GCSE Maths Practice: percentages

Question 9 of 10

This question helps you practise finding small percentages of numbers, such as 5%. Understanding these simple proportions is vital for financial and data-based GCSE Maths problems.

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\( \textbf{What is } 5\% \textbf{ of } 80? \)

Choose one option:

Divide the number by 20 for 5%, or find 10% and halve it to double-check your result.

Understanding 5% in Everyday Maths

Percentages smaller than 10% are common in GCSE Maths and in real life. A 5% change may seem small, but it plays a big role in discounts, taxes, and statistics. Knowing how to calculate 5% quickly helps you solve questions mentally and check larger percentage problems with confidence.

Concept Explained

The term percent means 'per hundred'. To find 5% of any number, you multiply that number by \( \dfrac{5}{100} \) or 0.05. This is the same as dividing the number by 20 because \( \dfrac{5}{100} = \dfrac{1}{20} \).

So, \[ 5\% \text{ of } n = \dfrac{5}{100} \times n = 0.05n = \dfrac{n}{20}. \]

Understanding this relationship helps with estimation and mental arithmetic.

Step-by-Step Method

  1. Write 5% as a decimal: \( 5\% = 0.05 \).
  2. Multiply the given number by 0.05.
  3. Alternatively, find 10% (divide by 10) and then halve that value to get 5%.
  4. Check your answer by estimation — 5% should be much smaller than 10%.

Worked Examples

  • Example 1: 5% of 200 = \( 0.05 \times 200 = 10 \).
  • Example 2: 5% of 60 = \( 0.05 \times 60 = 3 \).
  • Example 3: 5% of 150 = \( 0.05 \times 150 = 7.5 \).

These results show how proportional thinking makes small percentage calculations easy to predict and check.

Real-Life Applications

  • Banking: If a savings account gives 5% interest per year, a balance of £80 earns \( 0.05 \times 80 = £4 \) interest.
  • Shopping: If a 5% discount is offered on a £60 product, the price drops by \( 3 \) to £57.
  • Health: A medicine’s effectiveness increasing by 5% means a small but measurable improvement in results.
  • Data: A population drop of 5% in a town of 20,000 means \( 0.05 \times 20,000 = 1,000 \) fewer people.

Although 5% seems small, in large numbers or over time it can represent a big difference.

Common Mistakes to Avoid

  • Forgetting to divide by 100 after multiplying by 5.
  • Confusing 5% with 50% — one is much smaller!
  • Mixing up finding 5% with increasing or decreasing by 5%. This question is only about finding the portion, not adjusting the total.

Quick Mental Maths Strategies

When working without a calculator, remember these shortcuts:

  • Find 10% first (divide by 10) and halve it for 5%.
  • Use the 'divide by 20' trick. For example, 5% of 80 = 80 ÷ 20 = 4.
  • If you know 1%, multiply it by 5. For example, 1% of 300 = 3, so 5% = 15.

Frequently Asked Questions

Q1: How can I use 5% to estimate quickly?
Use it to check higher percentages. For example, 15% is just three times 5%.

Q2: Why divide by 20 for 5%?
Because 5 out of 100 is the same as one out of 20 — that’s the fraction \( \dfrac{1}{20} \).

Q3: How do I find 5% decrease or increase?
To increase, multiply by 1.05. To decrease, multiply by 0.95.

Summary

Calculating 5% is one of the simplest percentage skills in GCSE Maths. Multiply the number by 0.05, divide by 20, or halve the 10% value — whichever is fastest for you. Estimation is key: 5% should always be one-twentieth of the original number. This understanding helps with more complex problems like tax rates, interest, and growth over time, building confidence for both exams and real-life calculations.