# If adding is your aim

If adding or subtracting is your aim,

the bottom numbers must be the same

**Example 1**

`5/9+1/9=(5+1)/9=6/9=2/3`

This example the bottom numbers (denominators) are the same.

**Example 2**

`3/8+5/6`

Make the bottom denominator the same for both so multiply the bottom of the denominator by the other fraction denominator.

`3/8\times6/6+5/6\times8/8`

**NOTE:**

`6/6 or8/8=1`

When multiplying anything by 1 it does not alter the fraction.

Therefore `3/8\times6/6=(3times6)/(8times6)=18/48`

And

`5/6\times8/8=(5times8)/(6times8)=40/48`

So add fractions

`18/48\+40/48=(18+40)/48=58/48`

Now just make `58/48` simpler

`58/48=29/24=1\5/24`

**Example 3**

Work out `3/4+1/6`

Make the bottom denominator the same for both so multiply the bottom of the denominator by the other fractions denominator.

`3/4\times6/6+1/6times4/4`

**NOTE:**

`4/4 or 6/6=1`

Multiplying it by 1 does not alter it.

Therefore

`3/4\times6/6=(3times6)/(4times6)=18/24`

and

`1/6\times4/4=(1times4)/(6times4)=4/24`

So add fractions

`18/24\+4/24=(18+4)/(24)=22/24`

Now just make `22/24`simpler

`22/24=11/12`