What is R4: Ratio notation?

Ratio notation compares quantities in a fixed order, for example a:b. Before simplifying, express every quantity in the same units.

How many marks are R4 questions worth?

In verified past-paper appearances, R4 questions on Edexcel GCSE Maths 1MA1 have been worth 1–7 marks.

Which past exam papers has R4 appeared in?

R4 has appeared in 21 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Use ratio notation, including reduction to simplest form

Ratio notation

Worked answers, methods and verified real exam appearances for R4 on Edexcel GCSE Maths 1MA1.

Explanation

Ratio notation compares quantities in a fixed order, for example $a:b$ . Before simplifying, express every quantity in the same units.
An equivalent ratio is produced by multiplying or dividing every part by the same non-zero value.
For an integer ratio, divide all parts by their highest common factor; when decimals occur, first scale them to integers if helpful.
Ratios can have more than two parts, and a shared part can be matched using a common multiple.
Examiners require the stated order to be preserved and usually expect the simplest integer form.

Worked example

Given $x:y=4:7$ and $y:z=6:5$ , find $x:y:z$ in its simplest integer form.

1.Match the shared $y$ using $\operatorname{lcm}(7,6)=42$ .
2.Scale $4:7$ by $6$ to obtain $x:y=24:42$ .
3.Scale $6:5$ by $7$ to obtain $y:z=42:35$ , so $x:y:z=24:42:35$ .

Answer: $24:42:35$ .

Common mistakes

Don't change the order of the quantities while simplifying the ratio.
Don't divide only one part rather than every part by the same value.
Don't join two ratios without first making their shared part equal.

Exam tip

For linked ratios, show the common value of the repeated quantity to secure the method mark.

Worked practice

Tier 1 · Easy

Write the ratio

42:63

in its simplest form.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$2:3$	1	The highest common factor of $42$ and $63$ is $21$ . Dividing both parts by $21$ gives $2:3$ .

Tier 2 · Standard

Write

1.8\,\text{m}:75\,\text{cm}

as a ratio in its simplest form.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$12:5$	2	Convert $1.8\,\text{m}$ to $180\,\text{cm}$ . Then $180:75=12:5$ after dividing both parts by $15$ .

Tier 3 · Hard

Write

\dfrac{2}{3}:1.5:\dfrac{5}{6}

as a ratio in its simplest integer form.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$4:9:5$	3	Write $1.5=3/2$ . Multiplying every part by $6$ clears all the denominators: $6(2/3):6(3/2):6(5/6)=4:9:5$ .

Tier 1 · Easy

Write

0.6:1.5

as a ratio in its simplest form.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$2:5$	1	Multiply both parts by $10$ to get $6:15$ , then divide both parts by $3$ to get $2:5$ .

Tier 2 · Standard

Write

1.2\,\text{kg}:450\,\text{g}:750\,\text{g}

as a ratio in its simplest form.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$8:3:5$	2	Convert $1.2\,\text{kg}$ to $1200\,\text{g}$ . Then $1200:450:750=8:3:5$ after dividing every part by $150$ .

Tier 3 · Hard

The ratio

p:q:r

4:7:9

. Write

(p+2q):(2r-p)

in its simplest form.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$9:7$	3	Write $p=4k$ , $q=7k$ and $r=9k$ . Then $p+2q=4k+14k=18k$ and $2r-p=18k-4k=14k$ . The ratio $18k:14k$ simplifies to $9:7$ .

Tier 2 · Standard

A class contains

18

boys and

30

girls. On one day,

\dfrac{1}{3}

of the boys and

\dfrac{1}{5}

of the girls are absent. Write the ratio of boys present to girls present in its simplest form.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$1 : 2$	3	$18\times\dfrac{2}{3}=12$ boys and $30\times\dfrac{4}{5}=24$ girls are present. The ratio $12 : 24$ simplifies to $1 : 2$ .

Tier 3 · Hard

Write

2\,\text{m}/\text{s} : 150\,\text{cm}/\text{s} : 0.09\,\text{km}/\text{min}

as a ratio in its simplest integer form.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$4 : 3 : 3$	4	In metres per minute, the rates are $2\times60=120$ , $1.5\times60=90$ and $0.09\times1000=90$ . The ratio $120 : 90 : 90$ simplifies to $4 : 3 : 3$ .

Tier 3 · Hard

Write

32\% : 0.44 : \dfrac{3}{8}

as a ratio of whole numbers in its simplest form.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$64 : 88 : 75$	3	$32\%=\dfrac{8}{25}$ and $0.44=\dfrac{11}{25}$ . Multiplying all three parts by $200$ gives $64 : 88 : 75$ , which has no common factor.

Q10

Tier 3 · Hard

The ratios

a:b=3:5

and

b:c=10:7

. Work out

(a+c):(b-a)

in its simplest form.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$13 : 4$	4	Match the shared quantity $b$ : $a:b=6:10$ and $b:c=10:7$ , so take $a=6k$ , $b=10k$ and $c=7k$ . Then $a+c=13k$ and $b-a=4k$ , giving $13 : 4$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-06	1F	Q10	2	Non-calculator	Foundation	QP MS
2024-06	3F	Q20	5	Allowed	Foundation	QP MS
2024-11	1F	Q9	7	Non-calculator	Foundation	QP MS
2019-11	3F	Q6	1	Allowed	Foundation	QP MS
2022-11	1F	Q13	4	Non-calculator	Foundation	QP MS
2023-06	3F	Q28	4	Allowed	Foundation	QP MS
2023-11	2F	Q10	2	Allowed	Foundation	QP MS
2023-06	2F	Q9	3	Allowed	Foundation	QP MS
2022-06	3H	Q3	5	Allowed	Higher	QP MS
2021-11	3H	Q14	4	Allowed	Higher	QP MS
2022-11	3F	Q12	2	Allowed	Foundation	QP MS
2022-06	1F	Q29	3	Non-calculator	Foundation	QP MS
2022-11	1F	Q24	6	Non-calculator	Foundation	QP MS
2022-06	2F	Q9	3	Allowed	Foundation	QP MS
2019-11	1H	Q2	4	Non-calculator	Higher	QP MS
2024-11	2F	Q9	2	Allowed	Foundation	QP MS
2021-11	1F	Q12	3	Non-calculator	Foundation	QP MS
2019-11	1F	Q21	4	Non-calculator	Foundation	QP MS
2019-06	2F	Q14	1	Allowed	Foundation	QP MS
2022-11	1H	Q6	6	Non-calculator	Higher	QP MS
2022-06	3F	Q24	5	Allowed	Foundation	QP MS

Other points in R Ratio, proportion and rates of change

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