data-ad-format="horizontal">



 

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'.

While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at   patreon.com/mathopenref

Other fractions, percents, ratios topics