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:

8 | - | 2 |

9 | 5 |

We look for the smallest number that 9 and 5 go into.

This will be 45, so we change both fractions into 45ths.

5 × 9 = 45 and 9 × 5 = 45

We multiply top and bottom of 8 ninths by 5:

8 | = | 40 |

9 | 45 |

We multiply top and bottom of 2 fifths by 9:

2 | = | 18 |

5 | 45 |

So we now have:

40 | - | 18 |

45 | 45 |

The answer is:

22 |

45 |

**Example**

Work out the following, remembering to give your answer in its lowest terms.

2 | + | 3 |

3 | 4 |

**Answer**

The lowest common multiple of 3 and 4 is 12, because 4 × 3 = 3 × 4 = 12.

We multiply top and bottom of 2 thirds by 4:

2 | = | 8 |

3 | 12 |

We multiply top and bottom of 3 quarters by 3:

3 | = | 9 |

4 | 12 |

So we now have:

8 | + | 9 |

12 | 12 |

This gives:

17 |

12 |

But this must be changed to a mixed number.

17 ÷ 12 = 1 remainder 5.

The answer is:

1 | 5 |

12 |