GCSE Maths Practice: percentages

Question 8 of 10

This question helps you practise finding 50% of a number — a fundamental GCSE Maths skill that links percentages, fractions, and proportional reasoning.

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\( \textbf{What is } 50\% \textbf{ of } 400? \)

Choose one option:

Remember: 50% is always half. Divide by 2 for a quick check before finalising your answer.

Understanding 50% — The Concept of Half

In GCSE Maths, 50% is one of the most straightforward percentages to understand. It represents half of the total amount. The term 'percent' means 'per hundred', so 50% literally means 50 out of every 100 parts. Recognising that 50% is equal to one-half helps you calculate quickly without using a calculator.

Why 50% Equals One-Half

The fraction form of 50% is:

\[ 50\% = \dfrac{50}{100} = \dfrac{1}{2}. \]

This means any time you see 50%, you can replace it with 'divide by 2' or 'take half'. This connection between percentages and fractions is key for mental maths and ratio reasoning.

Step-by-Step Method

  1. Convert 50% to its decimal or fraction form: \( 50\% = 0.5 = \dfrac{1}{2}. \)
  2. Multiply the given number by 0.5 or divide it by 2.
  3. The result is half of the original number — your 50% value.

Worked Examples

  • Example 1: 50% of 600 = \( 600 \times 0.5 = 300. \)
  • Example 2: 50% of 120 = \( 120 \div 2 = 60. \)
  • Example 3: 50% of 18 = \( 9. \)

Because it’s half, the answer will always be exactly halfway between 0 and the original value.

Real-Life Applications

The idea of 50% appears constantly in real life:

  • Sharing Equally: If you share £400 evenly between two people, each gets 50% — or £200.
  • Sales and Discounts: A '50% off' sale means you pay half the original price. If something cost £80, the new price is £40.
  • Health and Fitness: If someone runs half their 10 km goal, they’ve completed 50%, or 5 km.
  • Finance: If your savings double, they’ve increased by 100%, but half that growth would be 50%.

These contexts show that percentages describe fairness, balance, and change across many areas of daily life.

Common Misunderstandings

  • Thinking 50% means add 50 — it’s not an addition; it’s a proportion.
  • Forgetting that 50% can represent either an increase or decrease, depending on the situation. Here, we’re only finding part of a total.
  • Using rounding too early when working with decimals — always keep one or two decimal places for accuracy.

Connections to Other Topics

Half (50%) links directly to fractions and ratios. For example, half of a pizza is \( \dfrac{1}{2} \), which is also 50%. One-quarter (\( \dfrac{1}{4} \)) is 25%, and three-quarters (\( \dfrac{3}{4} \)) is 75%. Recognising these equivalences helps when switching between different representations in GCSE questions.

Frequently Asked Questions

Q1: How do I find 75% if I know 50%?
Add half again of the half value. For example, 50% of 400 = 200, and half of that (25%) = 100, so 75% = 200 + 100 = 300.

Q2: How do I find 25%?
Divide by 4, because 25% = \( \dfrac{1}{4} \).

Q3: Is 50% always half, even with decimals?
Yes. For example, 50% of 7.6 = 3.8, exactly half.

Summary

50% represents perfect balance — half of a quantity. To find it, multiply by 0.5 or divide by 2. This quick method works for all numbers, big or small. It’s not only a foundation for percentages but also for proportional reasoning and fractions. Remember: 50% = one-half = 0.5 — three different ways of expressing the same mathematical idea.