### 2.2 Subtracting fractions

The methods used to subtract fractions are the same as are used to add them together. If the denominator is the same for both fractions:

5 | - | 3 | = | (5 - 3) | = | 2 | = | 1 |

8 | 8 | 8 | 8 | 4 |

If the two fractions do not have an obvious common denominator, the two denominators are multiplied together:

12 | - | 11 | = | (12 × 7) | - | (11 × 6) | = | (84 - 66) | = | 18 | = | 3 |

6 | 7 | (6 × 7) | (7 × 6) | 42 | 42 | 7 |

This is a slightly contrived example designed to yield an answer that simplifies easily. In this case it would have been simpler to have started by converting both fractions to mixed numbers:

12 | - | 11 | = 2 - 1 | 4 | = 1 - | 4 | = | 3 |

6 | 7 | 7 | 7 | 7 |

The choice of whether to work with improper fractions or mixed numbers will be based on the sizes of numerators and denominators.