# Ordering fractions by size - Method 1

Putting fractions in smallest to largest order can be completed if the bottom number (the denominator) are all the same.

Can't compare unless all the bottom numbers are the same

And to put all the fractions with the same bottom number you must:

Multiply each fraction by the other fractions bottom numbers

Who's got the biggest bottom

**NOTE:**

This is a very quick method if you have a calculator.

**Example 1**

Put the following fractions in order of the smallest to biggest fraction.

`8/3` `5/4` and `12/5`

To answer this we must multiply each fraction by the other fractions bottom numbers.

`8/3times4/4times5/5=(8times4times5)/(3times4times5)=(8times20)/60=160/60`

`5/4times3/3times5/5=(5times3times5)/(4times3times5)=75/60`

`12/5times3/3times4/4=(12times3times4)/(5times3times4)=(12times12)/60=144/60`

So `8/3=160/60` and `5/4=75/60` and `12/5=144/60`

Now we can clearly see that correct order is:

`5/4` (smallest), `12/5` (middle) and `8/3` (biggest)

**Example 2**

Put the following fractions in order of the smallest to biggest fractions.

`1/2` `1/3` `1/4` `1/6` `1/8`

To answer this we must multiply each fraction by the other fractions bottom numbers.

`1/2times3/3times4/4times6/6times8/8=(1times3times4times6times8)/(2times3times4times6times8)`

`=(72times8)/(24times6times8)=576/(144times8)=576/1152`

**NOTE:**

`1152` on the bottom is always the same

`1/3times2/2times4/4times6/6times8/8=(1times2times4times6times8)/(3times2times4times6times8)`

`=(64times6)/1152=384/1152`

`1/4times2/2times3/3times6/6times8/8=(1times2times3times6times8)/(4times2times3times6times8)`

`=(36times8)/1152=288/1152`

`1/6times2/2times3/3times4/4times8/8=(1times2times3times4times8)/(6times2times3times4times8)`

`=(48times4)/1152=192/1152`

`1/8times2/2times3/3times4/4times6/6=(1times2times3times4times6)/(8times2times3times4times6)`

`(36times4)/1152=144/1152`

So `1/2=576/1152` and `1/3=384/1152` and `1/4=288/1152` and `1/6=192/1152` and `1/8=144/1152`

Now we can see that

`1/8` is the smallest followed by `1/6`, `1/4`, `1/3` and `1/2`

**NOTE:**

You should be familiar enough with fractions to realise that the biggest number divided into `1` would be the smallest fraction.

**Example 3**

Which is greater `3/8` or `4/9`?

To answer this question we must multiply each fraction by the other fractions bottom number.

`3/8times9/9=(3times9)/(8times9)=27/72`

`4/9times8/8=(4times8)/(9times8)=32/72`

So `3/8=27/72` and `4/9=32/72`

Now we can clearly see that the greater number is `4/9`

**Example 4**

Put the following fractions in order of the smallest to biggest fractions.

`2/6` `1/2` `7/16` `3/4` `5/8`

To answer this we must multiply each fraction by the other fractions bottom number.

`2/6times2/2times16/16times4/4times8/8=2048/6144underset(larr always\ the\ same)()`

`1/2times6/6times16/16times4/4times8/8=3072/6144`

`7/16times6/6times2/2times4/4times8/8=2688/6144`

`3/4times6/6times2/2times16/16times8/8=4608/6144`

`5/8times6/6times2/2times16/16times4/4=3840/6144`

So `2/6=2048/6144` `1/2=3072/6144` `7/16=2688/6144`

`3/4=4608/6144` `5/8=3840/6144`

Now we can clearly see that the order is:

`2/6` followed by `7/16`, `1/2`, `5/8` and `3/4`