A LITTLE PRACTICE, EVERY DAY·GCSE MATHS
AQA·Edexcel·OCR|Foundation + Higher
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Number · Foundation & Higher

Negative numbers

Negative numbers lie to the left of zero on the number line. You must be able to add, subtract, multiply and divide with positive and negative numbers confidently.

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Revising negative numbers the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Negative numbers GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Two signs next to each other: same signs give a plus (−− = +), different signs give a minus (+− = −).
  • 2Multiplying or dividing: same signs → positive; different signs → negative.
  • 3Adding a negative is the same as subtracting: 5 + (−3) = 5 − 3 = 2.
  • 4Subtracting a negative is the same as adding: 5 − (−3) = 5 + 3 = 8.
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Worked examples

Example 1

Work out (−4) × (−3) + (−2).

Working

  1. (−4) × (−3) = +12 (negative × negative = positive)
  2. 12 + (−2) = 12 − 2 = 10
Answer10
Example 2

Work out −15 ÷ 3 − (−4).

Working

  1. −15 ÷ 3 = −5
  2. − (−4) = + 4
  3. −5 + 4 = −1
Answer−1
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Common mistakes

✗Forgetting that two negatives multiplied make a positive.
✗Confusing "subtract negative" with "subtract positive".
✗Losing track of signs in a multi-step calculation.
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Exam tips

✓Write every step — sign errors are the most common GCSE mistake.
✓Use a number line for add/subtract if you are unsure.
✓Remember: same signs → plus; different signs → minus.

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