This is an expression offered to gimpppa.orgmpare 2 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 amounts are separated by a gimpppa.orglon (:)

Example

There space two cats and also one dog.

The ratio of cats to dog is 2:1

cats | : | dogs |

2 | : | 1 |

The proportion of dogs to cats is 1:2

dogs | : | cats |

1 | : | 2 |

This means there room twice as numerous cats as dogs, or half as countless dogs together cats.

## Equivalence

There are six cats and three dogs. There room still twice as numerous cats together dogs.

Dividing with by the HCF to reduce the proportion to itssimplest form.

Here, the HCF of 6 and also 3 is 3, so divide both political parties by 3.

cats | : | dogs | ||

6 | : | 3 | ||

2 | : | 1 |

The proportion 6:3 reduces come the ratio 2:1 as soon as expressed in simplest form.

Multiplying the simplest kind will provide equivalent ratios

cats | : | dogs |

2 | : | 1 |

4 | : | 2 |

6 | : | 3 |

8 | : | 4 |

etc.

The proportion 8:4 is tantamount to 2:1 , 4:2, 200:100 etc.

So how deserve to this be provided ?

Given the ratio of guys to girls as 2:3 how countless girls will certainly there it is in if there room 10 boys ?

boys | : | girls |

2 | : | 3 |

10 | : | * |

notice that the original number of boys has actually been multiply by 5.

This means that the original variety of girls must also be multiply by 5

boys | : | girls | ||

2 | : | 3 | ||

10 | : | 15 |

So there room 15 girls.

Example

Given the proportion of girl to boys as 3:2 how many boys will there it is in if there are 12 girls?

girls | : | boys |

3 | : | 2 |

12 | : | * |

girls | : | boys | ||

3 | : | 2 | ||

12 | : | 8 |

There space 8 boys

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

## Other methods

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

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

Multiplying the external two number will have actually the exact same answer together multiplying the inner two numbers. A:b :: c:d gives advertisement =bc

Example discover the worth of x 3:2 :: 12:x

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

## Proportion

There space two cats and one dog.

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cats | : | dogs | Total animals |

2 | : | 1 | 3 |

The ratio of cats is 2/3 The relationship 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 proportion 3: 2

The total variety of parts is 5 each part has a worth of 45 ÷ 5 = 9Kg 9 x 3 = 27 Kg 9 x 2 = 18 kg therefore 3 parts is 27kg, 2 parts is 18 Kg

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

Example

A crate of 84 chogimpppa.orglates is shared among Tom, Ryan and Ashleigh in the ratio 3:4:5 respectively. How many chogimpppa.orglates walk each human get ?