Question

The sum of an integer and its additive inverse is always………
A) $1$
B) $ - 1$
C) $0$
D) $2$

Answer 1

Hint: According to the question we have to determine that sum of an integer and its additive inverse. So, first of all we have to understand about additive inverse of an integer which is explained below:
Additive inverse: The additive inverse of a number is a number that, when added to a integer it becomes or yields zero and this number is also known as the opposite, sign change, and negation and for a real number, it reverse its sign the opposite to a positive number or integer is negative and the opposite to a negative number is positive.

Complete step-by-step solution:
Step 1: First of all as mentioned in the solution hint we have to let a number or positive integer,
Let the positive integer is a
Step 2: Now, we have to find the additive inverse of the number we let in the solution step 1. Hence,
Additive inverse of a is = -a
Step 3: Now, we have to find the sum of integer a, and its additive inverse,
$
   = a + ( - a) \\
   = a - a \\
   = 0
 $
Hence, as explained in the solution hint we have determined the sum of an integer and its additive inverse is always zero.

Therefore option (C) is correct.

Note: To find the additive inverse of a number or integer we just need to convert the sign of that given integer mean if the sign of the given integer is positive then the converted sign will be negative and vice-versa.