2 part ratio and dealing with fractions

To work on ratios with fractions

 Get rid of the fractions
(we only work in integers)

By

 Multiply each fraction by the other fraction's bottom number

Example 1

Simplify the following ratio which has fractions

`2/5:3/4`

Multiply each fraction by the other fraction's bottom number

`2/5times4/4:3/4times5/5`

NOTE:

(`4/4=1` and `5/5=1` and we know that when you multiply a number by `1` it does not change its value)

`(2times4)/(5times4):(3times5)/(4times5)`

`8/20:15/20`

Now that the bottom denominator is the same and because whatever we do to one side we must do to the other, multiply both sides by 20.

`(8timescancel20)/cancel20:(15timescancel20)/cancel20`

Ratio `=8:15`

Example 2

Simplify the following ratio

`2\1/2:3/5`

In order to tackle this ratio, we must first turn `2\1/2` into an improper fraction.

(see our section on "improper fractions") 

`2\1/2` is really `2+1/2`

Which is the same as `2/1+1/2`

Now add these two together we get (see our section on "adding fractions")

`2/1times2/2+1/2times1/1`

is the same as

`4/2+1/2`

Which equals

`(4+1)/2=5/2`

So `2\1/2=5/2`

So the ratio is

`5/2:3/5`

Multiply each fraction by the other fraction's bottom number

`5/2times5/5:3/5times2/2`

Is the same as

`25/10:6/10`

Now that the bottom denominator is the same and because whatever we do to one side we must do to the other, multiply both sides by `10`.

`(25times10)/10:(6times10)/10`

`25:6`

The ratio `25:6` can not be simplified any further, so `25:6` is the answer.

Example 3

Turn `1/3:5` into a ratio with whole numbers (integers).

In order to tackle this ratio, we must multiply each fraction by the other fraction's bottom number.

Because remember

`1/3:5`

Is the same as

`1/3:5/1`

`1/3times1/1:5/1times3/3`

NOTE:

(`1/1=1` and `3/3=1` so has no impact on the ratio)

`(1times1)/(3times1):(5times3)/(1times3)`

`1/3:15/3`

Now that the bottom denominator is the same and because whatever we do to one side we must do to the other, multiply both sides by `3`

`cancel3times1/cancel3:(15timescancel3)/cancel3`

Ratio `=1:15`