Percentages Quizzes

GCSE Maths Revision Quiz: Simple Percentage Problems Without a Calculator

Difficulty: Foundation

Curriculum: GCSE

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GCSE Higher Tier Quiz: Real-World Percentage Problems (Discounts, Sales, Growth)

Difficulty: Higher

Curriculum: GCSE

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Visual overview of Percentages.

Introduction

Percentages are a core topic in GCSE Maths and appear in almost every exam paper. A percentage represents a part of a whole divided into 100 equal parts. Understanding percentages allows students to calculate discounts, interest, profit and loss, markups, and data comparisons in real-life contexts. Mastery of percentages also underpins other topics such as fractions, decimals, ratio, and probability.

For example, 25% means 25 parts out of 100, which is equivalent to the fraction \(\frac{25}{100}\) or the decimal \(0.25\). Being confident with percentages helps students solve a wide range of problems quickly and accurately.

Core Concepts

What is a Percentage?

A percentage is a number expressed as a fraction of 100. The symbol “%” indicates “per hundred.”

  • 50% = 50 out of 100 = \(\frac{50}{100}=0.5\)
  • 25% = 25 out of 100 = \(\frac{25}{100}=0.25\)
  • 125% = 125 out of 100 = \(\frac{125}{100}=1.25\)

Converting Between Percentages, Fractions, and Decimals

Percentage → Decimal: divide by 100.

  • 75% → \(75 \div 100 = 0.75\)
  • 12.5% → \(12.5 \div 100 = 0.125\)

Decimal → Percentage: multiply by 100.

  • 0.4 → \(0.4 \times 100 = 40\%\)
  • 0.075 → \(0.075 \times 100 = 7.5\%\)

Fraction → Percentage: convert to decimal, then multiply by 100.

  • \(\frac{3}{4}=0.75 \Rightarrow 0.75 \times 100 = 75\%\)
  • \(\frac{2}{5}=0.4 \Rightarrow 0.4 \times 100 = 40\%\)

Percentage → Fraction: write over 100 and simplify.

  • 75% → \(\frac{75}{100}=\frac{3}{4}\)
  • 12.5% → \(\frac{12.5}{100}=\frac{1}{8}\)
Tip: Think “per hundred”: percent → move decimal point two places left; decimal → percent → two places right.

Finding a Percentage of a Quantity

Multiply the number by the percentage in decimal form.

Example

Find 20% of 150.

20% → \(0.20\)

\(0.20 \times 150 = 30\)

Answer: 30

  • 15% of 200 → \(0.15 \times 200 = 30\)
  • 125% of 80 → \(1.25 \times 80 = 100\)

Finding the Whole from a Percentage

Sometimes you know the part and the percentage and need the whole.

\(\text{Whole}=\dfrac{\text{Part}}{\text{Percentage as decimal}}\)

Examples

30 is 25% of what number? \(\;30 \div 0.25 = 120\)

18 is 60% of what number? \(\;18 \div 0.6 = 30\)

Percentage Increase and Decrease

Increase: New amount \(=\) Original \(\times (1+\text{decimal})\)

Example

Increase £120 by 25% → \(120 \times (1+0.25)=120 \times 1.25=150\)

Decrease: New amount \(=\) Original \(\times (1-\text{decimal})\)

Example

Decrease £200 by 15% → \(200 \times (1-0.15)=200 \times 0.85=170\)

Finding the Percentage Change

\(\text{Percentage change}=\dfrac{\text{Change}}{\text{Original}} \times 100\%\)

Examples

Price rises £50→£60: change \(=10\), so \(\frac{10}{50}\times100\%=20\%\)

Population falls 12,000→11,400: change \(=600\), so \(\frac{600}{12000}\times100\%=5\%\)

Worked Examples

Example 1 (Foundation): Find percentage of a quantity

Find 30% of 250 → \(0.30 \times 250 = 75\)

Answer: 75

Example 2 (Foundation): Percentage increase

Increase 80 by 15% → \(80 \times 1.15 = 92\)

Answer: 92

Example 3 (Higher): Find original amount from percentage

36 is 45% of what number? \(\;36 \div 0.45 = 80\)

Answer: 80

Example 4 (Higher): Percentage decrease

Reduce 150 by 20% → \(150 \times 0.80 = 120\)

Answer: 120

Example 5 (Higher): Percentage change

Value increases from 45 to 60: change \(=15\)

\(\frac{15}{45} \times 100\% \approx 33.3\%\)

Common Mistakes

  • Forgetting to convert the percentage to a decimal before calculating.
  • Adding/subtracting percentage points instead of multiplying by \((1 \pm \text{decimal})\).
  • Confusing percentage increase and decrease formulas.
  • Rounding too early in multi-step problems.
  • Misreading the question (part vs whole confusion).
How to avoid: Convert to decimals first; check if it’s increase or decrease; estimate to check answers; keep units consistent; round only at the end.

Applications

  • Money: discounts, VAT, interest, profit & loss
  • Measurements & Data: exam scores, statistics, surveys
  • Business: profit margins, markups, commission
  • Science & Economics: growth rates, population changes

Strategies & Tips

  • Practise converting percentages, fractions, and decimals quickly.
  • Memorise benchmarks: 10%, 25%, 50%, 75%.
  • Use “part ÷ whole × 100” to find percentages from data.
  • Write intermediate steps to avoid slips; round at the end.

Summary / Call-to-Action

Percentages are essential for exams and daily life. Master conversions, percentage of a quantity, and increase/decrease to solve problems with confidence.

  • Try the percentage quizzes to reinforce learning.
  • Practise real-life problems (discounts, tax, interest).
  • Check answers using estimation or reverse calculations.
  • Push yourself with multi-step percentage problems.