What is R7: Proportion?

Proportion means that two corresponding ratios are equal. Keep the quantities in the same order on both sides, then solve by scaling, finding a unit value, or cross-multiplying.

How many marks are R7 questions worth?

In verified past-paper appearances, R7 questions on Edexcel GCSE Maths 1MA1 have been worth 3–4 marks.

Which past exam papers has R7 appeared in?

R7 has appeared in 6 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Understand and use proportion as equality of ratios

Proportion

Worked answers, methods and verified real exam appearances for R7 on Edexcel GCSE Maths 1MA1.

Explanation

Proportion means that two corresponding ratios are equal. Keep the quantities in the same order on both sides, then solve by scaling, finding a unit value, or cross-multiplying.
If $\dfrac{a}{b}=\dfrac{c}{d}$ with non-zero denominators, then $ad=bc$ .
A unitary method is often clearest in context: find the amount for one unit and scale to the required number.
Decimal answers involving money must be interpreted in pounds and pence.
Examiners award method for a correct proportional relationship even if a later arithmetic slip occurs, so show the equation or unit value.

Worked example

Eight identical notebooks cost £11.20. Use proportion to find the cost of $14$ notebooks.

1.Find the cost of one notebook: $11.20\div8=1.40$ .
2.Scale to $14$ notebooks: $14\times1.40=19.60$ .
3.State the money answer using two decimal places.

Answer: £19.60.

Common mistakes

Don't place corresponding quantities in different orders in the two ratios.
Don't add the same amount instead of multiplying by the same scale factor.
Don't write £19.6 without interpreting the final zero as pence in a money context.

Exam tip

Show either the equal-ratios equation or the value of one unit before giving the scaled answer.

Worked practice

Tier 1 · Easy

Solve the proportion

\frac{x}{15}=\frac{6}{10}

(2)

(Total for Question 1 is 2 marks)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$x=9$	2	$x=15\times\frac{6}{10}=9$ .

Tier 2 · Standard

A recipe uses

180

g of flour for every

120

g of sugar. Leo uses

315

g of flour and

200

g of sugar. Has Leo used flour and sugar in the correct proportion? Show your working.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	No, because $180:120=3:2$ but $315:200=63:40$ .	3	Simplify the recipe ratio to $180:120=3:2$ . Leo's ratio is $315:200=63:40$ , which is not equal to $3:2$ , so the ingredients are not in the correct proportion.

Tier 3 · Hard

Solve

\frac{2x+3}{18}=\frac{x+6}{12}

and verify that the two ratios are equal.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$x=12$ Both ratios equal $\frac{3}{2}$	4	Cross-multiply: $12(2x+3)=18(x+6)$ . This gives $24x+36=18x+108$ , so $6x=72$ and $x=12$ . Substitution gives $27/18=18/12=3/2$ .

Tier 1 · Easy

Which ratio is equal to

5:8

? A

10:18

15:24

20:30

. Write down the letter of the correct ratio.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	B	1	$15:24$ simplifies to $5:8$ after dividing both parts by $3$ , so the correct letter is B.

Tier 2 · Standard

A photograph has width to height ratio

7:4

. Work out its width when its height is

18\,\text{cm}

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$31.5\,\text{cm}$	2	The scale factor from $4$ to $18$ is $18\div4=4.5$ . The width is $7\times4.5=31.5\,\text{cm}$ .

Tier 3 · Hard

A printer produces

126

pages in

3.5

minutes at a constant rate. Work out how long it takes to produce

270

pages.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$7.5$ minutes	3	The printer produces $126\div3.5=36$ pages per minute. The time for $270$ pages is $270\div36=7.5$ minutes.

Tier 2 · Standard

Nine identical bolts have a total mass of

234\,\text{g}

. Work out the total mass of

14

of these bolts.

(2)

(Total for Question 7 is 2 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$364\,\text{g}$	2	One bolt has mass $234\div9=26\,\text{g}$ . Therefore $14$ bolts have mass $14\times26=364\,\text{g}$ .

Tier 3 · Hard

A fruit drink contains syrup and water in the ratio

3 : 8

. After

1.5

litres of water evaporates, the ratio is

3 : 7

. Work out the original volume of the drink.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$16.5$ litres	4	Let the original amounts be $3k$ and $8k$ litres. Equality of the new ratios gives $\dfrac{3k}{8k-1.5}=\dfrac{3}{7}$ . Hence $21k=24k-4.5$ , so $k=1.5$ . The original volume was $11k=16.5$ litres.

Tier 3 · Hard

A photograph is

24\,\text{cm}

wide and

16\,\text{cm}

high. A strip of width

x\,\text{cm}

is cut from both the left edge and the right edge. The new width and height are in the ratio

4 : 3

. Work out

x

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$x=\dfrac{4}{3}\,\text{cm}$	4	The new width is $24-2x$ . Equality of the ratios gives $\dfrac{24-2x}{16}=\dfrac{4}{3}$ . Hence $72-6x=64$ , so $6x=8$ and $x=\dfrac{4}{3}\,\text{cm}$ .

Q10

Tier 3 · Hard

A recipe uses

400\,\text{g}

of toasted oats to make

14

snack bars. During toasting, oats lose

4\%

of their mass. Work out the greatest number of complete snack bars that can be made from

1.875\,\text{kg}

of untoasted oats.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$63$ complete snack bars	4	$1.875\,\text{kg}=1875\,\text{g}$ . After toasting, $1875\times0.96=1800\,\text{g}$ remains. Since $1800\div400=4.5$ recipe batches, the number of bars is $4.5\times14=63$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-11	2F	Q24	3	Allowed	Foundation	QP MS
2022-11	2H	Q15	4	Allowed	Higher	QP MS
2023-06	2H	Q18	3	Allowed	Higher	QP MS
2024-11	3H	Q18	4	Allowed	Higher	QP MS
2022-06	2H	Q14	3	Allowed	Higher	QP MS
2019-06	1H	Q17	4	Non-calculator	Higher	QP MS

Other points in R Ratio, proportion and rates of change

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