Reciprocal

Formally: The reciprocal of a number is the number you multiply it by to get 1 (one).

So, for example the reciprocal of 2 is a half, since two times one half is one:

But in most cases there is a simpler way to find the reciprocal:

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 is that number.)

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:

Calculator

If you do it twice

If you take the reciprocal twice, you get what you started with. Foe example:

and

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