Finding a fraction of an amount

What is a fraction?

A fraction tells you how many parts of a whole there are.

When you find a fraction of an amount, you are working out how much that 'part' is worth within the whole.

You can see fractions of amounts all around you:

Shops have sales that say, “¹/₂ price!” or “¹/₃ free!”
You might use fractions when baking, for example, “add half a teaspoon of salt” or “use a ¹/₄ of a kilogram of flour”.

Method 1: Using images to group

Using images to help break up the fraction can be a helpful and visual way of finding a fraction of an amount.

For example:

What is \( \frac{5}{6} \) of 30?

Step 1: Look at the denominator to see how many groups you need to separate 30 into equally. The denominator is 6, so you need to split 60 into 6 groups.

Step 2: Now separate 30 into six groups. You can represent 30 by using circles.

Step 3: Look at the numerator. This tells you how many groups to look at in total (5).

Step 4: There are 25 counters in 5 groups.

⁵/₆ of 30 is 25

Method 2: Using division and multiplication

Another way to quickly work out the fraction of an amount is to remember this trick:

"Divide by the bottom and times by the top."

This means that you divide the amount by the denominator and then multiply that by the numerator to get the answer.

For example:

What is \( \frac{5}{12} \) of 96?

Step 1: Divide by the bottom…

96 ÷ 12 = 8

Step 2: …and times by the top.

8 x 5 = 40

Therefore:

\( \frac{5}{12} \) of 96 is 40

Method 3: Bar model and calculator

Watch the video below to see another method that you can use to find a fraction of an amount. By drawing out the fraction you can see what ¹/₆ looks like before you do the calculation.

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Activities

Activity 1

Try one of the methods above to work out the following question.

Out of 45 children, ‎¹/₃‎ have school dinners, while ⅔ bring a packed lunch.

How many children have school dinners?

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