Multiplicative relationships as ratios and fractions - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 19 exam-style questions on Multiplicative relationships as ratios and fractions 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.

19 questions
1–5 marks each
Instant marking
No sign-up needed

19 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

\(3a = 7b\)

Find the ratio \(a : b\).

Model answer

\(3a = 7b\)
Divide both sides by \(3b\): \(\frac{a}{b} = \frac{7}{3}\)
So \(a : b = 7 : 3\)

Explanation

Rearrange to get \(\frac{a}{b}\) on its own: \(\frac{a}{b} = \frac{7}{3}\), which gives \(a : b = 7 : 3\). A quick check is to try \(a = 7\) and \(b = 3\): \(3 \times 7 = 21\) and \(7 \times 3 = 21\). The common mistake is 3 : 7, from copying the numbers in order.

Mark scheme

1 mark
M1 for \(\frac{a}{b} = \frac{7}{3}\) or \(a = \frac{7}{3}b\) or for substituting values, e.g. \(a = 7, b = 3\)
oe; correct answer with no working scores full marks
1 mark
A1 for 7 : 3
cao; do not accept 3 : 7

Question 2

2 marks

\(a : b = 2 : 3\)

Sophie says, "This means that \(a\) is \(\frac{2}{5}\) of \(b\)."

Is Sophie correct?
Give a reason for your answer.

Model answer

No. If \(a : b = 2 : 3\) then \(\frac{a}{b} = \frac{2}{3}\), so \(a\) is \(\frac{2}{3}\) of \(b\).
\(\frac{2}{5}\) is \(a\) as a fraction of the total, \(a + b\).

Explanation

A ratio \(a : b = 2 : 3\) compares \(a\) directly with \(b\), so \(a = \frac{2}{3}b\). Sophie has added the parts to get 5, which gives \(a\) as a fraction of \(a + b\). Testing with numbers (\(a = 2\), \(b = 3\)) is a quick way to check a claim like this.

Mark scheme

1 mark
B1 for \(a = \frac{2}{3}b\) or \(a\) is \(\frac{2}{3}\) of \(b\)
oe
1 mark
C1 for No, with a correct reason, e.g. \(\frac{2}{5}\) is \(a\) as a fraction of \(a + b\), not of \(b\)
accept a correct counter-example, e.g. \(a = 2, b = 3\) and 2 is not \(\frac{2}{5}\) of 3

Question 3

3 marks

\(2x = 5y\), where \(y\) is not zero.

Find the ratio \((x + y) : (x - y)\).
Give your answer in its simplest form.

Model answer

\(2x = 5y\), so \(x = \frac{5}{2}y\)
\(x + y = \frac{5}{2}y + y = \frac{7}{2}y\)
\(x - y = \frac{5}{2}y - y = \frac{3}{2}y\)
\((x + y) : (x - y) = \frac{7}{2}y : \frac{3}{2}y = 7 : 3\)

Explanation

Write \(x\) in terms of \(y\) (or find \(x : y = 5 : 2\)), then substitute into both brackets. The \(y\)s cancel, which is why the answer is a fixed ratio. Using numbers that fit, such as \(x = 5\) and \(y = 2\), gives 7 : 3 quickly.

Mark scheme

1 mark
M1 for \(x = \frac{5}{2}y\) or \(x : y = 5 : 2\) or substituting values such as \(x = 5, y = 2\)
oe; correct answer with no working scores full marks
1 mark
M1 for \(x + y = \frac{7}{2}y\) and \(x - y = \frac{3}{2}y\), or 7 and 3 from their values
oe
1 mark
A1 for 7 : 3
cao

Question 4

4 marks

At a school:
• the number of students in Year 7 is 1.2 times the number of students in Year 8
• the number of students in Year 9 is \(\frac{5}{6}\) of the number of students in Year 8.

There are 910 students in Years 7, 8 and 9 altogether.

How many students are in Year 7?

Model answer

Let Year 8 have \(n\) students.
Year 7 = \(1.2n\), Year 9 = \(\frac{5}{6}n\)
\(1.2n + n + \frac{5}{6}n = 910\)
\(\frac{91}{30}n = 910\)
\(n = 300\)
Year 7 = 1.2 × 300 = 360

Explanation

Choose the year group that the other two are compared with (Year 8) and call it \(n\). Add the three expressions and solve. As a ratio, Year 7 : Year 8 : Year 9 = 1.2 : 1 : \(\frac{5}{6}\) = 36 : 30 : 25, which is 91 parts. Check: 360 + 300 + 250 = 910.

Mark scheme

1 mark
P1 for writing Year 7 and Year 9 in terms of Year 8, e.g. \(1.2n\) and \(\frac{5}{6}n\)
oe, e.g. Year 7 : Year 8 = 6 : 5 and Year 8 : Year 9 = 6 : 5; correct answer with no working scores full marks
1 mark
P1 for \(1.2n + n + \frac{5}{6}n = 910\) or the ratio 36 : 30 : 25
oe
1 mark
P1 for \(n = 300\) or \(910 \div 91\) (= 10)
1 mark
A1 for 360
cao

Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.

AI Tutor Hints first, answers after you try

Hi! Stuck? Ask me for a hint and I’ll help you work it out. Once you’ve checked your answer I can explain exactly where the marks are.