When we add or subtract two fractions, they must have the same denominator.

We use equivalent fractions to change them into two fractions with the same lowest common denominator.

**Example**

Simplify:

a + 2 | - | b - 5 |

10 | 15 |

**Answer**

We must first find the lowest common multiple of 10 and 15, which is 30.

Then we change each fraction into 30ths.

30 ÷ 10 = 3 so we multiply top and bottom of the first fraction by 3.

30 ÷ 15 = 2 so we multiply top and bottom of the second fraction by 2.

a + 2 | - | b - 5 |

10 | 15 |

= | 3(a + 2) |
- | 2(b - 5) |

10 x 3 | 15 x 2 |

= | 3a + 6 | - | 2b - 10 |

30 | 30 |

= | 3a + 6 - (2b - 10) |

30 |

= | 3a + 6 - 2b + 10 |

30 |

= | 3a - 2b + 16 |

30 |