This is an expression used to compare two or more

quantities relative to each other.

The quantities are separated by a colon (:)

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.

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 to

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.

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

There are two cats and one dog.

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.

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 chocolates is shared amongst

Tom, Ryan and Ashleigh in the ratio

3:4:5 respectively.

How many chocolates does each person

receive ?

Tom | : | Ryan | : | Ashleigh |
Total |

3 | : | 4 | : | 5 | 12 |