# Multiplicative Inverse / Reciprocal

Multiplicative Inverse / Reciprocal of Fractions Video

### Multiplicative Inverse / Reciprocal of Fractions

The Multiplicative Inverse, or Reciprocal, is one of a pair of numbers that, when multiplied together, equal 1.

$n * \frac{1}{n} = 1$

Let’s look at several examples to better understand what this means:

## ex.1 How to find the reciprocal of a simple fraction.

To find the reciprocal of $\tfrac{5}{7}$ you can just “flip it over”

Therefore, the reciprocal of $\tfrac{5}{7}$ is $\tfrac{7}{5}$

Because $\tfrac{5}{7} * \tfrac{7}{5}$ = 1

So, $\tfrac{5}{7}$ and $\tfrac{7}{5}$ are reciprocal of each other.

## ex.2 How to find the reciprocal of a whole number.

To find the reciprocal of $25$, you must first turn $25$ into a fraction.

$25 = \tfrac{25}{1}$

Therefore, the reciprocal of $25 is$\tfrac{1}{25}$Because$25 * \tfrac{1}{25}$= 1 So,$25$and$\tfrac{1}{25}$are reciprocal of each other. ## ex.3 How to find the reciprocal of a mixed number. To find the reciprocal of 4$\tfrac{2}{3}$you must first turn 4$\tfrac{2}{3}$into a fraction. 4$\tfrac{2}{3} = \tfrac{14}{3}$Therefore the reciprocal of 4$\tfrac{2}{3}$is$\tfrac{3}{14}$Because$\tfrac{14}{3} * \tfrac{3}{14}$= 1 So, 4$\tfrac{2}{3}$and$\tfrac{3}{14}$are reciprocal of each other. ## ex.4 How to find the reciprocal of a negative fraction. To find the reciprocal of$-\tfrac{6}{11}$you can just “flip it over” and keep the sign Therefore, the reciprocal of$-\tfrac{6}{11}$is$-\tfrac{11}{6}$Because$-\tfrac{6}{11} * -\tfrac{11}{6}$= 1 So,$-\tfrac{6}{11}$and$-\tfrac{11}{6}$are reciprocal of each other. ## So, to find the reciprocal of a number. You first turn the number into a fraction,$\color{blue}{n = \tfrac{n}{1}}$Then “flip it over,”$\color{blue}{\tfrac{1}{n}}$These pair of numbers,$\color{blue}{n}$and$\color{blue}{\tfrac{1}{n}}\$, are reciprocals of each other ### A little confused?

You may want to look at:

Mixed Numbers and Fractions

Multiplying by a Negative Number

### Hey!

This might be fun to look at next:

Division of Fractions