What is R5: Dividing in a ratio?

In a part:part ratio a:b the whole is a+b equal shares, so divide the quantity by a+b to find one share and multiply by each part; dividing by a and by b separately is the error every scheme lists. Check that the parts add back to the total.

How many marks are R5 questions worth?

In verified past-paper appearances, R5 questions on Edexcel GCSE Maths 1MA1 have been worth 1–5 marks.

Which past exam papers has R5 appeared in?

R5 has appeared in 67 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Divide a quantity in a given part:part or part:whole ratio; express division into two parts as a ratio; apply ratio to real problems (conversion, comparison, scaling, mixing, concentrations)

Dividing in a ratio

Worked answers, methods and verified real exam appearances for R5 on Edexcel GCSE Maths 1MA1.

Definition

Specification R5: divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems, such as those involving conversion, comparison, scaling, mixing and concentrations.

Explanation

In a part:part ratio $a:b$ the whole is $a+b$ equal shares, so divide the quantity by $a+b$ to find one share and multiply by each part; dividing by $a$ and by $b$ separately is the error every scheme lists. Check that the parts add back to the total.
A part:whole statement is read differently: if one part is $\dfrac{3}{8}$ of the whole, the other is $\dfrac{5}{8}$ and the ratio is $3:5$ . To express a division as a ratio, write the two amounts in order and simplify by their highest common factor.
Multi-step problems combine a ratio with fractions or percentages of the same total: remove the fraction and percentage shares first, then split the remainder in the ratio.
For mixing or concentration, track the actual amount of the ingredient, not an average of percentages.
Label which part is which in the final answer.

Worked example

Amira and Ben share

\pounds84

in the ratio

3:4

. Ben then gives Amira

\pounds12

. Write the ratio of the amount Amira now has to the amount Ben now has. Give your answer in its simplest form.

(4)

(Total for Question 1 is 4 marks)

Working

1.One share is $84\div(3+4)=84\div7=\pounds12$ .
2.Amira has $3\times12=\pounds36$ and Ben has $4\times12=\pounds48$ ; check $36+48=84$ .
3.After the transfer Amira has $36+12=\pounds48$ and Ben has $48-12=\pounds36$ .
4.The ratio $48:36$ simplifies by $12$ to $4:3$ .

Answer: $4:3$

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Additional guidance
1	for a process to find one share, eg $84\div(3+4)$ (= 12)	P1
	for a process to find both amounts, eg $3\times$ “12” (= 36) and $4\times$ “12” (= 48)	P1
	(dep) for a complete process, eg “36” $+12$ : “48” $-12$	P1
	for $4:3$	A1	cao

Common mistakes

Don't divide the total by one ratio part instead of by the sum of all parts.
Don't treat a part:whole ratio as though both numbers were separate parts.
Don't average two concentrations without accounting for the volumes mixed.

Mark-scheme wording to use

“Identifies a mistake in the working … Rob should divide by 8 … He should have added the 3 and 5 first” — Pearson 1MA1, November 2022 Paper 3H, Q2
“for a process to find the number of vanilla cakes, eg 420 × 2 ÷ 7 oe (= 120)” — Pearson 1MA1, June 2017 Paper 3H, Q4
“P1 for a process to start to work with the ratio, eg 240 ÷ (3 + 5) (= 30) … P1 for a complete process to find the number of pens and pencils, eg “30” × 3 (= 90) and “30” × 5 (= 150) … P1 for a process to find the total cost to buy or the total amount to sell for both, … P1 for a complete process to find the profit as a percentage or a decimal, … A1 answer in the range 45.6 to 45.62” — Pearson 1MA1, November 2024 Paper 3H, Q5

What the examiner wants

A correct first step from the ratio and a systematic layout. The November 2024 Paper 3H report says most began well by using the ratio to find the two quantities, but those who divided $240$ by $3$ and by $5$ separately lost the start, and others lost their way through a lack of a systematic approach to the later steps.

Exam tip

Label each share or variable, then check that the parts sum to the stated whole.

Worked practice

Tier 1 · Easy

Divide £84 in the ratio

3:4

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	£36 and £48	2	There are $3+4=7$ shares, so one share is £ $84/7=£12$ . The two amounts are $3\times£12=£36$ and $4\times£12=£48$ .

Tier 2 · Standard

A box holds

240

counters. Red counters make up

\frac{3}{8}

of the whole. Find the number of red and non-red counters, and state their ratio.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$90$ red counters $150$ non-red counters Ratio $3:5$	3	Red counters: $\frac{3}{8}\times240=90$ . The remainder is $240-90=150$ . Thus red:non-red is $90:150=3:5$ .

Tier 3 · Hard

Aisha and Ben share some money in the ratio

3:5

. Aisha gives £20 of her share to Ben. Their shares are now in the ratio

1:2

. Work out the total amount of money they shared.

(5)

(Total for Question 3 is 5 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	£480	5	Let the original shares be $3k$ pounds and $5k$ pounds. After the transfer, $2(3k-20)=5k+20$ , so $k=60$ . The original total was $8k=8\times60=£480$ .

Tier 1 · Easy

Two lengths are in the ratio

3:7

and differ by

28\,\text{cm}

. Work out the two lengths.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$21\,\text{cm}$ and $49\,\text{cm}$	2	The difference of $7-3=4$ shares represents $28\,\text{cm}$ , so one share is $7\,\text{cm}$ . The lengths are $3\times7=21\,\text{cm}$ and $7\times7=49\,\text{cm}$ .

Tier 2 · Standard

Red, blue and white paint are mixed in the ratio

2:5:3

, and

1.8

litres of white paint is used. Work out the total volume of paint.

(3)

(Total for Question 5 is 3 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$6$ litres	3	The $3$ white shares equal $1.8$ litres, so one share is $1.8\div3=0.6$ litres. There are $2+5+3=10$ shares, giving $10\times0.6=6$ litres in total.

Tier 3 · Hard

A drink is mixed using concentrate and water in the ratio

3:11

. Mia has

1.8

litres of concentrate and

7.2

litres of water. Work out the greatest volume of drink she can make.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$8.4$ litres	3	$1.8$ litres of concentrate needs $1.8\times\dfrac{11}{3}=6.6$ litres of water. Mia has enough water, so the concentrate is used up. The greatest volume is $1.8+6.6=8.4$ litres.

Tier 2 · Standard

A theatre sells

288

tickets. The ratio of adult tickets to child tickets is

7 : 5

. Adult tickets cost £11 and child tickets cost £7. Work out the total money received.

(4)

(Total for Question 7 is 4 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	£2688	4	There are $7+5=12$ shares, so one share is $288\div12=24$ tickets. There are $168$ adult tickets and $120$ child tickets. The total received is $168\times£11+120\times£7=£1848+£840=£2688$ .

Tier 3 · Hard

14

-litre fruit drink contains mango juice and apple juice in the ratio

2 : 5

. A different

12

-litre drink contains mango juice and apple juice in the ratio

1 : 3

. The two drinks are combined. Work out the ratio of mango juice to apple juice in the combined drink.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$7 : 19$	4	The first drink contains $14\times\dfrac{2}{7}=4$ litres of mango and $10$ litres of apple. The second contains $12\times\dfrac{1}{4}=3$ litres of mango and $9$ litres of apple. The combined amounts are $7$ litres and $19$ litres, giving ratio $7 : 19$ .

Tier 3 · Hard

A fund is divided between A, B and C. A receives

\dfrac{2}{5}

of the whole fund. The rest is divided between B and C in the ratio

3 : 4

. C receives £840. Work out the value of the whole fund.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	£2450	4	B and C share $\dfrac{3}{5}$ of the fund. C receives $\dfrac{4}{7}$ of this remainder, so C receives $\dfrac{4}{7}\times\dfrac{3}{5}=\dfrac{12}{35}$ of the whole fund. The whole fund is £ $840\times\dfrac{35}{12}=£2450$ .

Q10

Tier 3 · Hard

A container holds

12

litres of a drink that is

30\%

concentrate. Water is added so that the new drink is

18\%

concentrate. Work out the volume of water added.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$8$ litres	4	The amount of concentrate stays at $0.30\times12=3.6$ litres. If the final volume is $V$ litres, $0.18V=3.6$ , so $V=20$ . The volume of water added is $20-12=8$ litres.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-11	2H	Q20	3	Allowed	Higher	QP MS
2023-06	1H	Q18	4	Non-calculator	Higher	QP MS
2024-06	2F	Q25	4	Allowed	Foundation	QP MS
2019-11	3H	Q13	4	Allowed	Higher	QP MS
2019-11	3F	Q16	4	Allowed	Foundation	QP MS
2022-11	3H	Q19	3	Allowed	Higher	QP MS
2024-06	3H	Q10	3	Allowed	Higher	QP MS
2019-06	2F	Q26	4	Allowed	Foundation	QP MS
2023-11	2F	Q26	4	Allowed	Foundation	QP MS
2019-11	1F	Q24	4	Non-calculator	Foundation	QP MS
2021-11	2H	Q11	5	Allowed	Higher	QP MS
2024-11	3F	Q21	5	Allowed	Foundation	QP MS
2022-11	3F	Q22	1	Allowed	Foundation	QP MS
2024-06	1F	Q26	5	Non-calculator	Foundation	QP MS
2019-11	3H	Q14	4	Allowed	Higher	QP MS
2024-11	2H	Q3	3	Allowed	Higher	QP MS
2019-06	3H	Q14	4	Allowed	Higher	QP MS
2023-11	1F	Q23	4	Non-calculator	Foundation	QP MS
2022-11	3H	Q17	4	Allowed	Higher	QP MS
2022-06	1F	Q25	5	Non-calculator	Foundation	QP MS
2021-11	1F	Q24	3	Non-calculator	Foundation	QP MS
2021-11	3H	Q14	4	Allowed	Higher	QP MS
2024-06	2H	Q6	4	Allowed	Higher	QP MS
2019-11	2H	Q3	4	Allowed	Higher	QP MS
2023-11	1H	Q6	4	Non-calculator	Higher	QP MS
2023-06	2F	Q22	1	Allowed	Foundation	QP MS
2022-11	1F	Q18	5	Non-calculator	Foundation	QP MS
2019-06	1H	Q2	5	Non-calculator	Higher	QP MS
2022-11	1F	Q17	5	Non-calculator	Foundation	QP MS
2022-06	2H	Q15	4	Allowed	Higher	QP MS
2024-06	2H	Q4	4	Allowed	Higher	QP MS
2019-06	2H	Q7	4	Allowed	Higher	QP MS
2023-11	2H	Q5	4	Allowed	Higher	QP MS
2022-06	2H	Q5	4	Allowed	Higher	QP MS
2021-11	1H	Q18	5	Non-calculator	Higher	QP MS
2019-06	2F	Q9	5	Allowed	Foundation	QP MS
2023-06	2H	Q3	1	Allowed	Higher	QP MS
2024-06	1H	Q7	5	Non-calculator	Higher	QP MS
2023-06	2F	Q25	3	Allowed	Foundation	QP MS
2023-06	2H	Q6	3	Allowed	Higher	QP MS
2021-11	3F	Q22	4	Allowed	Foundation	QP MS
2024-11	3H	Q5	5	Allowed	Higher	QP MS
2019-11	1H	Q5	4	Non-calculator	Higher	QP MS
2021-11	3H	Q2	4	Allowed	Higher	QP MS
2019-11	1H	Q2	4	Non-calculator	Higher	QP MS
2019-06	1F	Q27	4	Non-calculator	Foundation	QP MS
2019-06	3F	Q23	5	Allowed	Foundation	QP MS
2022-11	3F	Q20	4	Allowed	Foundation	QP MS
2024-06	2F	Q23	4	Allowed	Foundation	QP MS
2019-06	2H	Q19	4	Allowed	Higher	QP MS
2022-11	3H	Q4	4	Allowed	Higher	QP MS
2024-11	1F	Q17	3	Non-calculator	Foundation	QP MS
2019-11	1F	Q21	4	Non-calculator	Foundation	QP MS
2022-06	3H	Q18	5	Allowed	Higher	QP MS
2022-06	2F	Q25	4	Allowed	Foundation	QP MS
2022-11	3H	Q2	1	Allowed	Higher	QP MS
2024-06	3F	Q17	3	Allowed	Foundation	QP MS
2022-11	3F	Q24	4	Allowed	Foundation	QP MS
2019-06	1H	Q6	4	Non-calculator	Higher	QP MS
2021-11	3F	Q13	4	Allowed	Foundation	QP MS
2021-11	1H	Q5	3	Non-calculator	Higher	QP MS
2019-11	1H	Q11	2	Non-calculator	Higher	QP MS
2019-11	2F	Q23	4	Allowed	Foundation	QP MS
2023-06	3F	Q15	2	Allowed	Foundation	QP MS
2022-06	1H	Q3	5	Non-calculator	Higher	QP MS
2019-06	3F	Q28	4	Allowed	Foundation	QP MS
2019-11	3H	Q24	5	Allowed	Higher	QP MS

Other points in R Ratio, proportion and rates of change

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