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Negative numbers – GCSE Maths

Foundation · Grade 1 · Non-calculator

Jump to the questions and answers · Download the worksheet (PDF)

Order, add, subtract, multiply and divide negative numbers, including temperature and money contexts. It is a Foundation topic, aimed at grade 1. Free questions with answers are on this page. Worked examples show each line before you try the questions.

Negative numbers live to the left of zero. is smaller than because it is further left, even though is bigger than . A number line (or a thermometer) is the safest picture for addition and subtraction: means start at and walk to the right, landing on . Subtracting a negative is a turn-around: minus a minus becomes plus.

Multiplication and division use a sign rule, not a number line. Two signs the same make a positive; two different signs make a negative. and . Decide the sign first, then work out the size, so the minus does not vanish in the last line.

Temperature questions are differences: from C to C you pass through zero, so the drop is degrees, not .

Objectives

Key points

Worked examples

Example 1

The temperature is −4°C and rises by 7 degrees. What is it now?

2 marks

  1. Start at −4.
  2. Move 7 steps right.
  3. −4 + 7 = 3

Answer: 3

Common slips
  • Slip: Start at 4. A rise from a negative still starts on the negative.
  • Slip: Move 7 steps left. A rise is a move towards the positives.
  • Slip: −4 + 7 = −11 Adding a positive does not make the negative “more negative”.

Example 2

A diver stands on a board 2 m above the water. He drops 6 m. Taking the water surface as 0 and down as negative, what is his position?

2 marks

  1. 2 − 6
  2. From 2, six steps left.
  3. The position is −4 m.

Answer: -4

Common slips
  • Slip: 2 + 6 Descending reduces the height.
  • Slip: Stop at 0. The dive does not stop at the surface.
  • Slip: The position is 4 m. He has gone past zero, so the position is negative.

Example 3

The overnight temperature is −6°C. It falls by 3 degrees, then rises by 11 degrees. What is the final temperature?

3 marks

  1. −6 − 3 = −9
  2. −9 + 11 = 2
  3. The final temperature is 2°C.

Answer: 2

Common slips
  • Slip: −6 − 3 = −3 A fall goes further left. −6 then 3 more left is −9.
  • Slip: −9 + 11 = −20 A rise of 11 from −9 crosses zero.
  • Slip: The final temperature is −9°C. −9 was only the middle reading.

Questions and answers

GCSE Maths negative numbers questions and answers. Try each one, then open the answer. Easy questions come first.

Question 1 Easy2 marks

What is −1 + 4?

Show answer

Answer: 3

  1. Start at −1 and move 4 right.
  2. −1 + 4 = 3.
  • M1 — Start at −1 and move 4 right.
  • A1 — Answer 3

Question 2 Easy2 marks

What is 3 − 8?

Show answer

Answer: -5

  1. From 3, move 8 left.
  2. 3 − 8 = −5.
  • M1 — From 3, move 8 left.
  • A1 — Answer -5

Question 3 Medium2 marks

What is −7 + 7?

Show answer

Answer: 0

  1. Seven steps right from −7 lands on 0.
  2. −7 + 7 = 0.
  • M1 — Seven steps right from −7 lands on 0.
  • A1 — Answer 0

Question 4 Medium2 marks

What is −3 − 4?

Show answer

Answer: -7

  1. Both moves go left.
  2. −3 − 4 = −7.
  • M1 — Both moves go left.
  • A1 — Answer -7

Question 5 Hard2 marks

Work out −8 + 3 − 2.

Show answer

Answer: -7

  1. −8 + 3 = −5.
  2. −5 − 2 = −7.
  • M1 — −8 + 3 = −5.
  • A1 — Answer -7

Question 6 Hard2 marks

From −12°C the temperature rises by 5 degrees and then by 9 degrees. What is it now?

Show answer

Answer: 2

  1. −12 + 5 = −7.
  2. −7 + 9 = 2.
  • M1 — −12 + 5 = −7.
  • A1 — Answer 2

Question 7 Exam-style3 marks

At 6 am the temperature is −4°C. By noon it has risen by 9 degrees, then by 6 pm it has fallen by 3 degrees. What is the 6 pm temperature?

Show answer

Answer: 2

  1. −4 + 9 = 5.
  2. 5 − 3 = 2.
  • M1 — Adds the morning rise
  • M1 — Subtracts the afternoon fall
  • A1 — Answer 2

Common mistakes

Most lost marks on this topic are one slip.

  1. Thinking a “bigger” digit with a minus is the greater number. −9 is less than −2.

    Further left means smaller. Compare positions, not the faces.

  2. Stopping at zero when a calculation crosses it.

    Keep counting in the same direction until the steps run out.

  3. Treating “add a negative” as a move right.

    Adding a negative goes left, the same way as subtraction.

Spot the slip

Which is colder, −3°C or 2°C?

  1. −3°C
  2. 2°C
  3. They are the same
Show the slip

−3°C On a number line, −3 is left of 2, so it is smaller and colder.

Exam tips

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

Or use Print in your browser. Answers under each question are included when you print.

Questions students ask

Is Negative numbers Foundation or Higher?

Negative numbers is Foundation, aimed at grade 1.

What is a common slip on Negative numbers?

Thinking a “bigger” digit with a minus is the greater number. −9 is less than −2. Further left means smaller. Compare positions, not the faces.

Where can I get Negative numbers questions and answers?

The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.

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Last updated 9 November 2026.

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