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Negative numbers

Understand negative numbers on a number line and calculate with negative values using reliable sign rules.

Number and Place ValueFoundationGrades 1 to 5Skill

Curriculum path: GCSE Maths > Edexcel > Number > Negative numbers

Pearson Edexcel GCSE Maths number: order and calculate with positive and negative integers.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Negative numbers are less than zero. They are used for temperatures below zero, bank balances, lifts below ground floor, and differences.

On a number line, moving right makes the number larger and moving left makes the number smaller.

Adding a positive number moves right. Subtracting a positive number moves left.

Adding a negative number has the same effect as subtracting. For example, 6 + -4 = 2.

Subtracting a negative number moves right because you are taking away a negative. For example, 6 - -4 = 10.

For multiplication and division, same signs give a positive answer. Different signs give a negative answer.

Key ruleFor multiply and divide: same signs positive, different signs negative.

Worked examples

Temperature change

The temperature is -3 degrees. It rises by 8 degrees. What is the new temperature?

  1. Start at -3 on the number line.
  2. Rising means add 8, so move 8 steps to the right.
  3. -3 + 8 = 5.

Answer: 5 degrees

Subtract a negative

Work out 7 - -5.

  1. Subtracting a negative moves right on the number line.
  2. 7 - -5 is the same as 7 + 5.
  3. 7 + 5 = 12.

Answer: 12

Multiply negatives

Work out -6 x 4.

  1. The signs are different: one negative and one positive.
  2. Different signs give a negative answer.
  3. 6 x 4 = 24, so the answer is -24.

Answer: -24

Common mistakes

  • Thinking every answer with a negative number must be negative.
  • Forgetting that subtracting a negative makes the value increase.
  • Mixing up addition/subtraction number-line rules with multiplication/division sign rules.
  • Writing -3 + 8 as -11 instead of 5.
  • Dropping the negative sign in a final answer.

Quick exercise

Try these before moving to the exam-style questions.

  1. Work out -4 + 9.
  2. Work out 3 - 8.
  3. Work out 6 - -2.
  4. Work out -7 x 3.
  5. Work out -20 divided by -5.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Work out -5 + 12.

negative numbersadditionnumber line
Standard exam styleFoundationNon-calculator3 marks

At midnight the temperature was -4 degrees. By midday it had increased by 11 degrees. By evening it had fallen by 6 degrees. What was the evening temperature?

temperaturenegative numbersmulti-step
ChallengeFoundation and HigherNon-calculator4 marks

Work out -3(4 - 9) - 8.

negative numbersbracketsBIDMASsign rules