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Percentages, Decimals and Fractions — GCSE Maths Revision

Convert between percentages, decimals and fractions. Learn percentage increase/decrease, reverse percentage, and compound interest for GCSE Maths exams.

percentagesfractionsdecimalspercentage changeGCSE number

Converting Between Fractions, Decimals and Percentages

These three forms represent the same value in different ways. Being fluent in converting between them is essential for many GCSE questions.

  • Fraction → Decimal: divide numerator by denominator (e.g., 3/4 = 0.75)
  • Decimal → Percentage: multiply by 100 (e.g., 0.75 = 75%)
  • Percentage → Fraction: write over 100 and simplify (e.g., 60% = 60/100 = 3/5)
  • Key facts to memorise: 1/3 ≈ 0.333..., 2/3 ≈ 0.667, 1/8 = 0.125

Percentage Increase and Decrease

Use a multiplier to apply a percentage change. For an increase, the multiplier is greater than 1; for a decrease, it's less than 1.

Worked Example

Increase £240 by 15%

  1. 1.Multiplier = 1 + 0.15 = 1.15
  2. 2.£240 × 1.15 = £276
Answer: £276

Percentage Change Formula

To calculate the percentage change between two values, use the formula: Percentage Change = (Change ÷ Original) × 100.

Worked Example

A jacket costs £80, reduced to £60. Find the percentage decrease.

  1. 1.Change = 80 − 60 = 20
  2. 2.Percentage decrease = (20 ÷ 80) × 100 = 25%
Answer: 25% decrease

Reverse Percentage (Finding the Original)

If you've been given the value after a percentage change and need the original, divide by the multiplier. Don't make the common mistake of applying the percentage to the new value.

Worked Example

After a 20% increase, a price is £72. Find the original price.

  1. 1.Multiplier for 20% increase = 1.20
  2. 2.Original = 72 ÷ 1.20 = £60
Answer: £60

Compound Interest and Repeated Percentage Change

Compound interest applies a percentage change repeatedly. Use the formula: Amount = Principal × (1 + r/100)^n, where r is the rate and n is the number of years.

Worked Example

£500 is invested at 3% compound interest for 4 years. Find the final amount.

  1. 1.Amount = 500 × (1.03)⁴
  2. 2.= 500 × 1.1255...
  3. 3.≈ £562.75
Answer: £562.75

Frequently Asked Questions

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal each year. Compound interest is calculated on the principal plus all previously earned interest, so it grows faster.

How do I find the original value after a percentage change?

Divide by the multiplier. For a 15% increase, the multiplier is 1.15, so original = new value ÷ 1.15. Never subtract the percentage from the new value.

What percentage questions come up on Foundation vs Higher?

Foundation covers conversions, percentage change, and reverse percentage. Higher adds compound interest, repeated percentage change, and interpreting percentage change in context.

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