GCSE Maths Practice: percentages

Question 2 of 10

This question practises decreasing a number by a percentage — a common GCSE Maths skill used in discounts, depreciation, and reduction problems.

‹ ›

\( \textbf{Decrease } 60 \textbf{ by } 30\%. \)

Choose one option:

Remember: for a decrease, multiply by less than 1. For a 30% decrease, use 0.7. Estimation helps ensure your answer makes sense.

Understanding Percentage Decrease

In GCSE Maths, percentage decrease is used to show how much a number has gone down compared to its original value. It appears everywhere — when prices drop in shops, when populations shrink, or when your phone battery percentage falls. Learning how to calculate percentage decreases helps you handle everyday problems quickly and confidently.

The General Rule

The formula for decreasing a number by a percentage is:

\[ \text{New Value} = \text{Original Value} \times \left(1 - \dfrac{\text{Percentage}}{100}\right) \]

The term inside the brackets represents the part you keep. If something is reduced by 30%, you are left with 70% of it — because \(100\% - 30\% = 70\%\).

Step-by-Step Method

  1. Write the percentage decrease as a decimal: \( 30\% = 0.3 \).
  2. Subtract it from 1 to find what remains: \( 1 - 0.3 = 0.7 \).
  3. Multiply the original number by \( 0.7 \).
  4. The answer is the new, smaller value after the decrease.

Worked Examples

  • Example 1: Decrease 100 by 10%. \( 100 \times 0.9 = 90 \).
  • Example 2: Decrease 80 by 25%. \( 80 \times 0.75 = 60 \).
  • Example 3: Decrease 50 by 20%. \( 50 \times 0.8 = 40 \).

Notice how you always multiply by a number smaller than 1 when decreasing.

Real-Life Applications

  • Sales and Discounts: A £60 jacket with 30% off costs \( 60 \times 0.7 = £42 \).
  • Energy Use: Reducing electricity usage by 30% saves nearly one-third of your bill.
  • Fitness Goals: If you cut your daily sugar intake by 30%, and you used to eat 60 g, you now have \( 60 \times 0.7 = 42 g \).
  • Finance: A car value that drops 30% in a year loses almost one-third of its price.

These examples show that percentage decrease is more than a formula — it’s a real-world reasoning tool.

Common Mistakes to Avoid

  • Subtracting 30 instead of 30% — never remove the percentage directly as a number.
  • Forgetting to convert the percentage to a decimal before multiplying.
  • Mixing up increase and decrease — increase uses (1 + fraction), decrease uses (1 − fraction).

Quick Mental-Maths Tricks

If you want to decrease by 30% mentally, first find 10%, then triple it, and subtract from the total. For example, 10% of 60 is 6, so 30% is 18. Subtract: 60 − 18 = 42. This method works for any round number and helps check calculator results.

Frequently Asked Questions

Q1: How do I find 70% directly?
Multiply by 0.7 — that’s what remains after a 30% decrease.

Q2: How is this different from a percentage increase?
For increases, you add the percentage to 1 before multiplying. For decreases, you subtract it from 1.

Q3: What happens if something decreases by 100%?
It means it is completely gone — the final value is 0.

Summary

Percentage decrease questions appear frequently in GCSE Maths exams and in daily decision-making. To reduce a number by a given percentage, multiply by a value smaller than 1 — for example, by 0.7 for a 30% decrease. Estimation helps check your work: a 30% decrease means the new amount should be a bit more than two-thirds of the original. Mastering this concept builds confidence for later topics such as compound interest, depreciation, and proportional reasoning.