Practise 18 exam-style questions on Fractions and percentages as operators for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
18 questions
1–5 marks each
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18 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
35% means \(\dfrac{35}{100}\), so 35% of £240 is \(0.35 \times 240\). Without a calculator, build it from easy parts: 10%, then 30% and 5% (half of 10%).
Mark scheme
1 mark
M1 for a correct method, e.g. \(0.35 \times 240\), or 10% = 24 and 5% = 12 with \(3 \times 24 + 12\)
or \(\dfrac{35}{100} \times 240\); correct answer with no working scores full marks
1 mark
A1 for £84
cao
Question 2
2 marks
Ali says, "If you increase a price by 20% and then decrease the new price by 20%, you get back to the original price."
Is Ali correct? You must show how you get your answer.
Model answer
Increase by 20%: multiply by 1.2 Decrease by 20%: multiply by 0.8 \(1.2 \times 0.8 = 0.96\) The final price is 96% of the original, so Ali is not correct. (For example, £100 → £120 → £96.)
Explanation
Each percentage change acts on the amount at the time. The 20% decrease is taken from a bigger amount than the 20% increase was, so more is taken off than was added. Combining the multipliers, \(1.2 \times 0.8 = 0.96\), shows the overall effect.
Mark scheme
1 mark
M1 for \(1.2 \times 0.8\) (= 0.96), or a correct numerical example, e.g. £100 → £120 → £96
1 mark
C1 for No, with a correct conclusion, e.g. the final price is 96% of the original (a 4% decrease)
Question 3
3 marks
25% of \(a\) is equal to 40% of \(b\).
Find the ratio \(a : b\). Give your answer in its simplest form.
Model answer
\(0.25a = 0.4b\) Multiply by 20: \(5a = 8b\) \(\dfrac{a}{b} = \dfrac{8}{5}\) \(a : b = 8 : 5\)
Explanation
Write the percentages as multipliers to form an equation, then rearrange to find \(\dfrac{a}{b}\). Since 25% of \(a\) equals 40% of \(b\), \(a\) must be the bigger number, so a ratio such as 5 : 8 cannot be right. Check: 25% of 40 = 10 and 40% of 25 = 10.
Mark scheme
1 mark
M1 for \(0.25a = 0.4b\)
oe, e.g. \(\dfrac{a}{4} = \dfrac{2b}{5}\); correct answer with no working scores full marks
1 mark
M1 for rearranging, e.g. \(5a = 8b\) or \(\dfrac{a}{b} = \dfrac{0.4}{0.25}\) or \(a = 1.6b\)
or a correct numerical pair, e.g. \(a = 40\), \(b = 25\)
1 mark
A1 for 8 : 5
cao
Question 4
4 marks
Kate earns £2400 each month. She pays \(\dfrac{1}{5}\) of this in tax. She spends 35% of what is left on rent. She saves \(\dfrac{1}{4}\) of the money she has left after paying tax and rent.
How much does Kate save each month?
Model answer
Tax = \(\dfrac{1}{5} \times 2400 = £480\), left = £1920 Rent = 35% of £1920: 10% = £192, 30% = £576, 5% = £96, so £672 Left = £1920 − £672 = £1248 Saves \(\dfrac{1}{4} \times 1248 = £312\)
Explanation
Each fraction or percentage acts on the amount left at that stage, so work through the steps in order. Taking 35% of £2400 instead of £1920 is the most common error. Check the order of operations in the wording: tax first, then rent, then savings.
Mark scheme
1 mark
P1 for the amount after tax, \(\dfrac{4}{5} \times 2400 = 1920\)
or tax = £480; correct answer with no working scores full marks
1 mark
P1 for 35% of their 1920 (= 672), or 65% of their 1920 (= 1248)
1 mark
P1 for \(\dfrac{1}{4}\) of their amount left after rent
1 mark
A1 for £312
cao
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