Question

Find the additive inverse of: $256$

Answer 1

Hint: In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation.

Complete step-by-step solution:
Here we have given, the number $256$

The inverse property of addition states that adding a number and the opposite sign of that number is zero, gives us the additive inverse of that number.
$ \Rightarrow $Given number is $256$,
According to definition, adding a negative of the number that is $ - $$256$ will give us Zero.
$ \Rightarrow $So, $256 + \left( { - 256} \right) = 0$
$ \Rightarrow $Hence, $ - $$256$ is the additive inverse of $256$.

Note: Properties of additive inverse are given below, based on negation of original number.
For example, $x$is the original number and $ - x$is the negation. So the properties of $ - x$are given,
\[ \Rightarrow - \left( { - x} \right){\text{ }} = {\text{ }}x\]
$ \Rightarrow {\left( { - x} \right)^2}\; = {\text{ }}{x^2}$
$ \Rightarrow - \left( {x{\text{ }} + {\text{ }}y} \right){\text{ }} = {\text{ }}\left( { - x} \right){\text{ }} + {\text{ }}\left( { - y} \right)$
$ \Rightarrow - \left( {x{\text{ }}-{\text{ }}y} \right){\text{ }} = {\text{ }}y{\text{ }} - {\text{ }}x$
$ \Rightarrow \left( { - x} \right)\, \times \,y{\text{ }} = {\text{ }}x\, \times \,\left( { - y} \right){\text{ }} = {\text{ }} - \left( {x\, \times \,y} \right)$
$ \Rightarrow \left( { - x} \right){\text{ }} \times {\text{ }}\left( { - y} \right){\text{ }} = {\text{ }}x{\text{ }} \times {\text{ }}y$.