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

Practise 18 exam-style questions on One quantity as a fraction of another for Edexcel GCSE Maths (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

There are 1248 students at a school.
546 of the students travel to school by bus.

What fraction of the students travel to school by bus?
Give your answer in its simplest form.

Model answer

\(\dfrac{546}{1248}\)
Highest common factor of 546 and 1248 is 78
\(\dfrac{546 \div 78}{1248 \div 78} = \dfrac{7}{16}\)

Explanation

The fraction is (number who travel by bus) ÷ (total number of students). Simplify by dividing by common factors, or use the fraction button on your calculator, which gives the simplest form directly.

Mark scheme

1 mark
M1 for \(\dfrac{546}{1248}\) or a correct partial simplification, e.g. \(\dfrac{273}{624}\) or \(\dfrac{91}{208}\)
correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{7}{16}\)
cao

Question 2

2 marks

Jamal earns £2240 each month.
He pays £680 each month in rent.

Jamal says, "I spend more than \(\dfrac{1}{3}\) of my earnings on rent."

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

Model answer

Rent as a fraction of earnings = \(\dfrac{680}{2240} = \dfrac{17}{56} = 0.3035...\)
\(\dfrac{1}{3} = 0.3333...\)
0.3035... is less than 0.3333..., so Jamal is not correct.

Explanation

Write the rent as a fraction of the earnings and compare it with \(\frac{1}{3}\), using decimals or a common denominator. Alternatively, work out \(\frac{1}{3}\) of £2240 (£746.67) and compare it with £680.

Mark scheme

1 mark
M1 for \(\dfrac{680}{2240}\) (= 0.303... or \(\dfrac{17}{56}\)), or for \(\dfrac{1}{3} \times 2240\) (= 746.66...)
1 mark
C1 for No, with correct comparable figures, e.g. 0.303... < 0.333... or £680 < £746.67

Question 3

3 marks

The pie charts show information about the favourite subjects of the students in Year 10 and in Year 11.
There are 144 students in Year 10 and 108 students in Year 11.

Write the number of Year 11 students whose favourite subject is Science as a fraction of the number of Year 10 students whose favourite subject is Science.
Give your answer in its simplest form.

Model answer

Year 10 Science: \(\dfrac{150}{360} \times 144 = 60\) students
Year 11 Science: \(\dfrac{140}{360} \times 108 = 42\) students
\(\dfrac{42}{60} = \dfrac{7}{10}\)

Explanation

The pie charts show different totals, so you cannot compare the angles directly: work out the actual number of students in each Science sector first. Then put the Year 11 number on top, because it is the quantity written as a fraction of the Year 10 number.

Mark scheme

1 mark
M1 for a correct method to find the number of students for one Science sector, e.g. \(\dfrac{150}{360} \times 144\) (= 60) or \(\dfrac{140}{360} \times 108\) (= 42)
correct answer with no working scores full marks
1 mark
M1 for both 60 and 42, and \(\dfrac{42}{60}\)
1 mark
A1 for \(\dfrac{7}{10}\)
cao

Question 4

4 marks

There are 240 students in Year 9.
\(\dfrac{5}{8}\) of the students are girls. The rest are boys.

\(\dfrac{3}{5}\) of the girls go on a school trip.
\(\dfrac{2}{3}\) of the boys go on the same school trip.

What fraction of the students who go on the trip are boys?

Model answer

Girls = \(\dfrac{5}{8} \times 240 = 150\); boys = \(240 - 150 = 90\)
Girls on the trip = \(\dfrac{3}{5} \times 150 = 90\)
Boys on the trip = \(\dfrac{2}{3} \times 90 = 60\)
Students on the trip = \(90 + 60 = 150\)
Fraction who are boys = \(\dfrac{60}{150} = \dfrac{2}{5}\)

Explanation

The denominator is the number of students on the trip, not the whole year group. Work out the numbers of girls and boys, then how many of each go. A common mistake is to give \(\frac{60}{240}\) or \(\frac{60}{90}\).

Mark scheme

1 mark
P1 for the number of girls, \(\dfrac{5}{8} \times 240\) (= 150), or boys (= 90)
correct answer with no working scores full marks
1 mark
P1 for girls on the trip, \(\dfrac{3}{5} \times 150\) (= 90), or boys on the trip, \(\dfrac{2}{3} \times 90\) (= 60)
1 mark
P1 for the total on the trip (150) and \(\dfrac{60}{150}\)
1 mark
A1 for \(\dfrac{2}{5}\)
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