# Reciprocal of a Fraction

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

*Like this:*

## Fractions

A Fraction (such as \frac{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 |
---|---|

\frac{3}{8} | \frac{8}{3} |

\frac{5}{6} | \frac{6}{5} |

\frac{19}{7} | \frac{7}{19} |

\frac{1}{2} | \frac{2}{1} = 2 |

That last example was interesting. The reciprocal of \frac{1}{2} is 2

Likewise the reciprocal of \frac{1}{3} is 3 and so on.

## Multiplying a Fraction by its Reciprocal

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

### Examples:

\frac{5}{6} × \frac{6}{5} = 1

\frac{1}{3} × 3 = 1

## 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 \frac{1}{3} (two and one-third)?

1. Convert it to an improper fraction: 2 \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}

2. Turn it upside down: \frac{3}{7}

**The Answer is: \frac{3}{7}**