*The reciprocal of a number is one divided by that number*

Table of Contents

## Reciprocal of a Fraction

To get the reciprocal of a fraction, simply switch the top and bottom of the fraction (numerator and denominator).

## Reciprocal of a Reciprocal

The reciprocal of a reciprocal takes you back to where we started:

## Examples

Number | Reciprocal | In Decimal | Reciprocal of Reciprocal |

2 | 1/2 | 0.5 | 2 |

4 | 1/4 | 0.25 | 4 |

10 | 1/10 | 0.1 | 10 |

1/2 | 2/1 | 2.0 | 1/2 |

1/4 | 4/1 | 4.0 | 1/4 |

1/10 | 10/1 | 10.0 | 1/10 |

2/3 | 3/2 | 1.5 | 2/3 |

3/4 | 4/3 | 1.33 | 3/4 |

5/6 | 6/5 | 1.2 | 5/6 |

## Not for Zero

Every number except 0 has a reciprocal, because 1/0 is undefined

## Reciprocal is what to multiply a value by to get 1

Try to multiply a number by its reciprocal:

5 × (1/5) = 5 x 0.2 = 1

Another example:

10 × (1/10) = 10 x 0.1 = 1

We always get 1

So:

Multiply a Number by Its Reciprocal Gets Us 1

The reciprocal is also called the “** Multiplicative Inverse**”