# Reciprocal of a Fraction

To get the reciprocal of a fraction, just turn it upside down.

*Like this:*

## Fractions

A Fraction (such as^{3}/

_{4}) has two numbers:

\frac{Numerator}{Denominator}

We call the top number the **Numerator**, it is the number of parts we have.

We call the bottom number the **Denominator**, it is the number of parts the whole is divided into.

## Reciprocal of a Fraction

To get the reciprocal of a fraction, just **turn it upside down**.

In other words swap over the Numerator and Denominator.

### Examples:

Fraction | Reciprocal |
---|---|

^{3}/_{8} |
^{8}/_{3} |

^{5}/_{6} |
^{6}/_{5} |

^{1}/_{3} |
^{3}/_{1} = 3 |

^{19}/_{7} |
^{7}/_{19} |

## Reciprocal of a Mixed Fraction

To find the reciprocal of a Mixed Fraction, we must first convert it to an Improper Fraction, then turn it upside down.

### Example: What is the reciprocal of 2 ^{1}/_{3} ?

1. Convert it to an improper fraction: 2 ^{1}/_{3} = ^{7}/_{3}

2. Turn it upside down: ^{3}/_{7}

**The Answer is: ^{3}/_{7}**

## Multiplying a Fraction by its Reciprocal

When we multiply a fraction by its reciprocal we get 1:

### Examples:

^{5}/_{6} × ^{6}/_{5} = 1

^{1}/_{3} × 3 = 1

*That is all. It is just too easy to talk any more about it.*