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 | + | b |

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 | + | b |

10 | 15 |

= | a x 3 | + | b x 2 |

10 x 3 | 15 x 2 |

= | 3a | + | 2b |

30 | 30 |

= | 3a + 2b |

30 |