# 3.3 Simplifying fractions

You may need to simplify a fraction. The following terms may also be used for this:

- cancelling
- express in the lowest terms
- express in the simplest form.

For example, is equivalent to (the same as) , which is the simplest way of writing this fraction.

## Example: Simplifying fractions

- Simplify .
- Simplify .

### Method

To simplify a fraction, you need to divide the top and bottom numbers by the same value. You keep dividing down until you cannot get the fraction any smaller. Each time you divide, you must divide the top and bottom numbers by the same value.

- In order to simplify , you need to find out what number will divide into 5 and 20. The only number that will divide into both 5 and 20 is 5:
- 5 ÷ 5 = 1
- 20 ÷ 5 = 4

So = .

- There are different ways to simplify to the lowest form. For example, you can divide both numbers in by 2:
- 20 ÷ 2 = 10
- 30 ÷ 2 = 15

However, not the simplest form of the fraction. You can simplify the fraction further by dividing the top and bottom numbers by 5:

- 10 ÷ 5 = 2
- 15 ÷ 5 = 3

is the simplest form of .

However, you may have recognised that 10 will go into both 20 and 30, so you may have divided by 10 straightaway:

- 20 ÷ 10 = 2
- 30 ÷ 10 = 3

The answer is the same, but dividing by 10 would have got you to the answer more quickly.

Now try the following activity.

## Activity 21: Simplifying fractions

Simplify the following fractions:

### Answer

- = (the top and bottom numbers are divided by 5)
- = (the top and bottom numbers are divided by 5)
- = (the top and bottom numbers are divided 2)
- = (the top and bottom numbers are divided 2)
- = (the top and bottom numbers are divided 3)