Question

Verify a – (– b) = a + b for the following values of a and b.
(i) a = 21, b = 18
(ii) a = 118, b = 125
(iii) a = 75, b = 84
(iv) a = 28, b = 11
NCERT Class 7th Mathematics Chapter 1 Integers

Answer 1

1). 21-(-18)=21+18=39
a+b=21+18=39.

2).118-(-125)=118+125=243
a+b=118-125=243.

3). 75-(-84)=75+84=159
a+b=75+84=159.

4). 28-(-11)=28+11=39
a+b=28+11= 39.

Answer 2

Answer:

The expression $a-(-b)=a+b$ is verified from the given values of a and b.

Solution:

Given that

$\begin{array} { l } { a - ( - b ) = a + b } \\\\ { ( i ) } \\\\ { a = 21 , b = 18 } \\\\ { L H S = a - ( - b ) = 21 - ( - 18 ) } \\\\ { = 21 + 18 } \\\\ { a - ( - b ) = 39 } \\\\ { R H S = a + b = 21 + 18 = 39 } \end{array}$

$\begin{array} { l } { \text { (ii) } } \\\\ { \mathrm { a } = 118 , \mathrm { b } = 125 } \\\\ { \mathrm { LHS } = \mathrm { a } - ( - \mathrm { b } ) = 118 - ( - 125 ) } \\\\ { = 118 + 125 } \\\\ { \mathrm { a } - ( - \mathrm { b } ) = 243 } \\\\ { \mathrm { RHS } = \mathrm { a } + \mathrm { b } = 118 + 125 = 243 } \end{array}$

$\begin{array} { l } { \text { (iii) } } \\\\ { \mathrm { a } = 75 , \mathrm { b } = 84 } \\\\ { \mathrm { LHS } = \mathrm { a } - ( - \mathrm { b } ) = 75 - ( - 84 ) } \\\\ { = 75 + 84 } \\\\ { a - ( - b ) = 159 } \\\\ { R H S = a + b = 75 + 84 = 159 } \end{array}$

$\begin{array} { l } { \text { (iv) } } \\\\ { \mathrm { a } = 28 , \mathrm { b } = 11 } \\\\ { \mathrm { LHS } = \mathrm { a } - ( - \mathrm { b } ) = 28 - ( - 11 ) } \\\\ { = 28 + 11 } \\\\ { \mathrm { a } - ( - \mathrm { b } ) = 39 } \\\\ { \mathrm { RHS } = \mathrm { a } + \mathrm { b } = 28 + 11 = 39 } \end{array}$

Hence, in all the terms we can find that the LHS is equal to the RHS.

Hence $a-(-b)=a+b$ is verified.