Question

How do you know that the additive inverse of $ - 20 $ is $ 20 $ ?

Answer 1

Hint: Additive inverse is the value of a number adding to a number that must yield zero. We will check whether the given number(20) is an additive inverse of 20 by using the below formula.
Formula to be used:
$ a + \left( { - a} \right) = 0 $
Here $ - a $ is the additive inverse of $ a $ .

Complete step by step answer:
An additive inverse of the given number is the number which on adding with the given number results in zero. That is, it is the number when added to a number that results in zero. It is also known as the opposite of the number, changed sign of the number, or negation of the number.
Let $ a $ be the given number and we are asked to find the additive inverse.
We need to just take the negation of the given number $ a $ .
That means $ - a $ is the required additive inverse.
To check whether $ - a $ is the desired inverse, we shall add $ - a $ and $ a $ .
 $ a + \left( { - a} \right) = 0 $ Hence we got zero and $ - a $ is the required additive inverse.
Now, let $ 20 $ be the given number and we are asked to check its additive inverse.
We need to just take the negation of the given number $ 20 $ .
That means $ - 20 $ is the required additive inverse.
To check whether $ - 20 $ is the desired inverse, we shall add $ - 20 $ and $ 20 $ .
 $ 20 + \left( { - 20} \right) = 0 $
Thus, we got zero and $ - 20 $ is the additive inverse of $20$.

Note:
 Suppose we are asked to find the additive inverse of zero. We can think about the negation of zero $ \left( { - 0} \right) $ , but it is not defined in Mathematics. Hence the negation of zero is zero. Now, we need to add zero and negation of zero. Thus, we get $ 0 + 0 = 0 $ and we get zero. Hence, we are able to say that the additive inverse of zero is zero.