What is N2: Four operations?

Written methods score for the method, then for the answer. In a decimal division such as 818.41.2, multiply both numbers by the same power of 10 so the divisor is an integer, divide, then place the decimal point by comparing the size of the numbers: 818.41.2 is a little less than 818, so 682 is sensible and 68.2 is not.

How many marks are N2 questions worth?

In verified past-paper appearances, N2 questions on Edexcel GCSE Maths 1MA1 have been worth 1–6 marks.

Which past exam papers has N2 appeared in?

N2 has appeared in 131 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers, positive and negative; understand and use place value

Four operations

Worked answers, methods and verified real exam appearances for N2 on Edexcel GCSE Maths 1MA1.

Definition

Specification N2: apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper) and mixed numbers, all both positive and negative, and understand and use place value.

Explanation

Written methods score for the method, then for the answer. In a decimal division such as $818.4\div1.2$ , multiply both numbers by the same power of $10$ so the divisor is an integer, divide, then place the decimal point by comparing the size of the numbers: $818.4\div1.2$ is a little less than $818$ , so $682$ is sensible and $68.2$ is not.
For fraction addition or subtraction, write both fractions over a common denominator and keep the answer in the form requested, usually a mixed number. For multiplication or division of mixed numbers, convert every mixed number to an improper fraction first; to divide, multiply by the reciprocal of the second fraction only.
A show-that question must display each stage, including the unsimplified product.
Track signs separately: like signs give a positive result, unlike signs a negative one.
Cancelling common factors before multiplying keeps the arithmetic small.

Worked example

Work out

-2\dfrac{1}{4}\div\dfrac{3}{5}

. Give your answer as a mixed number.

(3)

(Total for Question 1 is 3 marks)

Working

1.Convert the mixed number to an improper fraction: $-2\dfrac{1}{4}=-\dfrac{9}{4}$ .
2.Divide by multiplying by the reciprocal of $\dfrac{3}{5}$ : $-\dfrac{9}{4}\times\dfrac{5}{3}$ .
3.Cancel the common factor $3$ and multiply: $-\dfrac{3\times5}{4\times1}=-\dfrac{15}{4}$ .
4.Write as a mixed number: $-\dfrac{15}{4}=-3\dfrac{3}{4}$ .

Answer: $-3\dfrac{3}{4}$

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Additional guidance
1	for conversion to an improper fraction, eg $-\dfrac{9}{4}$	M1	Need not be shown with operators
	(dep) for a method to divide by multiplying by the reciprocal, eg $-\dfrac{9}{4}\times\dfrac{5}{3}$ or $-\dfrac{45}{12}$	M1	oe
	for $-3\dfrac{3}{4}$	A1	Accept $-\dfrac{15}{4}$ only if the mixed number is not required

Common mistakes

Don't add fraction denominators as well as numerators, writing $\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{a+c}{b+d}$ .
Don't divide by a fraction without inverting it.
Don't align the last digits of decimals instead of aligning their decimal points.

Mark-scheme wording to use

“M1 for a start to a method, eg 8184 ÷ 12 (or 818.4 ÷ 1.2) that leads to 6 as the first digit or for a complete method with no more than one arithmetic error … A1 for digits 682 A1 ft (dep M1) for correct placement of the decimal point into their final answer” — Pearson 1MA1, November 2024 Paper 1H, Q1
“M1 for conversion to improper fractions, eg 21/4 or 7/3 or 9/4 M1 (dep) for method to divide by a fraction, eg 21/4 × 3/7 or 63/12 ÷ 28/12 C1 for complete work showing each stage as far as 9/4 or 2 7/28 Must see an intermediate step, eg 63/28” — Pearson 1MA1, November 2024 Paper 1H, Q3(b)
“M1 for finding two fractions with a correct common denominator (multiple of 20), with at least one correct corresponding numerator, eg 12/20, 5/20 or 32/20, 45/20 … A1 for 3 17/20 or an equivalent mixed number” — Pearson 1MA1, November 2022 Paper 1H, Q2(a)

What the examiner wants

Sensible place value and a visible reciprocal step. The November 2024 Paper 1H report notes that after correctly finding $682$ many wrote $68.2$ or $6.82$ , and that in the division of mixed numbers some flipped the wrong fraction, flipped both, or multiplied whole numbers and fractions separately, scoring nothing.

Exam tip

Keep an exact fraction until the final line and show the reciprocal explicitly for the division method mark.

Worked practice

Tier 1 · Easy

Work out

-17+29

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$12$	1	The signs are different, so find $29-17=12$ and use the sign of the number with the larger magnitude. The result is $12$ .

Tier 2 · Standard

Work out

7.2\div0.06

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$120$	2	Multiply both numbers by $100$ so the divisor is an integer: $7.2\div0.06=720\div6=120$ .

Tier 3 · Hard

Work out

3.6-(-1.75)+\dfrac{5}{6}\div\left(-\dfrac{5}{9}\right)

. Give your answer as a decimal.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$3.85$	3	First $\dfrac{5}{6}\div\left(-\dfrac{5}{9}\right)=\dfrac{5}{6}\times\left(-\dfrac{9}{5}\right)=-\dfrac{3}{2}=-1.5$ . Then $3.6+1.75-1.5=5.35-1.5=3.85$ .

Tier 1 · Easy

Work out

42.7-18.95

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$23.75$	1	Align the decimal points and write $42.70-18.95$ . Column subtraction gives $23.75$ .

Tier 2 · Standard

Work out

2\dfrac{1}{3}+1\dfrac{5}{6}

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$4\dfrac{1}{6}$ (or $\dfrac{25}{6}$ )	2	$2\dfrac{1}{3}=\dfrac{14}{6}$ and $1\dfrac{5}{6}=\dfrac{11}{6}$ . Their sum is $\dfrac{25}{6}=4\dfrac{1}{6}$ .

Tier 3 · Hard

A container holds

12.5

litres. Then

2\dfrac{3}{4}

litres are removed and

1.6

litres are added. Work out the final volume.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$11.35$ litres	3	Convert $2\dfrac{3}{4}$ to $2.75$ . After the removal there are $12.5-2.75=9.75$ litres, and after the addition there are $9.75+1.6=11.35$ litres.

Tier 2 · Standard

A roll contains

8\dfrac{3}{5}

metres of ribbon. Six pieces, each

0.75

metres long, are cut from the roll. Work out the length of ribbon left.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$4.1$ metres	3	$8\dfrac35=8.6$ . The six pieces use $6\times0.75=4.5$ metres, so the length left is $8.6-4.5=4.1$ metres.

Tier 3 · Hard

An account has a balance of

-\pounds18.40

. A payment of

\pounds75.75

is added. A fee of

2\dfrac{2}{5}

pounds and three payments of

\pounds16.85

are then taken from the account. Work out the final balance.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$\pounds4.40$	4	After the payment, the balance is $-18.40+75.75=57.35$ . The fee is $2\dfrac25=2.40$ , leaving $54.95$ . The three later payments total $3\times16.85=50.55$ , so the final balance is $54.95-50.55=\pounds4.40$ .

Tier 3 · Hard

Work out

8.03-2.476+0.095\times16

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$7.074$	3	Do the multiplication first: $0.095\times16=1.52$ . Written subtraction gives $8.030-2.476=5.554$ , so the result is $5.554+1.52=7.074$ .

Q10

Tier 3 · Hard

Work out

\left(4\dfrac{1}{5}-2.85\right)\div\dfrac{3}{8}

. Give your answer as a decimal.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$3.6$	4	$4\dfrac15=4.2$ , so the value in brackets is $4.2-2.85=1.35=\dfrac{27}{20}$ . Dividing by $\dfrac38$ means multiplying by $\dfrac83$ : $\dfrac{27}{20}\times\dfrac83=\dfrac{18}{5}=3.6$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-06	1F	Q6	4	Non-calculator	Foundation	QP MS
2019-11	1F	Q3	1	Non-calculator	Foundation	QP MS
2022-11	3F	Q7	3	Allowed	Foundation	QP MS
2021-11	3F	Q14	3	Allowed	Foundation	QP MS
2022-06	1F	Q15	3	Non-calculator	Foundation	QP MS
2019-06	3H	Q7	2	Allowed	Higher	QP MS
2022-11	2F	Q5	1	Allowed	Foundation	QP MS
2019-06	3F	Q7	2	Allowed	Foundation	QP MS
2023-06	1F	Q11	6	Non-calculator	Foundation	QP MS
2019-06	3F	Q21	3	Allowed	Foundation	QP MS
2022-11	1F	Q6	4	Non-calculator	Foundation	QP MS
2024-11	1F	Q20	5	Non-calculator	Foundation	QP MS
2019-11	2F	Q12	2	Allowed	Foundation	QP MS
2024-11	2F	Q12	4	Allowed	Foundation	QP MS
2024-11	1H	Q3	5	Non-calculator	Higher	QP MS
2022-06	1F	Q12	4	Non-calculator	Foundation	QP MS
2022-06	3F	Q11	3	Allowed	Foundation	QP MS
2019-06	1F	Q18	4	Non-calculator	Foundation	QP MS
2019-06	1F	Q11	2	Non-calculator	Foundation	QP MS
2023-11	3F	Q7	3	Allowed	Foundation	QP MS
2019-11	3F	Q12	3	Allowed	Foundation	QP MS
2023-11	1F	Q2	1	Non-calculator	Foundation	QP MS
2024-06	1F	Q21	3	Non-calculator	Foundation	QP MS
2024-06	3F	Q8	3	Allowed	Foundation	QP MS
2024-06	3F	Q3	1	Allowed	Foundation	QP MS
2023-11	1F	Q18	3	Non-calculator	Foundation	QP MS
2021-11	1F	Q7	2	Non-calculator	Foundation	QP MS
2021-11	1F	Q14	4	Non-calculator	Foundation	QP MS
2023-11	2F	Q8	4	Allowed	Foundation	QP MS
2019-11	1F	Q22	3	Non-calculator	Foundation	QP MS
2024-11	2F	Q6	3	Allowed	Foundation	QP MS
2022-06	3F	Q7	3	Allowed	Foundation	QP MS
2019-11	2F	Q6	3	Allowed	Foundation	QP MS
2021-11	2F	Q7	3	Allowed	Foundation	QP MS
2022-11	3F	Q15	5	Allowed	Foundation	QP MS
2024-06	1F	Q14	3	Non-calculator	Foundation	QP MS
2024-11	2F	Q5	1	Allowed	Foundation	QP MS
2021-11	2F	Q8	3	Allowed	Foundation	QP MS
2022-06	2F	Q10	3	Allowed	Foundation	QP MS
2019-11	3F	Q11	5	Allowed	Foundation	QP MS
2022-06	1F	Q10	2	Non-calculator	Foundation	QP MS
2021-11	1F	Q9	3	Non-calculator	Foundation	QP MS
2023-06	1F	Q21	3	Non-calculator	Foundation	QP MS
2019-11	1F	Q6	4	Non-calculator	Foundation	QP MS
2022-06	1F	Q7	3	Non-calculator	Foundation	QP MS
2019-06	1H	Q2	5	Non-calculator	Higher	QP MS
2023-06	2F	Q18	6	Allowed	Foundation	QP MS
2024-11	3F	Q1	1	Allowed	Foundation	QP MS
2022-11	1F	Q20	4	Non-calculator	Foundation	QP MS
2023-06	1F	Q15	2	Non-calculator	Foundation	QP MS
2024-06	2F	Q18	3	Allowed	Foundation	QP MS
2023-06	3F	Q1	1	Allowed	Foundation	QP MS
2022-06	1H	Q18	4	Non-calculator	Higher	QP MS
2022-06	1F	Q11	4	Non-calculator	Foundation	QP MS
2022-11	1F	Q22	2	Non-calculator	Foundation	QP MS
2024-11	3F	Q8	6	Allowed	Foundation	QP MS
2023-11	3F	Q9	5	Allowed	Foundation	QP MS
2024-06	3F	Q11	2	Allowed	Foundation	QP MS
2023-11	1H	Q1	3	Non-calculator	Higher	QP MS
2024-06	1F	Q11	3	Non-calculator	Foundation	QP MS
2023-06	1F	Q4	1	Non-calculator	Foundation	QP MS
2019-06	1F	Q23	5	Non-calculator	Foundation	QP MS
2019-06	1F	Q19	4	Non-calculator	Foundation	QP MS
2022-11	2F	Q7	4	Allowed	Foundation	QP MS
2019-06	3F	Q11	4	Allowed	Foundation	QP MS
2023-11	3F	Q5	1	Allowed	Foundation	QP MS
2019-11	1F	Q4	1	Non-calculator	Foundation	QP MS
2019-11	3H	Q2	3	Allowed	Higher	QP MS
2019-06	2F	Q6	3	Allowed	Foundation	QP MS
2021-11	2F	Q18	3	Allowed	Foundation	QP MS
2019-11	1F	Q12	5	Non-calculator	Foundation	QP MS
2023-06	2F	Q20	3	Allowed	Foundation	QP MS
2023-11	2F	Q18	3	Allowed	Foundation	QP MS
2024-06	1F	Q6	4	Non-calculator	Foundation	QP MS
2022-06	2F	Q2	1	Allowed	Foundation	QP MS
2019-06	3F	Q8	3	Allowed	Foundation	QP MS
2023-11	3F	Q17	3	Allowed	Foundation	QP MS
2022-06	3F	Q15	2	Allowed	Foundation	QP MS
2019-11	1F	Q8	3	Non-calculator	Foundation	QP MS
2021-11	2F	Q12	3	Allowed	Foundation	QP MS
2019-06	2F	Q17	4	Allowed	Foundation	QP MS
2019-06	1F	Q27	4	Non-calculator	Foundation	QP MS
2021-11	1F	Q10	2	Non-calculator	Foundation	QP MS
2024-11	1F	Q6	3	Non-calculator	Foundation	QP MS
2022-11	1H	Q4	2	Non-calculator	Higher	QP MS
2022-11	3F	Q20	4	Allowed	Foundation	QP MS
2019-11	1H	Q3	3	Non-calculator	Higher	QP MS
2022-06	1F	Q20	3	Non-calculator	Foundation	QP MS
2022-11	1F	Q10	3	Non-calculator	Foundation	QP MS
2024-06	2F	Q9	4	Allowed	Foundation	QP MS
2024-11	1H	Q1	3	Non-calculator	Higher	QP MS
2024-11	1F	Q5	1	Non-calculator	Foundation	QP MS
2023-06	1H	Q2	3	Non-calculator	Higher	QP MS
2021-11	1H	Q3	3	Non-calculator	Higher	QP MS
2022-06	2F	Q14	2	Allowed	Foundation	QP MS
2019-11	1H	Q6	3	Non-calculator	Higher	QP MS
2024-06	2F	Q12	3	Allowed	Foundation	QP MS
2019-06	3F	Q10	3	Allowed	Foundation	QP MS
2022-11	1H	Q2	4	Non-calculator	Higher	QP MS
2023-06	1F	Q20	3	Non-calculator	Foundation	QP MS
2019-06	1F	Q14	2	Non-calculator	Foundation	QP MS
2019-06	1F	Q5	1	Non-calculator	Foundation	QP MS
2019-06	2F	Q13	3	Allowed	Foundation	QP MS
2019-06	2F	Q23	4	Allowed	Foundation	QP MS
2022-11	3F	Q17	3	Allowed	Foundation	QP MS
2019-06	2H	Q4	4	Allowed	Higher	QP MS
2023-06	1F	Q17	4	Non-calculator	Foundation	QP MS
2019-06	1H	Q9	3	Non-calculator	Higher	QP MS
2024-06	1H	Q2	3	Non-calculator	Higher	QP MS
2019-11	1F	Q14	2	Non-calculator	Foundation	QP MS
2021-11	1F	Q22	3	Non-calculator	Foundation	QP MS
2021-11	3F	Q8	3	Allowed	Foundation	QP MS
2021-11	2F	Q19	4	Allowed	Foundation	QP MS
2022-11	3F	Q8	3	Allowed	Foundation	QP MS
2023-06	2F	Q11	3	Allowed	Foundation	QP MS
2019-06	1H	Q6	4	Non-calculator	Higher	QP MS
2023-06	1H	Q1	3	Non-calculator	Higher	QP MS
2022-11	2F	Q13	4	Allowed	Foundation	QP MS
2021-11	1H	Q1	6	Non-calculator	Higher	QP MS
2019-11	1F	Q1	1	Non-calculator	Foundation	QP MS
2022-11	2F	Q11	4	Allowed	Foundation	QP MS
2024-11	1F	Q18	3	Non-calculator	Foundation	QP MS
2021-11	1F	Q17	5	Non-calculator	Foundation	QP MS
2024-06	3F	Q9	3	Allowed	Foundation	QP MS
2021-11	1F	Q20	6	Non-calculator	Foundation	QP MS
2024-11	2H	Q1	2	Allowed	Higher	QP MS
2021-11	3F	Q10	3	Allowed	Foundation	QP MS
2024-11	2F	Q8	2	Allowed	Foundation	QP MS
2023-11	1F	Q17	3	Non-calculator	Foundation	QP MS
2019-06	3F	Q14	2	Allowed	Foundation	QP MS
2023-06	1F	Q10	4	Non-calculator	Foundation	QP MS

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