Fractions of an Amount

Finding a fraction of an amount is a core skill that pops up everywhere in Maths. Whether you are dealing with money, measurements, or sharing out items, understanding how to apply fractions to whole numbers is essential.

What you'll learn:

How to calculate a basic fraction of a whole number.
How to apply these skills to real-world word problems.
How to work backwards to find the original amount when you are given a fraction of it.

The Basic Rule

To find a fraction of an amount, you need to understand what a fraction represents. The bottom number (denominator) tells you how many equal pieces the whole has been split into. The top number (numerator) tells you how many of those pieces you actually have.

Key Idea

Divide by the bottom, multiply by the top

To find a fraction of an amount:

Divide the amount by the denominator (the bottom number).
Multiply that result by the numerator (the top number).

Let's visualise this with a bar model. If we want to find $23\frac{2}{3}$ of 240, we imagine the number 240 being split into 3 equal blocks. Once we know the value of one block, we want exactly 2 of them.

Bar model showing 240 split into 3 blocks of 80

Example

Finding a fraction of a number

Find $23\frac{2}{3}$ of 240.

Divide the amount by the denominator (the bottom number) to find $13\frac{1}{3}$ :
$240 \div 3 = 80$
Multiply the result by the numerator (the top number) to find $23\frac{2}{3}$ :
$80 \times 2 = 160$

Tip

Order doesn't strictly matter

If it makes the mental maths easier, you can multiply by the top first, and then divide by the bottom. However, doing the division first usually keeps the numbers smaller and easier to work with!

Multi-Step Word Problems

Exam questions rarely just ask you to calculate a fraction. They wrap the maths in a real-world scenario where you have to find fractions of an amount, subtract them from a total, or compare them.

Example

Sharing and remaining amounts

Liam has £60. He spends $25\frac{2}{5}$ of his money on a video game. He spends $310\frac{3}{10}$ of his money on snacks. He saves the rest. Work out how much money Liam saves.

Find the amount spent on the video game:
$60÷5=1212×2=24\begin{aligned} 60 \div 5 &= 12 \\ 12 \times 2 &= 24 \end{aligned}$
He spends £24 on the game.
Find the amount spent on snacks:
$60÷10=66×3=18\begin{aligned} 60 \div 10 &= 6 \\ 6 \times 3 &= 18 \end{aligned}$
He spends £18 on snacks.
Calculate the total amount spent:
$24 + 18 = 42$
Subtract the total spent from his original amount to find his savings:
$60 - 42 = 18$
Liam saves £18.

Common Mistake

Fractions of what?

Always read carefully to see if the fraction is of the original total or the remainder. In IGCSE Grade 2 questions, it is almost always fractions of the original total, but if the question says "He spends $12\frac{1}{2}$ of the remaining money", you must recalculate the new total before applying the next fraction!

Working Backwards (Reverse Fractions)

Sometimes, you aren't given the starting amount. Instead, you are told what a fraction of an unknown number equals, and you have to work backwards to find the original whole.

If you know that $34\frac{3}{4}$ of a number is 39, you know that 3 equal pieces add up to 39. To find the whole, you first find the value of one piece, and then scale it up to the whole (which is 4 pieces).

Key Idea

Working backwards

When you know the value of a fraction and need to find the whole amount:

Divide by the numerator (top number) to find the value of one part.
Multiply by the denominator (bottom number) to find the whole.

Notice this is the exact opposite of finding a fraction of an amount!

Example

Finding the original number

$34\frac{3}{4}$ of a number is 39. Work out the number.

We know that 3 parts equal 39. Divide by the numerator (3) to find the value of 1 part ( $14\frac{1}{4}$ ):
$39 \div 3 = 13$
Multiply by the denominator (4) to find the total value of all 4 parts (the whole number):
$13 \times 4 = 52$

Exam technique

In the exam

Underline the key values: Highlight the total amount, the fractions, and exactly what the question is asking for (e.g., the amount spent vs. the amount left over).
Show every calculation: Even if you can do $240 \div 3 = 80$ in your head, write it down. Examiners award method marks for seeing the division and multiplication steps.
Check your answer makes sense: If you are finding $23\frac{2}{3}$ of an amount, your answer must be smaller than the original amount. If you are working backwards to find the whole, your answer must be larger.

Self review

Check yourself

Can you calculate $45\frac{4}{5}$ of 60? What is the first step you take?
If a coat costs £80 and has $14\frac{1}{4}$ off in a sale, do you know how to calculate the new price?
If $25\frac{2}{5}$ of a number is 14, what is the original number? How does the method change compared to a normal fraction calculation?

Fractions of an Amount

What you'll learn:

How to calculate a basic fraction of a whole number.
How to apply these skills to real-world word problems.
How to work backwards to find the original amount when you are given a fraction of it.

The Basic Rule

Key Idea

Divide by the bottom, multiply by the top

To find a fraction of an amount:

Divide the amount by the denominator (the bottom number).
Multiply that result by the numerator (the top number).

Bar model showing 240 split into 3 blocks of 80

Example

Finding a fraction of a number

Find $23\frac{2}{3}$ of 240.

Divide the amount by the denominator (the bottom number) to find $13\frac{1}{3}$ :
$240 \div 3 = 80$
Multiply the result by the numerator (the top number) to find $23\frac{2}{3}$ :
$80 \times 2 = 160$

Tip

Order doesn't strictly matter

If it makes the mental maths easier, you can multiply by the top first, and then divide by the bottom. However, doing the division first usually keeps the numbers smaller and easier to work with!

Multi-Step Word Problems

Exam questions rarely just ask you to calculate a fraction. They wrap the maths in a real-world scenario where you have to find fractions of an amount, subtract them from a total, or compare them.

Example

Sharing and remaining amounts

Liam has £60. He spends $25\frac{2}{5}$ of his money on a video game. He spends $310\frac{3}{10}$ of his money on snacks. He saves the rest. Work out how much money Liam saves.

Find the amount spent on the video game:
$60÷5=1212×2=24\begin{aligned} 60 \div 5 &= 12 \\ 12 \times 2 &= 24 \end{aligned}$
He spends £24 on the game.
Find the amount spent on snacks:
$60÷10=66×3=18\begin{aligned} 60 \div 10 &= 6 \\ 6 \times 3 &= 18 \end{aligned}$
He spends £18 on snacks.
Calculate the total amount spent:
$24 + 18 = 42$
Subtract the total spent from his original amount to find his savings:
$60 - 42 = 18$
Liam saves £18.

Common Mistake

Fractions of what?

Working Backwards (Reverse Fractions)

Sometimes, you aren't given the starting amount. Instead, you are told what a fraction of an unknown number equals, and you have to work backwards to find the original whole.

Key Idea

Working backwards

When you know the value of a fraction and need to find the whole amount:

Divide by the numerator (top number) to find the value of one part.
Multiply by the denominator (bottom number) to find the whole.

Notice this is the exact opposite of finding a fraction of an amount!

Example

Finding the original number

$34\frac{3}{4}$ of a number is 39. Work out the number.

We know that 3 parts equal 39. Divide by the numerator (3) to find the value of 1 part ( $14\frac{1}{4}$ ):
$39 \div 3 = 13$
Multiply by the denominator (4) to find the total value of all 4 parts (the whole number):
$13 \times 4 = 52$

Exam technique

In the exam

Underline the key values: Highlight the total amount, the fractions, and exactly what the question is asking for (e.g., the amount spent vs. the amount left over).
Show every calculation: Even if you can do $240 \div 3 = 80$ in your head, write it down. Examiners award method marks for seeing the division and multiplication steps.
Check your answer makes sense: If you are finding $23\frac{2}{3}$ of an amount, your answer must be smaller than the original amount. If you are working backwards to find the whole, your answer must be larger.

Self review

Check yourself

Can you calculate $45\frac{4}{5}$ of 60? What is the first step you take?
If a coat costs £80 and has $14\frac{1}{4}$ off in a sale, do you know how to calculate the new price?
If $25\frac{2}{5}$ of a number is 14, what is the original number? How does the method change compared to a normal fraction calculation?

Fractions of an Amount

The Basic Rule

Multi-Step Word Problems

Working Backwards (Reverse Fractions)

Recap questions

You've reached the end

Fractions of an Amount

The Basic Rule

Multi-Step Word Problems

Working Backwards (Reverse Fractions)

Recap questions

You've reached the end

Fractions of an Amount

The Basic Rule

Multi-Step Word Problems

Working Backwards (Reverse Fractions)

Recap questions

You've reached the end

Fractions of an Amount Revision Guide

Fractions of an Amount

The Basic Rule

Multi-Step Word Problems

Working Backwards (Reverse Fractions)

Recap questions

You've reached the end

Fractions of an Amount Revision Guide