2 part ratio and dealing with decimals

To work out ratios with decimals

Get rid of the decimal.
(We only work in integers.)

By

Keep multiplying both sides
BY 10.
Until Decimal disappears.

Example 1

Simplify the following ratio with decimals.

`0.26:0.13`

Multiply both sides by `10`

`0.26times10:0.13times10`

`2.6:1.3`

This still leaves decimals so multiply by `10` again.

`2.6times10:1.3times10`

`26:13`

Now we have removed the decimals we can now simplify `26:13`

(see our section on 2 part ratios - simplify integers)

First divide by `2` then `3` then `4` then `5.......` The first number that will divide both numbers is `13`.

Divide both sides by `13`

`26/13:13/13`

`2:1`

With `1` in the answer we know we can't divide down any further so this is the answer.

Example 2

Simplify the following ratio `2.5:0.05`

Multiply both sides by `10`

`2.5times10:0.05times10`

`25:0.5`

There is still a decimal in the ratio so multiply by `10` again.

`25times10:0.5times10`

`250:5`

Now we have whole numbers we can now simplify `250:5`

(see our section on 2 part ratios - simplify integers)

The first number that will divide both numbers is `5`.

`250/5:5/5`

`50:1`

With `1` in the answer we know we can't divide down any further so this is the answer.