer is :   3 in.
Q10John traveled a distance of 5059 km by his bike and car. He traveled 2079 km by his bike. Estimate the distance he traveled by car.

A. 26 km
B. 30 km
C. 20 km

Solutions
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Step: 1
5059 ≈ 51
  [Because 59 > 12, round up to 51.]
Step: 2
2079 ≈ 21
  [Because 79 > 12, round up to 21.]
Step: 3
5059 - 2079 ≈ 51 - 21 = 30
  [Subtract.]
Step: 4
So, John traveled about 30 km by car.
Correct Answer is :   30 km

HighSchool Math