Adding, subtracting, multiplying and dividing fractions

Adding and subtracting fractions

It is easy to add fractions when the numbers on the bottom are the same:

All you need to do is add the tops of the fractions together:

So

Sometimes you need to cancel down the answer to its simplest terms:

When the numbers on the bottom are not the same to start with, you use equivalent fractions to make them the same.

Multiplying and dividing fractions

Remember that to multiply fractions, you need to multiply the numerators together, and multiply the denominators together. Remember that you cannot cancel numbers that are both on the top of a fraction. Have a look at the examples below.

Example 1:

We multiply by ,

so we have .

Example 2:

Multiply then cancel:

or cancel between the top and the bottom then multiply:

 

Dividing by a fraction

How do you divide 12 by ? This isn't the same as 12 divided by 3.

means how many thirds are there in 12 whole units.

As there are 3 thirds in each whole unit, then there are 36 thirds in 12 whole units. Think how many 's there are in one pie, then 12 pies.

A simple way to divide by a fraction is to turn the fraction upside down and multiply.

It works with all fractions. For example dividing by is the same as multiplying by .

Notice that when you divide by a fraction the answer is larger than the