# Reciprocal

The reciprocal of a number is one divided by that number. Formally

So, for example the reciprocal of 4 is one quarter:

## Reciprocal of a fraction

To find the reciprocal of a fraction, simply exchange the top and bottom of the fraction (numerator and denominator). For example: (Recall that any number divided by one leaves it unchanged.)

## Reciprocal of a number

The reciprocal of a number is one over that number. So for example the reciprocal of 6 is one over 6: This is really the same as the previous case since a number can be written as a fraction with a denominator) of one. For example and so

## Reciprocal of a decimal

This is treated the same as a number. It is one over that number. For example: If you use a calculator to divide one by 1.38 you will get 0.725, so:

## If you do it twice

If you take the reciprocal twice, you get what you started with. For example: and if you take the reciprocal again: which is what we started with.

## Other notation

The reciprocal of a number is sometimes expressed as the number raised to the power of negative one: Raising any quantity the power of -1 is the same as taking its reciprocal.

The reciprocal of a number is also sometimes called its 'multiplicative inverse'.