GCSE Maths Practice: integers-and-directed-numbers

Question 5 of 10

This question shows how adding a negative value represents a real-world decrease, such as a drop in temperature.

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\( \begin{array}{l}\text{The temperature is } 10^{\circ}C. \text{ It drops by } 8^{\circ}C. \\ \text{What is the new temperature?}\end{array} \)

Choose one option:

Whenever something decreases, add a negative value. The result moves left on the number line.

Adding a Negative in Real Context

In GCSE Maths, adding a negative number often represents a decrease. Real-life examples include falling temperatures, reduced profits, or a car slowing down. This question uses temperature to show how addition with a negative value translates to real change.

Scenario

The temperature one afternoon is 10°C. A cold front passes, and the temperature drops by 8°C. We can model this as:

10 + (−8) = 2

The phrase “drops by 8°C” means we add a negative change. Since adding a negative is the same as subtracting, the temperature decreases from 10°C to 2°C.

Step-by-Step Method

  1. Identify the starting value (10).
  2. Recognise the change (a drop of 8) as −8.
  3. Add the change: 10 + (−8).
  4. Result: 2°C.

Understanding Why

Adding a positive moves right on the number line, while adding a negative moves left. The sign tells you the direction of the change, not the size. This rule is consistent across all real-world applications involving increases and decreases.

Worked Examples

  • 20 + (−5) = 15 → drop of 5°C.
  • 7 + (−9) = −2 → below zero, meaning freezing conditions.
  • 10 + (−8) = 2 → mild temperature after a drop.

Common Errors

  • Confusing “add” with always increasing.
  • Forgetting to apply the negative sign to the change.
  • Writing 10 − 8 = −2 instead of 2 due to sign reversal mistakes.

Real-Life Applications

Understanding how to add negatives helps when working with financial statements, scientific data, or programming variables. For instance, adding a negative expense in a budget actually decreases total costs, while adding a negative acceleration reduces velocity.

FAQs

  • Q: Why does adding a negative make the number smaller?
    A: Because the negative indicates movement in the opposite direction on the number line.
  • Q: How is this different from subtraction?
    A: It’s equivalent, but expressed as addition of a negative value — the process reinforces sign logic.
  • Q: What if the drop is bigger than the starting number?
    A: The result becomes negative, showing values below zero (e.g., −3°C).

Study Tip

Visualise changes on a number line or thermometer: right means positive, left means negative. This helps avoid confusion when adding or subtracting signed numbers in GCSE Maths.