# 2 part ratios - simplifying integers

Just like equations, whatever you do to one side you do to the other. This becomes very handy when you simplify ratios.

RATIOS

What you do to one side you do to the other

and just like our section on simplifying fractions

Simplifying ratios divide left and right by

`2,3,4,5......`

until you can't go any further

**Example 1**

Simplify the ratio `32:48`

First we can divide by `2`

`32/2:48/2`

and this becomes:

`16:24`

We can divide again by `2`

`16/2:24/2`

and this becomes:

`8:12`

We can divide again by `2`

`8/2:12/2`

and this becomes:

`4:6`

We can divide again by `2`

`4/2:6/2`

which becomes:

`2:3`

Nothing else will divide into these equally so `2:3` is the answer

**Example 2**

Simplify `5m:50cm`

**NOTE:**

The ratio must be in the same units

(It's best to simplify from the smaller units)

and as `5m=500cm` the ratio now reads:

`500cm:50cm`

Now we simplify as follows `2,3,4,5........` The first number that will divide into this is `2`

`500/2:50/2`

which becomes:

`250:25`

The next number we can divide by is `5`

`250/5:25/5`

which becomes:

`50:5`

Now can divide by `5` again

`50/5:5/5`

which becomes:

`10:1`

**NOTE:**

`1` is the lowest ratio we can go to so `10:1` must be the answer.

**Example 3**

A magazine includes 24 pages of writing/pictures and 16 pages of adverts, a total of 40 pages. What is the ratio of writing/pictures to adverts? (you must simplify the answer)

The ratio is `24` to every `16`

`24:16`

But this can be simplified as follows:

`2,3,4,5.......` The first number that will divide into this is `2`

`24/2:16/2`

which becomes:

`12:8`

Now we can divide by `2` again

`12/2:8/2`

which becomes:

`6:4`

Now we can divide by `2` again

`6/2:4/2`

which becomes:

`3:2`

Nothing else will divide into these equally so

`3:2` is the answer