GCSE Maths Practice: integers-and-directed-numbers

Question 4 of 10

This question uses temperature to show how subtracting a positive number makes a value more negative.

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\( \begin{array}{l}\text{The temperature is } -8^{\circ}C. \text{ It drops by } 5^{\circ}C. \\ \text{What is the new temperature?}\end{array} \)

Choose one option:

For every degree the temperature falls, move left on the number line. Subtract positive changes from the starting temperature.

Temperature and Negative Numbers

Negative numbers appear naturally when we measure temperatures below zero. Understanding how to combine and subtract them helps in interpreting weather data and solving real-world problems. This question models a temperature drop scenario where each decrease is represented by subtraction.

Step-by-Step Reasoning

  1. Start temperature: −8°C.
  2. The temperature falls by 5°C, meaning we subtract 5 from −8.
  3. Calculation: −8 − 5 = −13.
  4. The new temperature is −13°C.

Subtracting a positive number from a negative pushes the value further into the negatives — the temperature becomes even lower.

Visualising on the Number Line

Begin at −8 on the number line. Moving 5 steps to the left (since the temperature is dropping) lands at −13. This visual method is useful for students developing number sense around negative values.

Worked Examples

  • Temperature = −4°C, drop by 6°C → −10°C.
  • Temperature = −2°C, fall by 9°C → −11°C.
  • Temperature = −8°C, fall by 5°C → −13°C.

Common Mistakes

  • Thinking subtraction always makes numbers smaller regardless of signs.
  • Adding instead of subtracting when the phrase “drop by” appears.
  • Forgetting that negative temperatures increase leftward on the number line.

Real-Life Applications

Negative subtraction occurs not only in temperatures but also in finance (losses increasing), physics (velocity changes), and computing (relative coordinates). For example, if a company’s debt grows from −£8,000 by another £5,000, the new balance is −£13,000.

FAQs

  • Q: Why does the temperature go down when we subtract?
    A: Because subtraction represents a decrease — each unit removed makes the value smaller.
  • Q: Does the same apply if the temperature rises?
    A: Yes, rising means adding a positive number, moving right on the number line.
  • Q: Can subtraction ever make the value increase?
    A: Only if we subtract a negative (− − = +).

Study Tip

When dealing with temperature or money changes, identify whether the phrase means adding or subtracting, then apply the correct sign rule. Visualising on a thermometer or number line strengthens intuition about negative numbers.