Fractions of Amounts
Master fractions of amounts for GCSE Maths with structured, exam-style practice. This Foundation resource covers finding fractions of amounts and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Divide by the denominator, then multiply by the numerator.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
Finding a fraction of an amount means splitting the amount into equal parts and taking some of them. The denominator tells you how many parts to divide into, and the numerator tells you how many to take.
The method is to divide by the denominator, then multiply by the numerator. For three quarters of \(£60\), divide by \(4\) to get \(£15\), then multiply by \(3\) to get \(£45\).
Doing it in that order keeps the numbers small and manageable. Multiplying first also works and gives the same answer, but you end up handling much larger figures, which invites arithmetic errors in a non-calculator paper.
Revision notes
Divide then multiply
Divide the amount by the denominator to find one part, then multiply by the numerator to find the required number of parts.
For \(\frac{2}{5}\) of \(£45\): \(45 \div 5 = 9\), and \(9 \times 2 = 18\), so the answer is \(£18\). Showing both steps earns method marks.
Checking the answer is sensible
A proper fraction of an amount is always smaller than the amount. A fraction close to \(1\), such as \(\frac{7}{8}\), gives an answer close to the original.
If your answer is larger than the starting amount, you have multiplied and divided the wrong way round.
Working backwards
Some questions give you the fraction and the part, and ask for the whole. Reverse the steps: divide by the numerator, then multiply by the denominator.
If \(\frac{3}{4}\) of a number is \(60\), one quarter is \(20\), so the whole is \(80\).
Key points
- The denominator tells you how many parts to divide into.
- The numerator tells you how many parts to take.
- Divide first, then multiply, to keep numbers small.
- A proper fraction of an amount is always smaller than the amount.
- The word of means multiply.
- To find the whole from a part, reverse the two steps.
Worked examples
Example 1
Find \(\frac{3}{5}\) of \(£40\).
Working
Example 2
Find \(\frac{5}{8}\) of \(£72\).
Working
Example 3
\(\frac{2}{3}\) of a number is \(18\). Find the number.
Working
Common mistakes
Multiplying by the denominator instead of dividing.
That makes the answer far larger than the original amount, which cannot be right for a proper fraction.
Dividing by the numerator by mistake.
For 3/5 of 40 you divide by 5, not 3. The denominator sets the number of parts.
Stopping after the division.
Finding one fifth is only half the method. The numerator step must follow.
Not reversing the steps in a working-backwards question.
If a part is given and the whole is wanted, you divide by the numerator, not the denominator.
Exam tips
- Write the division and multiplication as two separate lines.
- Sense-check that the answer is smaller than the original amount.
- Include units such as the pound sign in money answers.
- For working backwards, find one part first, then scale up to the whole.
Key terms
- Numerator
- The top of a fraction, showing how many parts are taken.
- Denominator
- The bottom of a fraction, showing how many equal parts make a whole.
- Proper fraction
- A fraction less than 1, where the numerator is smaller than the denominator.
- Of
- In fraction questions, an instruction to multiply.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.