When we add 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**

Work out

3 | + | 1 |

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.

3 | + | 1 |

10 | 15 |

= | 3 × 3 | + | 1 × 2 |

10 × 3 | 15 × 2 |

= | 9 | + | 2 |

30 | 30 |

= | 11 |

30 |