﻿ Adding Real Numbers Worksheet | Problems & Solutions

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1.
Find the sum.
(- $\frac{5}{9}$) + $\frac{2}{9}$ + (- $\frac{7}{9}$)
 a. - $\frac{10}{9}$ b. - $\frac{1}{9}$ c. - $\frac{14}{9}$

Solution:

(- 5 / 9) + 2 / 9+ (- 7 / 9)
[Original Expression.]

= (- 5 / 9) + (- 7 / 9) + 2 / 9
[Use commutative property.]

= ((- 5 / 9 ) + (- 7 / 9)) + (2 / 9)
[Use associative property.]

= (- 12 / 9) + (2 / 9)

= - 10 / 9

2.
Find the sum.
$2\frac{1}{5}$ + $1\frac{2}{5}$ + $4\frac{1}{5}$
 a. $7\frac{1}{5}$ b. $7\frac{4}{5}$ c. $7\frac{5}{5}$ d. $1\frac{4}{5}$

Solution:

= 115 + 75 + 215
21 / 5 + 12 / 5 + 41 / 5
[Write mixed fraction as improper fraction.]

= (115 + 75 ) + (215)
[Use associative property.]

= 185 + 215

= 395
[Write improper fraction as mixed fraction.]

The sum is 74 / 5.

3.
Find the sum.
(- $\frac{5}{7}$) + $\frac{2}{7}$ + $\frac{9}{7}$
 a. $\frac{6}{7}$ b. - $\frac{7}{6}$ c. - $\frac{6}{7}$ d. $\frac{7}{6}$

Solution:

(- 5 / 7) + 2 / 7 + 9 / 7
[Original Expression.]

= (- 5 / 7) + 9 / 7 + 2 / 7
[Use commutative property.]

= (- 5 / 7 + 9 / 7) + (2 / 7)
[Use associative property.]

= (4 / 7) + (2 / 7)

= 6 / 7

4.
Find the sum.
15 + 39
 a. 44 b. 74 c. 54 d. 64

Solution:

15 + 39
[To add two numbers with same sign, first add their absolute values.]

= 54
[Attach the common sign.]

5.
Find the sum.
16 + (- 64)
 a. 48 b. - 48 c. 58 d. 63

Solution:

To add two numbers with opposite sign, first subtract the smaller absolute value from the larger one and attach the sign of the larger absolute value.

16 + (- 64)

= - ( | - 64 | - | 16 | )

= - (64 - 16)
[Find the absolute value of the numbers.]

= - 48

6.
Find the sum.
- 52 + (- 19)
 a. - 71 b. - 76 c. 76 d. 71

Solution:

To add two numbers with same sign, first add their absolute values and attach the common sign.

- 52 + (- 19)

= - (| - 52 | + | - 19 |)

= - (52 + 19)
[Find absolute value of the numbers.]

= - 71

7.
(- 8 + 6) + 13
 a. 14 b. 16 c. 8 d. 11

Solution:

(- 8 + 6) + 13 = - 8 + (6 + 13)
[Use associative property.]

= - 8 + 19

= 11
[Subtract their absolute values and attach the sign of the number with larger absolute value.]

8.
- 0.9 + 8 + 0.9
 a. 7.1 b. 8 c. 9.8 d. 8.9

Solution:

- 0.9 + 8 + 0.9 = - 0.9 + 0.9 + 8
[Use commutative property.]

= (- 0.9 + 0.9) + 8
[Use associative property.]

= 0 + 8
[Use inverse property.]

= 8
[Use identity property.]

9.
8 + (- $\frac{5}{6}$) + (- $\frac{1}{6}$)
 a. 7 b. 8 c. 10 d. 4

Solution:

8 + (- 56) + (- 16) = 8 + [(- 56) + (- 16)]
[Use associative property.]

= 8 + (- 1)
[Add - 5 / 6 and - 1 / 6.]

= 7

10.
Find the sum.
(- $\frac{2}{5}$) + (- $\frac{3}{5}$) + $\frac{2}{5}$
 a. - $\frac{1}{3}$ b. - $\frac{3}{5}$ c. - $\frac{6}{7}$ d. - $\frac{4}{5}$

Solution:

(- 2 / 5) + (- 3 / 5) + 2 / 5
[Original Expression.]

= - 2 / 5 + 2 / 5 - 3 / 5
[Use commutative property.]

= (- 2 / 5 + 2 / 5) + (- 3 / 5)
[Use associative property.]

= 0 + (- 3 / 5)
[Use inverse property.]

= - 3 / 5
[Use identity property.]