﻿ Adding and Subtracting Positive and Negative Numbers Worksheet | Problems & Solutions

# Adding and Subtracting Positive and Negative Numbers Worksheet

Adding and Subtracting Positive and Negative Numbers Worksheet
• Page 1
1.
Find the difference.
(- 53) - 48
 a. - 101 b. - 111 c. - 13 d. - 5

#### Solution:

(- 53) - 48
[Original expression.]

= (- 53) + (- 48)
[Since opposite of 48 is - 48.]

Add 53 and 48. Keep the sign as negative.
(- 53) + (- 48) = - 101

Therefore, (- 53) - 48 = - 101.

2.
What is the value of the expression - 82 - (- 4)?
 a. 86 b. 78 c. - 78 d. - 86

#### Solution:

- 82 - (- 4)
[Original expression.]

= - 82 + 4
[To subtract - 4, add its opposite, 4.]

= 4 + (- 82)
[Since - 82 has greater absolute value, the sum is negative.]

= - 78
[Simplify.]

3.
What is the value of 8 + (- 23)?
 a. 31 b. - 15 c. 15 d. - 31

#### Solution:

8 + (- 23)
[Original expression.]

|23| - |8| = 23 - 8
[Find the difference of absolute values.]

= 15
[Subtract.]

8 + (- 23) = - 15
[Since the absolute value of - 23 is greater, the sum is negative.]

4.
During selection trials for the Olympic games, the qualifying time set for 100 meters sprint is 11 seconds. Nina's current speed for 100 meters dash is 16 seconds. How much time should Nina save in order to qualify?
 a. 4 seconds b. 6 seconds c. 5 seconds d. 7 seconds

#### Solution:

Nina takes 16 seconds, but the time to qualify is 11 seconds.

So, the time to be saved = 16 - 11

= 16 + (- 11)
[To subtract 11, add its opposite.]

= 5

Nina should save 5 seconds in order to qualify for the Olympic games.

5.
Quincy had $368. She spent$197 on her birthday. What was the amount she was left with?
 a. $241 b.$146 c. $221 d.$171

#### Solution:

Quincy spent $197 out of$368.

So, the remaining amount = 368 - 197

= 368 + (- 197)
[To subtract 197, add its opposite.]

= $171 [Add.] So, Quincy is left with$171.

6.
What is the value of 11 - (- 7)?
 a. - 18 b. 4 c. - 4 d. 18

#### Solution:

11 - (- 7)
[Original expression.]

11 + 7 = 18
[To subtract - 7, add its opposite, 7.]

7.
What is the value of 69 - |- 18|?
 a. - 51 b. 87 c. 56 d. 51

#### Solution:

69 - |- 18|
[Original expression.]

= 69 - (18)
[Absolute value of -18 is its distance from 0 on the number line, which is 18.]

= 69 + (- 18)

[To subtract 18, add its opposite, - 18.]

= 51
[Simplify]

8.
Find the common difference and the next four terms for the series. 7, 5, 3, 1...
 a. common difference = -2 and the next terms of the series are -1, -3, -5 and -8 b. common difference = -2 and the next terms of the series are -1, -3, -6 and -7 c. common difference = -2 and the next terms of the series are -1, -3, -5 and -7 d. None of the above

#### Solution:

7, 5, 3, 1...
[Original series.]

The common difference is the difference between two consecutive terms of the series.

5 - 7 = - 2, 3 - 5 = - 2, 1 - 3 = - 2
[Common difference.]

To get the next terms of the series add the common difference to the last term of the series.

1 + (- 2) = -1, -1 + (- 2) = -3, -3 + (- 2) = -5 and -5 + (- 2) = -7

The next four terms of the series are -1, -3, -5 and -7.

9.
What is the value of 3 + (- 10)?
 a. - 7 b. - 30 c. 13 d. 3

#### Solution:

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.

3 + (- 10)
[Original equation.]

10 - 3 = 7
[Consider the numbers as whole numbers and find their difference.]

3 + (- 10) = - 7
[As the larger number has negative sign, the result will also be negative.]

10.
What is the value of |- 83| + |- 22|?
 a. - 105 b. - 61 c. 61 d. 105

#### Solution:

|- 83| + |- 22|
[Original equation.]

|- 83| = 83
[Absolute value of 83 is its distance from 0 on the number line and distance is always positive.]

|- 22| = 22
[Absolute value of 22 is its distance from 0 on the number line and distance is always positive.]

83 + 22 = 105
[Simplify]