### 3.2 Dividing fractions

Whilst multiplying fractions looks very much like adding or subtracting, it is not quite so easy to see how you can divide one fraction by another:

( | 5 | ) | ÷ | ( | 3 | ) | = | ( | 5 | ) | / | ( | 3 | ) |

8 | 4 | 8 | 4 |

This expression is a fraction itself, with the numerator equal to:

5 |

8 |

And the denominator equal to:

3 |

4 |

By analogy with multiplication, the answer should look like this:

( | 5 | ) | ÷ | ( | 3 | ) | = | (5 ÷ 3) |

8 | 4 | (8 ÷ 4) |

However, it is quite likely that either the numerator or denominator will not be a whole number - in this case the numerator is equal to:

1 | 2 |

3 |

The way to solve this is to turn the sum into a multiplication, and this is done by inverting the denominator:

( | 5 | ) | ÷ | ( | 3 | ) | = | ( | 5 | ) | × | ( | 4 | ) | = | (5 × 4) | = | 20 | = | 5 |

8 | 4 | 8 | 3 | (8 × 3) | 24 | 6 |

For the purists, we can write this expression as:

( | 5 | ) | ÷ | ( | 3 | ) | = | ( | 5 | ) | × | ( | 3 | ) | ^{-1} |
= | ( | 5 | ) | × | ( | 4 | ) |

8 | 4 | 8 | 4 | 8 | 3 |