Question

Find the additive inverse of: $ - 83$

Answer 1

Hint:
Here, we will first write the given number by ignoring its sign. Then, we will put the opposite sign in front of that number to find the required additive inverse. The negative sign is the opposite of the positive sign and vice-versa. Two numbers are called the additive inverse of each other if their sum gives us a zero.

Complete step by step solution:
In order to find the additive inverse of any number, we just write the given number and add a ‘minus’ sign in front of it if the given number is positive. If the given number is negative, we remove the ‘minus’ sign to find the required additive inverse of that particular number.
Here, the given number is $ - 83$
Hence, to find the additive inverse of this given number, we will write the same number but with the opposite sign, i.e. since the given number has a negative sign thus, we will add a positive sign in front of the given number.
Therefore, the required number will become: $ + 83$
Thus, the additive inverse of $ - 83$ is $ + 83$
We can also check this by adding both these numbers together,
Hence, we get,
$ - 83 + 83 = 0$
Therefore, the required additive inverse of $ - 83$ is 83.

Hence, 83 is the required answer.

Note:
Similar to the additive inverse identity, we have another identity i.e. the multiplicative inverse.
According to this, if we are given a number $x$, then, the reciprocal of that number, i.e. $\dfrac{1}{x}$ or ${x^{ - 1}}$ will be its required multiplicative inverse. This is because of the fact that, when we will multiply a given number by its reciprocal, then, both the numbers will cancel out from the numerator as well as the denominator, hence, we will be left with the number 1 as our answer. Thus, the multiplicative identity is 1.