GCSE Maths Practice: percentages

Question 6 of 10

This question helps you practise finding 15% of a number — an essential GCSE Maths skill. Understanding partial percentages prepares you for topics like profit, loss, and compound growth.

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\( \textbf{What is } 15\% \textbf{ of } 120? \)

Choose one option:

Estimate first: find 10%, then half of it for 5%, and add them together to check your answer.

Understanding Percentages like 15%

In GCSE Maths, percentages are one of the most important everyday skills. The percentage 15% means 15 parts out of 100. To calculate this, you multiply the number by 15 and divide by 100. This process helps you find a specific proportion of any quantity, whether it's money, marks, or measurements.

Concept Explained

The general rule to find a percentage of a number is:

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

For example, to find 15% of a number \( n \):

\[ 15\% \text{ of } n = \dfrac{15}{100} \times n = 0.15n \]

This formula works for any percentage value, whether you are finding 5%, 12%, or even 125% of something.

Step-by-Step Method

  1. Write the percentage as a fraction or decimal. \( 15\% = 0.15 = \dfrac{15}{100} \).
  2. Multiply the original number by \( 0.15 \).
  3. Check that the result makes sense — 15% should be smaller than the full number.

Worked Examples

  • Example 1: 15% of 200 = \( 0.15 \times 200 = 30 \).
  • Example 2: 15% of 60 = \( 0.15 \times 60 = 9 \).
  • Example 3: 15% of 400 = \( 0.15 \times 400 = 60 \).

Notice that 15% is slightly less than one-fifth, so the answer will always be a bit smaller than dividing by 5.

Common Mistakes to Avoid

  • Forgetting to divide by 100 after multiplying by the percentage number.
  • Mixing up 15% with \( \dfrac{1}{15} \) — they are completely different.
  • Confusing 'percentage of' with 'percentage increase or decrease'.

Real-Life Applications

Understanding how to find 15% is practical in many real situations:

  • Shops and Discounts: If a jacket costs £80 and there is a 15% sale, the discount is \( 0.15 \times 80 = 12 \). The sale price becomes £68.
  • Exams: If a test has 60 marks and you get 15% extra for effort, that’s \( 0.15 \times 60 = 9 \) bonus marks.
  • Finance: If your savings grow by 15%, and you had £200, your increase is \( 0.15 \times 200 = 30 \), giving you £230 total.

These examples show how percentages appear in all aspects of life, from shopping to managing money.

Quick Estimation Tips

To estimate 15% quickly, find 10% and 5% separately, then add them together:

\[ 15\% = 10\% + 5\% \]

So, for example, if a number is 300: 10% = 30, 5% = 15, total 15% = 45. This technique helps in mental maths when you don’t have a calculator handy.

Frequently Asked Questions

Q1: How can I find 5% easily?
Find 10% first, then halve it. For example, 10% of 240 = 24, so 5% = 12.

Q2: Can I use fractions instead of decimals?
Yes. 15% is \( \dfrac{15}{100} \), which simplifies to \( \dfrac{3}{20} \). Multiply the number by \( \dfrac{3}{20} \) for the same result.

Q3: How do I find 15% increase or decrease?
For an increase, multiply by 1.15. For a decrease, multiply by 0.85. For example, increasing 200 by 15% gives \( 200 \times 1.15 = 230 \).

Summary

Calculating 15% builds on your understanding of 10% and 5%. Multiply the number by 15, then divide by 100, or combine mental steps (10% + 5%) for faster answers. Always estimate before confirming your final result — 15% should be roughly between one-tenth and one-fifth of the total. Mastering this helps with GCSE percentage questions and real-life tasks like discounts, profit margins, and test marks.