GCSE Maths Practice: integers-and-directed-numbers

Question 7 of 10

This question tests your ability to add and subtract several signed numbers. Pay close attention to sign changes and order of operations.

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\( \begin{array}{l}\text{What is } -12 + 9 + 8?\end{array} \)

Choose one option:

Handle one operation at a time. Combine negatives and positives step by step to avoid sign errors.

Combining Several Positive and Negative Numbers

In GCSE Maths, it’s important to handle questions where multiple numbers with different signs appear. This helps you prepare for algebraic manipulation and arithmetic reasoning in later topics. When a problem includes more than two terms, the best strategy is to work systematically — from left to right or by grouping signs.

Step-by-Step Solution

  1. Start with −12 + 9 + 8.
  2. Combine the first two numbers: −12 + 9 = −3.
  3. Now add −3 + 8 = 5.
  4. Final answer: 5.

Understanding the Rule

When adding numbers with different signs, think about their direction on the number line. A negative moves you left, and a positive moves you right. The number with the larger absolute value determines the final sign. In this case, the positives outweigh the negatives, resulting in a positive sum.

Worked Examples

  • (−10) + 15 + (−3) = 2
  • (−5) + (−7) + 9 = −3
  • (−12) + 9 + 8 = 5
  • 7 + (−4) + (−5) = −2

Common Mistakes

  • Adding numbers without paying attention to their signs.
  • Assuming all negatives cancel automatically.
  • Skipping a term or switching signs mid-calculation.

Real-Life Applications

In real-world contexts, this skill appears in money problems, temperature changes, and elevation differences. For example, if a climber descends 12 metres, climbs up 9, and then another 8, their overall position is 5 metres above the starting point. Understanding signed addition helps interpret real changes precisely.

FAQs

  • Q: Does the order of addition matter?
    A: No, but following left to right reduces mistakes when signs vary.
  • Q: What if there are brackets?
    A: Simplify inside brackets first before applying the rule of signs.
  • Q: How can I check my result quickly?
    A: Use a number line or a calculator to confirm the directional changes.

Study Tip

Group all negative terms and positive terms separately, then combine them. This visual separation makes it easier to see which side (positive or negative) dominates, a key strategy for GCSE problem-solving accuracy.