Finding a fraction of an amount

The numerator is 1 and the denominator is 4. You need to know these values to help you calculate a fraction of an amount.

You can see fractions of amounts all around you.

Shops have sales that say "\(\frac{1}{2}\) price" or "\(\frac{2}{3}\) off".

You might use fractions when baking, for example, “add half a teaspoon of salt” or “use a \(\frac{1}{4}\) of a kilogram of flour”.

A bar model is helpful for finding fractions of amounts.

Let's use a bar model to find \(\frac{2}{5}\) of 20.

First you need to label the whole.

\(\frac{2}{5} \) is two of the parts in the bar model because each part represents \(\frac{1}{5}\).

They can be any two parts since they are all equal.

If \(\frac{1}{5}\) equals 4, then \(\frac{2}{5}\) equals 8. So:

\(\frac{2}{5}\) of 20 = 8

Finding fractions with a bar model

Let's try another one.

This time let's find \(\frac{4}{6} \) of 54.

First you need to label the whole.

Next, you find \(\frac{1}{6}\). You can use your times table facts to help you.

6 × ? = 54

Or you can use your division tables facts.

54 ÷ 6 = ?

54 ÷ 6 = 9

Therefore each sixth is worth 9.

You need to find \(\frac{4}{6}\) so you find the total of four parts.

9 × 4 = 36

Therefore:

\(\frac{4}{6}\) of 54 = 36

Finding fractions of amounts

You may have noticed that you are following rules when you are using a bar model.

Once you know the rules, you may not need to have a visual to help you.

Rule 1 - Divide by the denominator

Rule 2 - Multiply by the numerator

Let’s try one without using a bar model.

Let's find \(\frac{7}{9}\) of 72.

First, you divide the whole amount by the denominator to find \(\frac{1}{9} \).

72 ÷ 9 = 8

\(\frac{1}{9}\) = 8

Then you multiply this by the numerator. You do this because you have only found \(\frac{1}{9} \).

In this question you need to find \(\frac{7}{9}\) so you multiply by 7.

8 × 7 = 56

\(\frac{7}{9}\) of 72 = 56