# 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