Solved Examples and Worksheet for Adding Rational Numbers

Q1Find the sum of - 57 and 67.
A. 14
B. 17
C. 13
D. 25

Solutions
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Step: 1
- 57 + 67
  [Original expression.]
Step: 2
= - 5+67
  [Since the denominators are equal, add the numerators.]
Step: 3
= 17
  
Step: 4
The sum of - 57 and 67 is 17.
Correct Answer is :   17
Q2What is the value of 3 + (- 21)?
A. 18
B. - 18
C. - 24
D. 24

Solutions
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Step: 1
3 + (- 21)
  [Original expression.]
Step: 2
|21| - |3| = 21 - 3
  [Find the difference of absolute values.]
Step: 3
= 18
  [Subtract.]
Step: 4
3 + (- 21) = - 18
  [Since the absolute value of - 21 is greater, the sum is negative.]
Correct Answer is :   - 18
Q3Find the value of - 23 + 56.

A. 49
B. 27
C. 611
D. 16

Solutions
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Step: 1
- 23 + 56
  [Original expression.]
Step: 2
= - 46 + 56
  [Write the equivalent fractions with LCD 6 as the denominator.]
Step: 3
= - 4 + 56
  [Add the numerators.]
Step: 4
= 16
  
Step: 5
The value of the fraction - 23 + 56 is 16.
Correct Answer is :   16
Q4Find the sum of 78 and 89.
A. 7217
B. 12772
C. 78
D. 1517

Solutions
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Step: 1
78 + 89
  [Write the expression.]
Step: 2
The LCM of 8 and 9 is 72, so the LCD of 78 and 89 is 72.
Step: 3
78 + 89= (78 × 99) + (89 × 88)
  [Write equivalent fractions with a denominator of 72.]
Step: 4
= (6372) + (6472)
  [Simplify.]
Step: 5
= 63 + 6472
  [Write the sum over the common denominator.]
Step: 6
= 12772
  [Simplify.]
Step: 7
The sum of 78 and 89 is 12772.
Correct Answer is :   12772
Q5Find the value of - 37 + 9.

A. - 28
B. - 27
C. 29
D. 28

Solutions
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Step: 1
- 37 + 9
  [Original expression.]
Step: 2
|- 37| - |9|
  [Find the difference of the absolute values.]
Step: 3
= 37 - 9 = 28
  [Subtract.]
Step: 4
- 37 + 9 = - 28
  [Since - 37 has the greater absolute value, the sum is negative.]
Correct Answer is :   - 28
Q6What is the value of - 4 + (- 7) + 6 + (- 2)?

A. 9
B. - 10
C. 8
D. - 7

Solutions
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Step: 1
- 4 + (- 7) + 6 + (- 2)
  [Original expression.]
Step: 2
= - 4 - 7 + 6 + (- 2)
  [To add - 7, subtract its opposite, 7.]
Step: 3
= - 4 - 7 + 6 - 2
  [To add - 2, subtract its opposite, 2.]
Step: 4
= - (4 + 7 + 2) + 6
  [Group numbers with same sign.]
Step: 5
= - 13 + 6
  [Add inside the grouping symbols.]
Step: 6
= - 7
  
Correct Answer is :   - 7
Q7What is the value of - 100 + 140 + (- 120) + 100?
A. 40
B. 20
C. 30
D. 10

Solutions
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Step: 1
- 100 + 140 + (- 120) + 100
  [Original expression.]
Step: 2
= - 100 + 140 - 120 + 100
  [To add - 120, subtract its opposite 120.]
Step: 3
= - (100 + 120) + (140 + 100)
  [Group numbers with same sign.]
Step: 4
= - 220 + 240
  [Add inside the grouping symbols.]
Step: 5
= 20
  
Correct Answer is :   20
Q8Find the sum.
313 + 415
A. 11315
B. 11516
C. 11416
D. 11415

Solutions
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Step: 1
313 + 415
  [Original expression.]
Step: 2
= 103 + 215
  [Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 3 and 5 is 15, so the LCD of 103 and 215 is 15.
Step: 4
103 + 215 = 5015 + 6315
  [Write equivalent fractions with a denominator of 15.]
Step: 5
= 50+6315
  [Write the sum over the common Denominator.]
Step: 6
= 11315.
  [Simplify.]
Correct Answer is :   11315
Q9A person has done 310 of a job in one week. The next week, he is only able to complete 110 of the job. Find the fraction of work he completed in the two weeks.
A. 18
B. 25
C. 16
D. 17

Solutions
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Step: 1
Work done by the person in the first week = 310
Step: 2
Work done by the person in the second week = 110
Step: 3
Total work done by the person in the past two weeks = 310 + 110
Step: 4
3 + 1 = 4
  [Denominators are equal. So, add the numerators.]
Step: 5
310 + 110 = 410
  
Step: 6
410 = 25
  [Divide.]
Step: 7
The work done by the person during the two weeks = 25.
Correct Answer is :    25
Q10What is the value of the expression 10 + (- 11) + (- 37)?

A. -43
B. -38
C. -36
D. 48

Solutions
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Step: 1
10 + (- 11) + (- 37)
  [Original expression.]
Step: 2
= 10 - 11 + (- 37)
  [To add - 11, subtract its opposite, 11.]
Step: 3
= 10 - 11 - 37
  [To add - 37, subtract its opposite, 37.]
Step: 4
= 10 - (11 + 37)
  [Combine the negative numbers.]
Step: 5
= 10 - 48
  [Add inside the grouping symbols.]
Step: 6
= -38
  [Simplify.]
Correct Answer is :   -38
Q11Find the sum.
513 + 615
A. 17315
B. -1316
C. 18815
D. 15815

Solutions
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Step: 1
513 + 615
  [Original expression.]
Step: 2
= 163 + 315
  [Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 3 and 5 is 15, so the LCD of 163 and 315 is 15.
Step: 4
163 + 315 = 8015 + 9315
  [Write equivalent fractions with a denominator of 15.]
Step: 5
= (80+93)(15)
  [Write the sum over the common Denominator.]
Step: 6
= 17315
  [Simplify.]
Correct Answer is :   17315
Q12Jake and Henry are painting the fence. Jake painted 312 of it and Henry painted 512 of it. What fraction of the fence is painted?

A. 23
B. 212
C. 57
D. 73

Solutions
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Step: 1
Fraction of fence painted = Fraction of fence painted by Jake + Fraction of fence painted by Henry
= 312 + 512
  [Substitute the values.]
Step: 2
= 3 + 512
  [Write the sum of the numerators over common denominator.]
Step: 3
= 812 = 23
  [Simplify the fraction.]
Step: 4
So, 23 of the fence is painted.
Correct Answer is :   23
Q13What is the value of 2 + (- 11)?
A. 2
B. - 9
C. 13
D. - 22

Solutions
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Step: 1
To add two integers with different signs, consider the numbers as whole numbers and find their difference. Put the sign of the larger number to the result.
Step: 2
2 + (- 11)
  [Original equation.]
Step: 3
11 - 2 = 9
  [Consider the numbers as whole numbers and find their difference.]
Step: 4
2 + (- 11) = - 9
  [As the larger number has negative sign, the result will also be negative.]
Correct Answer is :   - 9
Q14What is the value of n + (- 57), when n = 11?

A. - 50
B. 46
C. - 46
D. 50

Solutions
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Step: 1
n + (- 57)
  [Original expression.]
Step: 2
= 11 + (- 57)
  [Substitute 11 for n.]
Step: 3
= - 46
  [When two integers with different signs are added, the sum has the sign of the integer with the greater absolute value.]
Correct Answer is :   - 46
Q15What is the value of the expression, 5 + (- 47) + (- 4)?
A. 46
B. 51
C. - 46
D. - 51

Solutions
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Step: 1
5 + (- 47) + (- 4)
  [Original expression.]
Step: 2
= 5 - 47 + (- 4)
  [To add - 47, subtract its opposite, 47.]
Step: 3
= 5 - 47 - 4
  [To add - 4, subtract its opposite, 4.]
Step: 4
= 5 - (47 + 4)
  [Combine the negative numbers.]
Step: 5
= 5 - 51
  [Add inside the grouping symbols.]
Step: 6
= - 46
  [Simplify.]
Correct Answer is :   - 46

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