GCSE Maths Practice: integers-and-directed-numbers

Question 6 of 10

This question reviews the rule for multiplying negative numbers. When two numbers share the same sign, their product is positive.

‹ ›

\( \begin{array}{l}\text{What is } (-3) \times (-2)?\end{array} \)

Choose one option:

Multiply the absolute values, then assign the correct sign using the rule: same signs make a positive result.

Understanding Negative Multiplication

In GCSE Maths, understanding how to multiply negative numbers is essential for solving algebraic equations, simplifying expressions, and handling directed numbers. The rule is simple but often misunderstood: a negative times a negative equals a positive. This comes directly from the properties of number operations on the number line.

Why the Rule Works

Multiplication can be thought of as repeated addition or as scaling. When you multiply a number by a negative, you reverse its direction on the number line. Reversing direction twice (for two negatives) returns it to the original positive direction.

Step-by-Step Method

  1. Ignore the signs and multiply the absolute values.
  2. If both numbers have the same sign, the answer is positive.
  3. If the signs differ, the answer is negative.

Worked Examples

  • (-4) × (-5) = 20
  • (-7) × (-3) = 21
  • (-2) × (-9) = 18

Common Mistakes

  • Forgetting that two negatives give a positive.
  • Confusing negative addition with multiplication.
  • Dropping one of the negative signs when multiplying.

Real-Life Applications

Negative multiplication appears in real-world contexts such as calculating changes in temperature, direction, or profit and loss. For example, if a company reduces losses (a negative value) over several years, the result becomes a positive gain.

FAQs

  • Q: What happens when multiplying a positive and a negative?
    A: The answer is negative because the signs are different.
  • Q: Does this rule apply in algebra?
    A: Yes, the same rule applies to variables. For instance, (-x) × (-y) = xy.
  • Q: Why do negatives cancel out?
    A: Because multiplying two opposites reverses direction twice, returning to positive.

Study Tip

Remember this quick rule: Same signs → Positive, Different signs → Negative. Practising simple problems like this builds strong algebra foundations for GCSE success.