GCSE Maths Practice: integers-and-directed-numbers

Question 8 of 10

This question tests your understanding of dividing negative numbers. When both numbers are negative, the quotient is positive.

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\( \begin{array}{l}\text{What is } -12 \div (-4)?\end{array} \)

Choose one option:

Ignore the negative signs, divide normally, then apply the rule: same signs make a positive result.

Understanding Division with Negative Numbers

In GCSE Maths, knowing how to divide negative numbers is an essential part of mastering directed numbers. The rule is straightforward: dividing two numbers with the same sign gives a positive result. This applies whether the numbers are both positive or both negative.

Why This Rule Works

Division is the inverse of multiplication. If we know that negative × negative = positive, then to reverse that operation, dividing one negative number by another must also result in a positive value. This rule keeps mathematical consistency across all operations.

Step-by-Step Method

  1. Ignore the signs and divide the absolute values.
  2. Determine the sign of the result:
    • Same signs → Positive answer
    • Different signs → Negative answer
  3. Apply the correct sign to the quotient.

Worked Examples

  • (−20) ÷ (−5) = 4
  • (−15) ÷ (−3) = 5
  • (−12) ÷ (−4) = 3
  • (−36) ÷ (−6) = 6

Common Mistakes

  • Forgetting that two negatives divide to make a positive result.
  • Confusing subtraction with division — they are not the same operation.
  • Leaving out one of the negative signs when simplifying.

Real-Life Applications

Understanding negative division helps in contexts such as calculating average losses or changes in direction. For example, in finance, dividing total losses (a negative value) by the number of years (also represented as negative if measuring reduction) gives a positive average change, meaning progress over time.

FAQs

  • Q: What happens when you divide a positive by a negative?
    A: The result is negative because the signs are different.
  • Q: Does this rule apply to decimals and fractions?
    A: Yes, the same rule applies. For example, (−0.8) ÷ (−0.2) = 4.
  • Q: How is this used in algebra?
    A: In algebraic expressions, (−x) ÷ (−y) simplifies to x/y because the negatives cancel.

Study Tip

When dividing or multiplying signed numbers, remember this simple rule: Same signs give positive results; different signs give negative results. Practise with both positive and negative pairs to reinforce accuracy and speed for GCSE exams.