What is N12: Fractions and percentages as operators?

To find a/b of an amount, divide by b and multiply by a, or multiply by the fraction directly: 2/7 of 420 is 42027=120. A percentage becomes a decimal or fraction operator, 35% of 420 being 4200.35=147.

How many marks are N12 questions worth?

In verified past-paper appearances, N12 questions on Edexcel GCSE Maths 1MA1 have been worth 1–6 marks.

Which past exam papers has N12 appeared in?

N12 has appeared in 37 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

N12

Interpret fractions and percentages as operators

Fractions and percentages as operators

Worked answers, methods and verified real exam appearances for N12 on Edexcel GCSE Maths 1MA1.

Definition

Specification N12: interpret fractions and percentages as operators. A fraction or percentage “of” a quantity means multiply by it, and a sequence of operators is applied in order, each to the current amount.

Explanation

To find $\dfrac{a}{b}$ of an amount, divide by $b$ and multiply by $a$ , or multiply by the fraction directly: $\dfrac{2}{7}$ of $420$ is $420\times2\div7=120$ . A percentage becomes a decimal or fraction operator, $35\%$ of $420$ being $420\times0.35=147$ .
A percentage change is one multiplier: a $15\%$ decrease multiplies by $0.85$ , an increase of $15\%$ by $1.15$ .
When several operators apply, each acts on the amount that remains, not on the original: “ $\dfrac{3}{8}$ of the reduced price” means multiply the reduced price by $\dfrac{3}{8}$ .
Problems that mix a fraction, a percentage and a ratio are worked one step at a time, subtracting the shares already taken before splitting the remainder, and the scheme gives a process mark for each share.
A correct answer with no working scores nothing on these questions.

Worked example

A machine costs

\pounds640

. Its price is reduced by

15\%

. A customer pays

\dfrac{3}{8}

of the reduced price as a deposit and the rest in one further payment. Work out the amount of the further payment.

(4)

(Total for Question 1 is 4 marks)

Working

1.Apply the reduction multiplier: $640\times0.85=\pounds544$ .
2.Find the deposit as a fraction of the reduced price: $544\times\dfrac{3}{8}=\pounds204$ .
3.Subtract to find the balance: $544-204=\pounds340$ , or directly $544\times\dfrac{5}{8}$ .

Answer: $\pounds340$

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Additional guidance
1	for a process to find the reduced price, eg $640\times0.85$ or $640-640\times15\div100$ (= 544)	P1	oe
	for a process to find the deposit, eg “544” $\times3\div8$ (= 204)	P1
	(dep) for a complete process, eg “544” $-$ “204” or “544” $\times5\div8$	P1
	for $340$	A1	cao

Common mistakes

Don't divide by the numerator and multiply by the denominator for a fraction of an amount.
Don't use $0.15$ as the multiplier for the price after a $15\%$ decrease.
Don't calculate the deposit from the original price instead of the reduced price.

Mark-scheme wording to use

“P1 for 160 ÷ (3+7) (= 16) or 3/(3 + 7) (= 3/10) P1 for “16” × 3 (= 48) or “3/10” × 160 (= 48) P1 for a correct step using 48 eg “48” ÷ 8 (= 6) or “48” × 25 ÷ 100 (= 12) … P1 for a complete process to find the number of petrol cars, eg “48” – “6” – “12” oe … A1 cao … Award no marks for a correct answer with no supportive working” — Pearson 1MA1, June 2022 Paper 1H, Q3
“for a process to find the number of banana cakes, eg 420 × 0.35 oe (= 147)” — Pearson 1MA1, June 2017 Paper 3H, Q4
“P1 Process to find number of boys walking and number of girls walking P1 Complete process to find probability A1 10/26 oe” — Pearson 1MA1, Sample Paper 3F, Q15

What the examiner wants

Each operator applied to the right amount, in order. The November 2024 Paper 3H report describes a ratio and percentage problem where students who found the quantities correctly then worked out a percentage profit for each item separately and added them, giving $88.8\%$ , and the Paper 3H report of the same series notes that increasing or decreasing $\pounds46.75$ by $15\%$ scored nothing when the operator had to be reversed.

Exam tip

Write each fraction or percentage as a multiplier beside the amount it operates on.

Worked practice

Tier 1 · Easy

Work out

\dfrac{3}{5}

70

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$42$	1	Divide by $5$ and multiply by $3$ : $70\div5\times3=14\times3=42$ .

Tier 2 · Standard

Work out

17.5\%

240

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$42$	2	Use the decimal operator $17.5\%=0.175$ . Then $0.175\times240=42$ .

Tier 3 · Hard

A machine costs

\pounds640

. Its price is reduced by

15\%

, then a customer pays

\dfrac{3}{8}

of the reduced price as a deposit. Work out the balance still to pay.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$\pounds340$	4	After the reduction, the price is $0.85\times640=544$ . The deposit is $\dfrac{3}{8}\times544=204$ . Therefore the remaining balance is $544-204=340$ .

Tier 1 · Easy

Work out

30\%

90

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$27$	1	$10\%$ of $90$ is $9$ , so $30\%$ is $3\times9=27$ .

Tier 2 · Standard

A museum ticket costs

\pounds35

. Its price is increased by

18\%

. Work out the new price.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$\pounds41.30$	2	$18\%$ of $\pounds35$ is $0.18\times35=\pounds6.30$ . Adding the increase gives $\pounds35+\pounds6.30=\pounds41.30$ .

Tier 3 · Hard

\dfrac{3}{5}

250

students travel by bus. Of these students,

40\%

buy lunch at school. Work out how many bus students buy lunch at school.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$60$ students	3	The number travelling by bus is $\dfrac35\times250=150$ . Then $40\%$ of $150$ is $0.4\times150=60$ , so $60$ bus students buy lunch at school.

Tier 2 · Standard

35\%

of a number is

84

. Work out the number.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$240$	3	$35\%=\dfrac{35}{100}$ . If $35\%$ is $84$ , then $5\%$ is $84\div7=12$ , so $100\%$ is $12\times20=240$ .

Tier 3 · Hard

A charity receives

480

entries. Of these entries,

35\%

are made online. Three eighths of the online entries are incomplete. Work out the number of complete online entries.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$105$ entries	4	The number made online is $0.35\times480=168$ . The complete fraction is $1-\dfrac38=\dfrac58$ . Therefore the number of complete online entries is $\dfrac58\times168=105$ .

Tier 3 · Hard

Three fifths of a positive number is

42

greater than

25\%

of the number. Work out the number.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$120$	4	The difference between $\dfrac35=60\%$ and $25\%$ is $35\%$ . Therefore $35\%$ of the number is $42$ , so the number is $42\div0.35=120$ .

Q10

Tier 3 · Hard

A tank loses

15\%

of its water. It then loses one quarter of the water that remains. Zoya says the tank has lost

40\%

of its original amount. Is Zoya correct? Give a reason.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	No; the tank has lost $36.25\%$ (or $\dfrac{29}{80}$ ) of its original amount.	4	After the first loss, $85\%$ remains. Three quarters of this then remains, so the final fraction is $0.85\times\dfrac34=0.6375$ . The fraction lost is $1-0.6375=0.3625=36.25\%=\dfrac{29}{80}$ , not $40\%$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2022-11	3F	Q7	3	Allowed	Foundation	QP MS
2021-11	3F	Q14	3	Allowed	Foundation	QP MS
2024-06	2F	Q25	4	Allowed	Foundation	QP MS
2019-11	3F	Q2	1	Allowed	Foundation	QP MS
2023-11	2F	Q15	3	Allowed	Foundation	QP MS
2024-11	3F	Q9	5	Allowed	Foundation	QP MS
2023-11	2F	Q5	1	Allowed	Foundation	QP MS
2024-06	1F	Q26	5	Non-calculator	Foundation	QP MS
2021-11	1F	Q11	6	Non-calculator	Foundation	QP MS
2019-11	3F	Q15	4	Allowed	Foundation	QP MS
2023-06	1F	Q14	5	Non-calculator	Foundation	QP MS
2022-06	1F	Q25	5	Non-calculator	Foundation	QP MS
2019-11	3F	Q11	5	Allowed	Foundation	QP MS
2024-06	2H	Q6	4	Allowed	Higher	QP MS
2019-06	2F	Q15	4	Allowed	Foundation	QP MS
2022-11	2F	Q12	4	Allowed	Foundation	QP MS
2022-11	1F	Q18	5	Non-calculator	Foundation	QP MS
2023-06	2F	Q13	2	Allowed	Foundation	QP MS
2019-06	3H	Q10	3	Allowed	Higher	QP MS
2021-11	3F	Q4	1	Allowed	Foundation	QP MS
2022-06	3F	Q2	1	Allowed	Foundation	QP MS
2024-06	1H	Q7	5	Non-calculator	Higher	QP MS
2022-11	1F	Q12	5	Non-calculator	Foundation	QP MS
2019-06	3F	Q8	3	Allowed	Foundation	QP MS
2023-11	1F	Q5	1	Non-calculator	Foundation	QP MS
2023-06	3H	Q2	5	Allowed	Higher	QP MS
2019-06	3F	Q23	5	Allowed	Foundation	QP MS
2024-06	2F	Q12	3	Allowed	Foundation	QP MS
2019-06	1F	Q14	2	Non-calculator	Foundation	QP MS
2022-11	1H	Q5	2	Non-calculator	Higher	QP MS
2023-06	3H	Q9	2	Allowed	Higher	QP MS
2021-11	2F	Q19	4	Allowed	Foundation	QP MS
2022-06	3F	Q19	4	Allowed	Foundation	QP MS
2024-11	3F	Q2	1	Allowed	Foundation	QP MS
2019-06	3F	Q6	2	Allowed	Foundation	QP MS
2023-06	1F	Q10	4	Non-calculator	Foundation	QP MS
2022-06	1H	Q3	5	Non-calculator	Higher	QP MS

Other points in N Number

Want help turning this into marks?

Bring N12 or any tricky specification point, and we can work through the method and exam wording together.

Book a free intro call