This is an expression used to tennis2007.orgmpare two or more quantities relative to each other.

You are watching: In an animal shelter, the ratio of dogs to cats is 5 to 3

The quantities are separated by a tennis2007.orglon (:)

Example

There are two cats and one dog.

The ratio of cats to dogs is 2:1

cats | : | dogs |

2 | : | 1 |

The ratio of dogs to cats is 1:2

dogs | : | cats |

1 | : | 2 |

This means there are twice as many cats as dogs, or half as many dogs as cats.

## Equivalence

There are six cats and three dogs. There are still twice as many cats as dogs.

Dividing through by the HCF reduces the ratio to itssimplest form.

Here, the HCF of 6 and 3 is 3, so divide both sides by 3.

cats | : | dogs | ||

6 | : | 3 | ||

2 | : | 1 |

The ratio 6:3 reduces to the ratio 2:1 when expressed in simplest form.

Multiplying the simplest form will give equivalent ratios

cats | : | dogs |

2 | : | 1 |

4 | : | 2 |

6 | : | 3 |

8 | : | 4 |

etc.

The ratio 8:4 is equivalent tennis2007.orgme 2:1 , 4:2, 200:100 etc.

So how can this be used ?

Given the ratio of boys to girls as 2:3 how many girls will there be if there are 10 boys ?

boys | : | girls |

2 | : | 3 |

10 | : | * |

Notice that the original number of boys has been multiplied by 5.

This means that the original number of girls must also be multiplied by 5

boys | : | girls | ||

2 | : | 3 | ||

10 | : | 15 |

So there are 15 girls.

Example

Given the ratio of girls to boys as 3:2 how many boys will there be if there are 12 girls?

girls | : | boys |

3 | : | 2 |

12 | : | * |

girls | : | boys | ||

3 | : | 2 | ||

12 | : | 8 |

There are 8 boys

Notice that the term which has both known quantities goes on the left.

## Other methods

These are sometimes written as ratio equations e.g. 3:2 :: 12:x

In Vedic maths, *the product of the means * *equals the product of the extremes*

Multiplying the outer two numbers will have the same answer as multiplying the inner two numbers. a:b :: c:d gives ad =bc

Example Find the value of x 3:2 :: 12:x

Find the value of x 5:x :: 35:9

## Proportion

There are two cats and one dog.

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cats | : | dogs | Total animals |

2 | : | 1 | 3 |

The proportion of cats is 2/3 The proportion of dogs is 1/3

Two thirds of the animals are cats. One third of the animals are dogs.

## Sharing in proportion

Example

Divide 45 Kg in the ratio 3: 2

The total number of parts is 5 each part has a value of 45 ÷ 5 = 9Kg 9 x 3 = 27 Kg 9 x 2 = 18 kg so 3 parts is 27kg, 2 parts is 18 Kg

( check: 27 + 18 = 45, the original number)

Example

A box of 84 chotennis2007.orglates is shared amongst Tom, Ryan and Ashleigh in the ratio 3:4:5 respectively. How many chotennis2007.orglates does each person receive ?