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

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title: Reciprocal
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## 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 <sup>1</sup>⁄<sub>3</sub>.

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 <sup>2</sup>⁄<sub>3</sub> is <sup>3</sup>⁄<sub>2</sub> since 1/(<sup>2</sup>⁄<sub>3</sub>) = <sup>3</sup>/<sub>2</sub>, or (<sup>2</sup>⁄<sub>3</sub>)<sup>-1</sup> = <sup>3</sup>/<sub>2</sub>.

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

#### Example 

The reciprocal of 23 is <sup>1</sup>⁄<sub>23</sub>. Now if we look at the reciprocal of <sup>1</sup>⁄<sub>23</sub> we get <sup>23</sup>⁄<sub>1</sub>, which is the original number.

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

#### Example 

The reciprocal of 16 is <sup>1</sup>⁄<sub>16</sub>. If you multiply <sup>1</sup>⁄<sub>16</sub> by 16, you get 1.