# 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 22/24simpler

22/24=11/12