GCSE Maths Practice: percentages

Understanding 10% Calculations

Percentages are used to describe parts of a whole, and 10% is one of the easiest values to work with in GCSE Maths. The word 'percent' means 'per hundred', so 10% represents ten out of every hundred. Understanding how to calculate 10% helps with many real-life problems like discounts, exam marks, and financial percentages.

Concept Explained

To find a percentage of any number, multiply the number by the percentage and then divide by 100. For 10%, the calculation simplifies nicely because dividing by 10 is the same as finding one-tenth of the number:

\[ 10\% \text{ of a number } = \dfrac{10}{100} \times \text{Number} = \dfrac{1}{10} \times \text{Number} \]

This makes 10% problems easy to solve mentally — just divide the number by 10.

Step-by-Step Method

1. Convert the percentage to a fraction or decimal: \( 10\% = 0.1 = \dfrac{1}{10} \).
2. Multiply the given number by 0.1 (or divide by 10).
3. Write down your answer and check that it makes sense. The result should be smaller than the original number.

Worked Examples

• Example 1: 10% of 500 = 500 × 0.1 = 50.
• Example 2: 10% of 90 = 90 ÷ 10 = 9.
• Example 3: 10% of 120 = (10 ÷ 100) × 120 = 12.

Notice that each answer is exactly one-tenth of the starting number.

Common Mistakes to Avoid

• Multiplying by 10 instead of dividing by 10.
• Forgetting to divide by 100 when using the full percentage formula.
• Rounding too early — keep the full decimal until the final step for accuracy.

Real-Life Applications

Understanding 10% calculations helps you make better decisions in daily life. For example:

• Shops often show prices like '10% off everything'. If a laptop costs £250, the discount is \( 0.1 \times 250 = 25 \), so the sale price is £225.
• If a runner completes 10% of a 4000 m race, they have covered \( 0.1 \times 4000 = 400 \) m.
• If your test mark improves by 10%, and your original score was 60, the new score is \( 60 + (0.1 \times 60) = 66 \).

Percentages are not just academic — they connect directly to real-world reasoning.

Quick Mental Maths Tip

Since 10% is one-tenth, dividing by 10 gives the answer immediately. To find 5%, simply halve the 10% value. For example, if 10% of 300 = 30, then 5% = 15. Similarly, 20% is double 10%, so 20% of 300 = 60. These quick tricks make mental calculations faster and reduce calculator dependence in exams.

Frequently Asked Questions

Q1: Why divide by 10 for 10%?
Because 10% is one-tenth, dividing by 10 gives exactly the right portion.

Q2: How can I find 1% of a number?
Divide the number by 100. For example, 1% of 800 = 8.

Q3: What if the number has decimals?
The method is the same. For example, 10% of 47.5 = 4.75.

Summary

Calculating 10% is a core GCSE Maths skill. Always remember that \( 10\% = \dfrac{1}{10} \). Multiply the number by 0.1 or divide by 10 for a quick answer. This skill forms the base for more complex percentage questions, such as finding 15%, 25%, or percentage increases and decreases. Check your answer using estimation — 10% should always be roughly one-tenth of the original number. With practice, you can solve these instantly in your head, which will also improve your confidence in more advanced percentage problems.