# Multiplicative inverse definition explained with examples

Learn what is the meaning of multiplicative inverse in math? In the lower classes this concept plays a crucial role in mathematics. There is an other name for multiplicative inverse, that is, it is also called as reciprocal. Which means we can also call a multiplicative inverse as a reciprocal.

The Definition of the multiplicative inverse as follows: suppose if the product of any two numbers or fractions or decimals is equals to “1” then each is called as multiplicative inverse of the other. Finding the multiplicative inverse for numbers, fractions and decimals are explained in detail with examples. So go through them and learn.

## How do we find the multiplicative inverse for the any given numbers in math?

Let us consider one number say “g” then $\frac { 1 }{ g }$ is called as the multiplicative inverse of “g”.

Example:

If the given number is 7 then the multiplicative inverse is equal to $\frac { 1 }{ 7 }$.

The multiplicative inverse of the number 54 is $\frac { 1 }{ 54 }$ .

## How do we find the multiplicative inverse for the any given fractions

Let $\frac { m }{ n }$ be a fraction then $\frac { n }{ m }$ is called as the multiplicative inverse of $\frac { m }{ n }$.

Example

If $\frac { 8 }{ 17 }$ is a fraction then $\frac { 17 }{ 8 }$ is called as multiplicative inverse of $\frac { 8 }{ 17 }$

$\frac { 316 }{ 17 }$ is the multiplicative inverse of $\frac { 17 }{ 316 }$

## The Method to find the Multiplicative inverse for the any given decimals as follows?

If we want to find multiplicative inverse of a decimal, first the decimal as a fraction (learn how to convert decimals to fractions) then find its multiplicative inverse.

Example:

The decimal 3.2 is written as $\frac { 32 }{ 10 }$  . so the multiplicative inverse of $\frac { 32 }{ 10 }$  is $\frac { 10 }{ 32 }$

9.47 is written as $\frac { 947 }{ 100 }$  , so multiplicative inverse of $\frac { 947 }{ 100 }$  is $\frac { 100 }{ 947 }$

## How to find the multiplicative inverse for the given mixed fractions?

If we need to find the multiplicative inverse of a mixed fraction. Convert mixed fraction as improper fraction (learn how to convert mixed fraction to improper fraction) then find its multiplicative inverse.

Example:

2$\frac { 4 }{ 7 }$ is a mixed fraction. So, covert the given mixed fraction as the improper fraction. In improper fraction, 2$\frac { 4 }{ 7 }$ is written as  $\frac { 18 }{ 7 }$ .

Therefore, the multiplicative inverse of $\frac { 18 }{ 7 }$  is $\frac { 7 }{ 18 }$

Hope now you have understood how to find multiplicative inverse clearly.