One quantity as a fraction of another - Edexcel GCSE Maths (Non-calculator) Exam Questions

Practise 18 exam-style questions on One quantity as a fraction of another 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.

Question 1

2 marks

Write 750 g as a fraction of 2 kg.
Give your answer in its simplest form.

Model answer

2 kg = 2000 g
\(\dfrac{750}{2000} = \dfrac{75}{200} = \dfrac{3}{8}\)

Explanation

Change both quantities to the same units before writing the fraction: 2 kg = 2000 g. Then cancel step by step (by 10, then by 25).

Mark scheme

1 mark
M1 for \(\dfrac{750}{2000}\) oe, i.e. both quantities in the same units
or \(\dfrac{0.75}{2}\); correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{3}{8}\)
cao

Question 2

2 marks

Write \(3x\) centimetres as a fraction of \(2y\) metres.
Give your answer in its simplest form.

Model answer

\(2y\) m \(= 200y\) cm
Fraction \(= \dfrac{3x}{200y}\)

Explanation

The method is the same as with numbers: put both lengths in the same units, then write the first over the second. 1 m = 100 cm, so \(2y\) m is \(200y\) cm.

Mark scheme

1 mark
M1 for converting to the same units, e.g. \(2y\) m \(= 200y\) cm
or \(3x\) cm \(= 0.03x\) m; correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{3x}{200y}\)
oe in simplest form

Question 3

3 marks

The population of a village was 2400 in 2015.
The population was 3000 in 2025.

Ben says,
"The population went up by \(\dfrac{1}{4}\), so the 2015 population was \(\dfrac{1}{4}\) less than the 2025 population."

Is Ben correct?
You must show how you get your answer.

Model answer

2025 as a fraction of 2015: \(\dfrac{3000}{2400} = \dfrac{5}{4}\), so it went up by \(\dfrac{1}{4}\).
2015 as a fraction of 2025: \(\dfrac{2400}{3000} = \dfrac{4}{5}\)
So the 2015 population was \(\dfrac{1}{5}\) less than the 2025 population.
Ben is not correct.

Explanation

The fraction depends on which quantity you compare with. The increase of 600 is \(\dfrac{1}{4}\) of 2400 but only \(\dfrac{1}{5}\) of 3000, so going backwards the decrease is \(\dfrac{1}{5}\), not \(\dfrac{1}{4}\).

Mark scheme

1 mark
M1 for \(\dfrac{3000}{2400} = \dfrac{5}{4}\), or the increase \(\dfrac{600}{2400} = \dfrac{1}{4}\)
1 mark
M1 for \(\dfrac{2400}{3000} = \dfrac{4}{5}\), or \(\dfrac{600}{3000} = \dfrac{1}{5}\)
1 mark
C1 for No, the 2015 population was \(\dfrac{1}{5}\) less than the 2025 population

Question 4

4 marks

A train takes 2 hours 30 minutes to travel 240 km between two cities.
A car travels the same 240 km at an average speed of 80 km/h.

Write the time taken by the train as a fraction of the time taken by the car.
Give your answer in its simplest form.

Model answer

Car: time = 240 ÷ 80 = 3 hours = 180 minutes
Train: 2 hours 30 minutes = 150 minutes
\(\dfrac{150}{180} = \dfrac{5}{6}\)

Explanation

First find the car's time using time = distance ÷ speed. Then write both times in minutes (or in hours as decimals, not 2.30) before forming the fraction.

Mark scheme

1 mark
P1 for the time taken by the car, 240 ÷ 80 = 3 hours
correct answer with no working scores full marks
1 mark
P1 for both times in the same units, e.g. 150 minutes and 180 minutes, or 2.5 hours and 3 hours
1 mark
P1 for \(\dfrac{150}{180}\) or \(\dfrac{2.5}{3}\)
ft their car time
1 mark
A1 for \(\dfrac{5}{6}\)
cao

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