GCSE Maths Practice: integers-and-directed-numbers

Question 10 of 10

This question uses a bank-balance story to show how subtracting a negative increases the total. Removing a debt adds value.

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\( \begin{array}{l}\text{Your bank balance is £10. You cancel a £5 debt.} \\ \text{What is your new balance?}\end{array} \)

Choose one option:

Think of negatives as debts. Subtracting a debt increases your total — a minus minus becomes plus.

Money Context and Directed Numbers

Subtraction of negative numbers can feel abstract, so thinking in money terms makes it easier. Balances can be positive (credit) or negative (debt). Subtracting a negative represents removing debt — effectively the same as adding money.

Step-by-Step Reasoning

  1. Imagine your bank balance is £10.
  2. You owe a friend £5, which is recorded as −5.
  3. When that debt is cancelled or removed, you subtract −5 from your account.
  4. Mathematically: 10 − (−5) = 10 + 5 = 15.
  5. Your new balance is £15.

Number-Line Explanation

Starting at +10 on the number line, subtracting a negative means reversing direction. Instead of moving left, you move right because you’re removing something that was already below zero.

Worked Examples

  • 8 − (−3) = 11 → removing £3 of debt increases your balance by £3.
  • −2 − (−7) = 5 → cancelling a £7 debt when £2 in debt leaves £5 credit.
  • 10 − (−5) = 15 → balance rises from £10 to £15.

Common Misunderstandings

  • Thinking subtraction always decreases a number.
  • Dropping one negative sign instead of changing both to addition.
  • Misinterpreting subtraction of a debt as paying more instead of gaining value.

Real-Life Applications

This principle appears in business, finance, and computing. When reversing losses or cancelling liabilities, you’re mathematically subtracting a negative. In spreadsheets and programming, double negatives often occur when reversing a previous deduction.

FAQs

  • Q: Why does subtracting a negative increase the total?
    A: Because removing a debt has the same effect as adding credit.
  • Q: Does this rule work for any numbers?
    A: Yes, regardless of size or decimals: a − (−b) = a + b.
  • Q: How can I remember the rule?
    A: Two negatives make a positive — subtracting a negative turns into addition.

Study Tip

Whenever you see two signs side-by-side, simplify them first: −(−) becomes +. Visualising with money or temperature makes this idea concrete for GCSE Maths questions.