# Additive inverse of a number explained

Learn and know what is additive inverse in mathematics and know how to find additive inverse of a any number.

In the lower classes of mathematics, additive identity, multiplicative identity, multiplicative inverse (reciprocal), additive inverse are most important concepts. All these four are very simple concepts which we can understand easily. Now we will learn about what is additive inverse? How to find additive inverse for any number, fractions and for a rational number.

## What is meant by the additive inverse in math?

First we will know the meaning of additive inverse. We have a very simple meaning i.e. for any number if we add another number such that the result should become zero. Each of these numbers will be additive inverse of other number.

For example, consider number 8. So now we need to add another number such that result should become zero. Can you say what is that number we need to add? We need to add -8 because 8 + (-8) =0. So now we say that the additive inverse of 8 is -8 and also the additive inverse of -8 is 8.

## How do we write the additive inverse for numbers?

To find additive inverse of a number there exists 2 methods. In first method, just writing the opposite sign to the given number.

For example, the additive inverse of 9 will be -9.

In the second method, for the given number add a any variable and make it equal to zero (0). Then find variable value. Here variable value will be additive inverse of the given number.

For example, let us take a number. Am considering -2. So add a variable to -2 and make it equal to zero and simplify for variable.

-2 + y = 0

Y = 2

Now we say that additive inverse of -2 is 2 or additive inverse of 2 is -2.

## How do we find Additive inverse of any given fraction?

The method for finding additive inverse of a fraction is same as the methods which we applied in the above. Just change the sign of a fraction or add a variable to the given fraction and make it equal to zero then find variable value.

For example, if $\frac { 2 }{ 3 }$ is a fraction then the $\frac { -2 }{ 3 }$ will be the additive inverse of that fraction.

## How do we find additive inverse of any given rational numbers?

Additive inverse of rational numbers also follows the above given methods only. Just changing the sign will give you additive inverse of rational numbers.

For example, $\frac { -5 }{ 7 }$ is a rational number then $\frac { 5 }{ 7 }$ will be additive inverse of that rational number.