Fractions of an amount – GCSE Maths

Foundation · Grade 2

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Finding a fraction of an amount is divide by the bottom, multiply by the top. $\frac{3}{5}$ of $45$ is $45÷5=9$, then $9\times 3=27$. The 'of' is a multiply, so you can also write $\frac{3}{5}\times 45$. Divide first when the numbers are friendly, because $45÷5$ is nicer than multiplying $3\times 45$ and then dividing by $5$.

If a fraction of something is used up, the rest is $1$ minus that fraction, then that fraction of the original amount. With two groups, find each amount (or add the fractions first) and subtract from the total. Both routes must agree.

Keep the units. $\frac{7}{8}$ of $640$ g is $560$ g, not $560$. And do not stop after the divide: one eighth is a stepping stone, not the answer, unless the question asked for $\frac{1}{8}$.

Objectives

• The denominator says how many equal parts.
• 3/5 is three of those parts.
• 3/5 of 40 is the same as 40 × 3 ÷ 5.

Key points

• Find a unit fraction of an amount, e.g. $\frac{1}{5}$ of 45.
• Find any fraction of an amount, e.g. $\frac{3}{5}$ of 45.
• Find the amount that is left after a fraction has been used.
• Solve two-step problems where two different fractions of the same total are given.

Worked examples

Questions and answers

GCSE Maths fractions of an amount questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Multiplying by the denominator.

   Divide by the denominator to find one part.

2. Stopping after one part when the numerator is more than 1.

   Multiply the one part by the numerator.

3. Taking the fraction of the wrong total.

   Read which amount the fraction applies to.

4. Giving the part that was used when the question asks for what is left.

   Take the part used away from the total, then write the amount left.

5. Leaving the unit off the answer.

   Write the unit with the number, for example 560 g.

Exam tips

• This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Write the division and the multiplication on separate lines: each is a method mark.
• If the total does not divide exactly by the denominator, check you have read the question correctly — GCSE numbers are usually chosen to work.

Printable worksheet

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Questions students ask

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More on Fractions of an amount

• Fractions of an amount worked examples and method
  The method in order, key facts and the full lesson explanation

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.