Before we add or subtract fractions, we try to get them to have the same **denominators**.

We do this by using **lowest common multiples**.

Suppose we wish to subtract:

7 | - | 4 |

9 | 6 |

We look for the smallest number that 9 and 6 go into.

This will be 18, so we change both fractions into 18ths.

We multiply both the numerator and the denominator of 7/9 by 2:

7 | = | 14 |

9 | 18 |

We multiply the numerator and the denominator of 4/6 by 3:

4 | = | 12 |

6 | 18 |

So we now have:

14 | - | 12 |

18 | 18 |

The answer is:

2 | = | 1 |

18 | 9 |

**Example**

When we work out this calculation, what is the lowest common denominator we should choose for both fractions?

7 | - | 4 |

15 | 10 |

**Answer**

The lowest common multiple of 15 and 10 is 30, because 2 × 15 = 30 and 3 × 10 = 30.

So the answer is** 30**.

We need to multiply both the numerator and denominator of 7/15 by 2, which gives us 14/30

We need to multiply both the numerator and denominator of 4/10 by 3, which gives us 12/30

14/30 - 12/30 = **2/30** which can be simplified to **1/15**.

Now it's time to try some questions.