Many ratios can be written with smaller numbers. This is called writing ratios in their simplest form , or simplifying ratios.

Simplifying ratios makes them easier to work with.

Note: To simplify ratios you can use the same technique that is used to simplify fractions.

As the two examples below show, you simplify ratios by dividing the number on each side by their greatest common factor.

#### Simplify 15 : 9

Ratio | 15 : 9 |

Factors of 15 | 1 , 3 , 5 , 15 |

Factors of 9 | 1 , 3 , 9 |

Greatest Common Factor (G.C.F) | 3 |

Divide both by G.C.F | 15 ÷ 3 = 5 9 ÷ 3 = 3 |

Ratio in simplest form | 5 : 3 |

#### Simplify 8 : 36

Ratio | 8 : 36 |

Factors of 8 | 1 , 2 , 4, 8 |

Factors of 36 | 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 |

Greatest Common Factor (G.C.F) | 4 |

Divide both by G.C.F | 8 ÷ 4 = 2 36 ÷ 4 = 9 |

Ratio in simplest form | 2 : 9 |

### Simplifying Ratio Worksheets

- Simplifying Ratios (1 of 2) – 4:2 = 2:1 (includes prompts to divide by G.C.F)
- Simplifying Ratios (2 of 2) – identify and simplify ratios

You will find more ratio and proportion worksheets here.