GCSE Maths Practice: percentages

Question 3 of 10

This question introduces percentage increase — a common GCSE Maths skill used in real situations like price rises, profit margins, and population growth.

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\( \textbf{Increase } 200 \textbf{ by } 25\%. \)

Choose one option:

Always think of increases as more than 100%. For a 25% rise, multiply by 1.25 — not 0.25.

Understanding Percentage Increase

In GCSE Maths, percentage increase describes how much a number grows compared to its original value. It’s a vital skill for real-life contexts such as price rises, population growth, and profit calculations. When a number increases by a certain percentage, you are adding that percentage of the original number to itself.

The Formula

The rule for percentage increase is:

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

Here, the \(1\) represents 100% of the original value, and the fraction represents the increase. For example, increasing a price by 25% means the final amount is 125% of the original.

Step-by-Step Method

  1. Convert the percentage increase into a decimal. For 25%, write \( 0.25 \).
  2. Add 1 to this value (because you are keeping the original 100%). \( 1 + 0.25 = 1.25 \).
  3. Multiply the original number by \( 1.25 \) to find the new amount.

This gives the final result directly, without having to find 25% separately and then add it back on.

Worked Examples

  • Example 1: Increase 80 by 25%.
    \( 80 \times 1.25 = 100 \).
  • Example 2: Increase 160 by 10%.
    \( 160 \times 1.10 = 176 \).
  • Example 3: Increase 240 by 50%.
    \( 240 \times 1.50 = 360 \).

Each example shows how multiplying by the correct multiplier quickly produces the new total.

Real-Life Applications

Percentage increases are everywhere in daily life. You’ll see them when:

  • Shopping: Prices rise by a certain percentage due to inflation or added tax (VAT).
  • Business: Profits or sales are reported as a percentage increase compared to last year.
  • Science: Population growth or bacteria counts are measured using percentage increases.
  • Fitness: A 25% increase in running distance shows improvement over time.

Being able to calculate these changes quickly helps you interpret data and make smart financial or personal decisions.

Common Mistakes to Avoid

  • Adding 25 directly to the number instead of 25% — always multiply by the multiplier (1.25).
  • Forgetting to add 1 to the percentage fraction — this results in finding only the increase, not the total new value.
  • Mixing up percentage increase with percentage of — these are different operations.

Quick Mental Maths Tip

To increase by 25% without a calculator, find a quarter (\( \dfrac{1}{4} \)) of the number and add it on. For example, to increase 200 by 25%, one quarter of 200 is 50, and \( 200 + 50 = 250 \). This trick works well for common percentages like 5%, 10%, 20%, and 25%.

Frequently Asked Questions

Q1: What is the difference between finding 25% of a number and increasing by 25%?
Finding 25% gives the part only. Increasing by 25% means you add that part to the whole. For example, 25% of 200 is 50, but increasing 200 by 25% gives 250.

Q2: How do I find a percentage decrease?
Use the same formula but subtract instead of add: \( \text{New Value} = \text{Original} \times (1 - \dfrac{\text{Percentage}}{100}) \).

Q3: Why multiply by 1.25 instead of adding 25% later?
It combines the original and the increase in one step, saving time and reducing rounding errors.

Summary

To increase a number by a percentage, multiply by a value greater than 1. For a 25% increase, use \( 1.25 \). This principle underpins many GCSE Maths questions about profit, growth, and inflation. Remember: increase = add the percentage fraction to 1; decrease = subtract it from 1. Estimating first (for instance, '25% is roughly one-quarter more') helps you check that your final answer makes sense.