### Answers − Ratios

#### 1. Share £400 in the ratio 1 : 3

(a) | Add the separate parts of the ratio to find the total number of parts 1 + 3 = 4 |

(b) | Divide 400 by 4 to find the value for each part: 100 |

(c) | Multiply each term in the ratio by 100: 1 x 100 = 100, 3 x 100 = 300 |

So £400 shared in the ratio 1 : 3 is £100 and £300

#### 2. Divide 225 grams in the ratio 1 : 2

(a) | Add the separate parts of the ratio to find the total number of parts 1 + 2 = 3 |

(b) | Divide 225 by 3 to find the value for each part: 75 |

(c) | Multiply each term in the ratio by 75: 1 x 75 = 75, 2 x 75 = 150 |

So £225 shared in the ratio 1 : 2 is £75 and £150

#### 3. Share £560 in the ratio 3 : 5

(a) | Add the separate parts of the ratio to find the total number of parts 3 + 5 = 8 |

(b) | Divide 560 by 8 to find the value for each part: 70 |

(c) | Multiply each term in the ratio by 70: 3 x 70 = 210, 5 x 70 = 350 |

So £560 shared in the ratio 3 : 5 is £210 and £350

#### 4. Divide 270 kg in the ratio 2 : 7

(a) | Add the separate parts of the ratio to find the total number of parts 2 + 7 = 9 |

(b) | Divide 270 by 9 to find the value for each part: 30 |

(c) | Multiply each term in the ratio by 30: 2 x 30 = 60, 7 x 30 = 210 |

So 270 kg shared in the ratio 2 : 7 is 60 kg and 210 kg

#### 5. Share £440 in the ratio 3 : 8

(a) | Add the separate parts of the ratio to find the total number of parts 3 + 8 = 11 |

(b) | Divide 440 by 11 to find the value for each part: 40 |

(c) | Multiply each term in the ratio by 12: 3 x 40 = 120, 8 x 40 = 320 |

So £440 shared in the ratio 3 : 8 is £120 and £320

#### 6. The cost of a weekend break is divided between two families in the ratio of 3 : 7 the smaller share was £90. How much is the total cost of the weekend break?

(a) | Add the separate parts of the ratio to find the total number of parts 3 + 7 = 10 |

(b) | 3/10 of the cost was £90, so 1/10 is £30 |

(c) | The total cost is: 10 x £30 = £300 |

So the total cost is £300

#### 7. The cost of a holiday is divided between two families in the ratio of 3 : 8 the smaller share was £240. How much is the total cost of the holiday?

(a) | Add the separate parts of the ratio to find the total number of parts 3 + 8 = 11 |

(b) | 3/11 of the cost was £240, so 1/11 is £80 |

(c) | The total cost is: 11 x £80 = £880 |

So the total cost is £880

#### 8. The ratio of male teachers to female teachers is 2 : 7. If there are 84 female teacher, how many male teachers are there?

(a) | Add the separate parts of the ratio to find the total number of parts 2 + 7 = 9 |

(b) | So 7/9 are female teachers is 84, so 1/9 is 12 |

(c) | The number of male teachers: 2 x 12 = 24 |

So the total number of male teachers is 24

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