# 3 part ratios - simplifying integers

Just like equations, whatever you do to one side you do to the other. Only in the case of three part ratios you do it to all three sides.

What you do to one you do to all the others

and just like our section on simplifying fractions.

Simplifying ratios divide all three parts first by `2` then `3,4,5......` until you can't go any further

**Example 1**

Simplify the ratio `2:6:4`

First we try dividing by `2`

`2/2:6/2:4/2`

which becomes:

`1:3:2`

This can not be divided down any more so it is the answer.

**Example 2**

Simplify the ratio `6:15:21`

`2,3,4,5....` The first number that will divide into all of them is `3`

`6/3:15/3:21/3`

which becomes:

`2:5:7`

This can not be divided down any more so it is the answer.

**Example 3**

Simplify the ratio `12:6:48`

First we can divide by `2`

`12/2:6/2:48/2`

which becomes:

`6:3:24`

`2` won't divide again but we can try the next in `2,3,4,5.....` etc

Try dividing by `3`

`6/3:3/3:24/3`

`2:1:8`

Once you have a `1` in the ratio you know you can't divide down any more so `2:1:8` is the answer.