freeCodeCamp/guide/english/mathematics/reciprocal/index.md

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Reciprocal

Reciprocal

The reciprocal of a number is 1 divided by that number. Every non-zero number has a reciprocal, and 0 does not.

Example

The reciprocal of 3 is 13.

You can also get the reciprocal of a fraction by flipping the fraction, or equivalently, the reciprocal of a number can be defined as that number taken to the power of -1.

Example

The reciprocal of 23 is 32 since 1/(23) = 3/2, or (23)-1 = 3/2.

Note

  1. The reciprocal of the reciprocal of a number is the original number.

Example

The reciprocal of 23 is 123. Now if we look at the reciprocal of 123 we get 231, which is the original number.

  1. If you multiply a non-zero number by its reciprocal, you always get 1.

Example

The reciprocal of 16 is 116. If you multiply 116 by 16, you get 1.