What is N11: Fractions in ratio problems?

Fractions and ratios describe the same partition in different forms. If a group is 3/5 of the whole, the remainder is 2/5, so the part-to-part ratio is 3:2.

How many marks are N11 questions worth?

In verified past-paper appearances, N11 questions on Edexcel GCSE Maths 1MA1 have been worth 2–6 marks.

Which past exam papers has N11 appeared in?

N11 has appeared in 5 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

N11

Identify and work with fractions in ratio problems

Fractions in ratio problems

Worked answers, methods and verified real exam appearances for N11 on Edexcel GCSE Maths 1MA1.

Explanation

Fractions and ratios describe the same partition in different forms. If a group is $\dfrac35$ of the whole, the remainder is $\dfrac25$ , so the part-to-part ratio is $3:2$ .
Conversely, in a ratio $a:b$ , the first share is $\dfrac{a}{a+b}$ of the whole and the second is $\dfrac{b}{a+b}$ .
In multi-step problems, first use the ratio to find each share, then apply any fraction operator to the relevant share.
Keep the named order of the groups throughout.
Examiners commonly award one mark for finding one ratio part and a later accuracy mark for the required fractional amount.

Worked example

$\pounds330$ is shared between Imran and Jo in the ratio $4:7$ . Imran spends $\dfrac38$ of his share and Jo spends $\dfrac27$ of hers. Find the total left.

1.There are $11$ parts, so one part is $330\div11=30$ .
2.Imran gets $120$ and keeps $\dfrac58\times120=75$ ; Jo gets $210$ and keeps $\dfrac57\times210=150$ .
3.Add the amounts kept: $75+150=225$ .

Answer: $\pounds225$ .

Common mistakes

Don't say the remainder of $\dfrac35$ is $\dfrac55$ instead of $\dfrac25$ .
Don't use one ratio part as the denominator of the fraction of the whole.
Don't apply a spending fraction as though it were the fraction left.

Exam tip

Label each share and write the total number of ratio parts before applying any later fraction.

Worked practice

Tier 1 · Easy

\dfrac{3}{5}

of the beads in a bag are red and the rest are blue. Write the ratio of red beads to blue beads.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$3:2$	1	The blue fraction is $1-\dfrac{3}{5}=\dfrac{2}{5}$ . Therefore red : blue is $\dfrac{3}{5}:\dfrac{2}{5}=3:2$ .

Tier 2 · Standard

The ratio of Ava's tokens to Ben's tokens is

5:7

. Ben has

84

tokens. Work out

\dfrac{3}{4}

of Ava's number of tokens.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$45$ tokens	3	Seven ratio parts represent $84$ , so one part is $84\div7=12$ . Ava has $5\times12=60$ tokens. Then $\dfrac{3}{4}\times60=45$ .

Tier 1 · Easy

The ratio of silver counters to gold counters is

4:9

. Write the fraction of the counters that are gold.

(1)

(Total for Question 3 is 1 mark)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$\dfrac{9}{13}$	1	There are $4+9=13$ equal parts altogether and $9$ are gold, so the required fraction is $\dfrac9{13}$ .

Tier 2 · Standard

\dfrac{2}{5}

of some tiles are yellow. One quarter of the remaining tiles are green and the rest are blue. Write the ratio yellow : green : blue.

(3)

(Total for Question 4 is 3 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$8:3:9$	3	Use $20$ equal parts. Yellow tiles take $8$ parts, leaving $12$ . Green tiles take one quarter of the remainder, so take $3$ parts, leaving $9$ blue parts. The ratio is $8:3:9$ .

Tier 3 · Hard

Red, blue and green beads are in the ratio

2:5:3

. Half of the red beads are removed. Work out the fraction of the remaining beads that are blue.

(3)

(Total for Question 5 is 3 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$\dfrac{5}{9}$	3	Start with $2+5+3=10$ equal parts. Removing half of the red beads removes $1$ part, so $9$ parts remain. The $5$ blue parts are therefore $\dfrac59$ of the remaining beads.

Tier 2 · Standard

The ratio of adults to children at an event is

7 : 4

. Three eighths of the children wear hats. Work out the fraction of all the people at the event who are children wearing hats.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$\dfrac{3}{22}$	3	Children make up $\dfrac4{11}$ of all the people. The required fraction is $\dfrac38\times\dfrac4{11}=\dfrac{12}{88}=\dfrac3{22}$ .

Tier 3 · Hard

The ratio

A : B

4 : 9

. The amount

A

\dfrac27

of the amount

C

. Work out the fraction of the total amount

A+B+C

that is

B

(4)

(Total for Question 7 is 4 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$\dfrac13$	4	Use $A=8$ equal parts. Then $A : B=4 : 9$ gives $B=18$ parts. Since $A=\dfrac27C$ , $C=28$ parts. The total is $8+18+28=54$ parts, so the fraction that is $B$ is $\dfrac{18}{54}=\dfrac13$ .

Tier 3 · Hard

The ratio of adults to children at a show is

7:5

. One third of the adults and one fifth of the children leave. There are then

78

people at the show. Work out the number of people who were at the show before anyone left.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$108$ people	4	Let the original numbers be $7k$ and $5k$ . The numbers remaining are $\dfrac23\times7k=\dfrac{14k}{3}$ adults and $\dfrac45\times5k=4k$ children. Thus $\dfrac{26k}{3}=78$ , so $k=9$ . Originally there were $12k=108$ people.

Tier 3 · Hard

Two positive amounts are

A

and

B

. Two fifths of

A

is equal to three sevenths of

B

. Work out the fraction of

A+B

that is

A

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$\dfrac{15}{29}$	3	$\dfrac25A=\dfrac37B$ . Multiplying by $35$ gives $14A=15B$ , so $A:B=15:14$ . There are $29$ ratio parts altogether and $15$ belong to $A$ , so the required fraction is $\dfrac{15}{29}$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2022-11	3H	Q17	4	Allowed	Higher	QP MS
2022-11	1F	Q24	6	Non-calculator	Foundation	QP MS
2023-11	3F	Q11	2	Allowed	Foundation	QP MS
2022-06	1H	Q11	3	Non-calculator	Higher	QP MS
2022-11	1H	Q6	6	Non-calculator	Higher	QP MS

Other points in N Number

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