GCSE Maths Practice: integers-and-directed-numbers

Question 9 of 10

This question involves adding and subtracting several signed numbers. You’ll need to combine negatives first and then handle the positive term carefully.

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\( \begin{array}{l}\text{What is } -3 + (-8) + 4?\end{array} \)

Choose one option:

When multiple signs appear, simplify step by step: add negatives together, then apply any positives.

Adding and Subtracting Multiple Negative Numbers

In GCSE Maths, questions often include more than two terms with both positive and negative numbers. Understanding how to combine them step by step is crucial for success. This type of question builds confidence when simplifying expressions or balancing equations.

Step-by-Step Reasoning

  1. Start with −3 + (−8). Both are negative, so add their absolute values: 3 + 8 = 11. Keep the negative sign → −11.
  2. Now combine −11 + 4. Since signs differ, subtract the smaller absolute value (4) from the larger (11), giving 7, and keep the sign of the larger number (negative).
  3. Final answer: −7.

Number Line Interpretation

Starting at zero, move left 3 spaces (−3), then move another 8 left (−8), ending at −11. Moving right 4 brings you to −7. Visualising this helps reinforce direction changes caused by positive and negative operations.

Worked Examples

  • (−5) + (−2) + 9 = 2
  • (−10) + 7 + (−3) = −6
  • (−4) + (−6) + 5 = −5
  • (−3) + (−8) + 4 = −7

Common Mistakes

  • Mixing addition and subtraction signs incorrectly.
  • Forgetting that adding a negative is the same as subtracting.
  • Not following order when multiple signs appear.

Real-Life Applications

This rule applies in real contexts like budgeting and temperature change. Suppose you spent £3, then another £8, but later gained £4 — overall, your balance decreased by £7. Understanding how to add and subtract signed numbers directly supports everyday reasoning.

FAQs

  • Q: How do I know whether to add or subtract?
    A: When signs match, add absolute values and keep the sign. When signs differ, subtract and keep the sign of the larger number.
  • Q: Does order matter?
    A: No, addition is commutative — but keeping sign grouping clear prevents mistakes.
  • Q: Can this appear in algebra?
    A: Yes. Expressions like −x + (−y) + z follow the same rule.

Study Tip

When you see more than two numbers with different signs, group negatives first, simplify, then handle positives. This prevents confusion and makes multi-step calculations reliable in GCSE Maths exams.