NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 1: Number System - Multiple Choice Questions
Question 14

Question. 14

Which of the following is not the additive inverse of \(a\)?

(a)

–(–a)

(b)

\(a\times(-1)\)

(c)

–a

(d)

\(a\div(-1)\)

Idea: The additive inverse of a number is the number you add to it to get 0.

For (a), the additive inverse is (-a) because:

(a + (-a) = 0)

Check each option:

(a) (-(-a))

First, the negative of (a) is (-a).

Now, the negative of (-a) is (-(-a)).

(-(-a) = a) (a negative of a negative becomes positive).

So (a) equals (a), not (-a). This is not the additive inverse.

(b) (a imes (-1))

(a imes (-1) = -a)

This is the additive inverse.

This is already (-a), so it is the additive inverse.

(d) (a div (-1))

(a div (-1) = -a)

This is the additive inverse.

Answer: (a) (-(-a)) is not the additive inverse of (a) because it equals (a), not (-a).