GCSE Maths Practice: percentages

What Does 20% Really Mean?

When you read 20%, it means '20 out of every 100'. In other words, it represents one-fifth of the total quantity. In GCSE Maths, percentages like 20% are commonly used to describe parts, comparisons, or changes. Understanding 20% helps with discounts, taxes, data analysis, and even sports statistics.

How to Calculate 20% of a Number

The basic formula for percentage calculations is:

\[ \text{Percentage of a number} = \dfrac{\text{Percentage}}{100} \times \text{Number} \]

So, \( 20\% \text{ of } n = 0.2n \) or equivalently \( \dfrac{1}{5} \times n \). This is a simple and consistent rule that works for any number, big or small.

Step-by-Step Method

1. Convert 20% into decimal or fraction form: \( 20\% = 0.2 = \dfrac{1}{5} \).
2. Multiply the original number by \( 0.2 \) (or divide by 5).
3. Check that your answer is smaller than the original number but not by too much — 20% is roughly one-fifth.

Worked Examples

• Example 1: 20% of 150 = \( 0.2 \times 150 = 30 \).
• Example 2: 20% of 250 = \( 0.2 \times 250 = 50 \).
• Example 3: 20% of 80 = \( 0.2 \times 80 = 16 \).

These show that once you know one-fifth of a number, you’ve automatically found 20%.

Everyday Applications

Percentages like 20% appear in countless real-life contexts. Here are some examples to make the concept more visual and relatable:

• Shopping and Discounts: A phone originally costs £500 and has a 20% discount. The saving is \( 0.2 \times 500 = 100 \), so you pay £400.
• Health and Fitness: Reducing your daily calorie intake by 20% can mean cutting 400 calories from a 2000-calorie diet.
• Business and Sales: A company that increases its revenue by 20% grows from £25,000 to £30,000 — a significant improvement.
• Population Data: If a town has 20% children, that means one-fifth of the residents are under 18.

These examples show how percentages are not just mathematical ideas — they describe real-world relationships and trends.

Common Mistakes

• Multiplying by 20 instead of 0.2 — forgetting to divide by 100.
• Confusing 20% with 2%, which is ten times smaller.
• Rounding too early in long calculations, leading to small but important errors.

Quick Mental Maths Strategy

Finding 20% is easy using mental shortcuts. Because 20% equals one-fifth, just divide the number by 5. For example, 20% of 400 = 400 ÷ 5 = 80. If you already know 10%, you can double it: 10% of 400 = 40, so 20% = 80. These tricks make it possible to check answers without a calculator — very useful in non-calculator GCSE papers.

Frequently Asked Questions

Q1: How do I find 40% of a number?
Double the 20% value. For example, 40% of 90 = (20% of 90) × 2 = 18 × 2 = 36.

Q2: What’s the easiest way to check my answer?
Estimate. Since 20% is one-fifth, the answer should be roughly a fifth of the number.

Q3: How do I find 80%?
Subtract 20% from the full value. For instance, 80% of 250 = 250 − 50 = 200.

Summary

20% represents one-fifth of a total. To find it, multiply by 0.2 or divide by 5. This idea connects many real GCSE Maths topics, including ratio, proportion, and financial literacy. Estimation is key — if your answer isn’t close to one-fifth of the original number, check your calculation again. The more you practise with different contexts, the more confidently you’ll handle all percentage questions in exams and daily life.