Question

Addition of integer and its additive inverse is
(a) Zero
(b) double the number
(c) half the number
(d) none

Answer 1

Hint: Find the definitions of integer and its additive inverse then find the sum of both.

Complete step-by-step solution -
Integer: A number which comes under the category of real numbers which cannot have any fraction part (i.e. we can write that number without any fraction or decimal) is called Integer.
For example, -1, 0, 2, 3 are integers whereas 0.5, \[\sqrt{2},\dfrac{3}{4}\] are not integers
Additive Inverse: In mathematics, the additive inverse of a number is a number that when added to the number yields 0 as the result. The number is also known as the opposite, sign change, and negation of a particular number. For a real number reversing the sign automatically generates the additive inverse of that number.
For example: we have a real number then let p be a number which when added with a yield to 0.
$\begin{align}
  & \Rightarrow a+p=0 \\
 & \Rightarrow p=-a \\
\end{align}$
Then p is the additive inverse of a and its value is $-a$ .
Now let us taken an integer
By above condition additive inverse of integer is (- integer)
By applying this to question, we get:
Integer + additive inverse = integer + (- integer) = 0
So, the sum of an integer and its additive inverse is always 0.

Note: Be careful while writing the definition of additive inverse. In simple words an additive inverse of any number only has an opposite sign by which adding with the given number we get 0 as result.