Convert between percentages, decimals and fractions. Learn percentage increase/decrease, reverse percentage, and compound interest for GCSE Maths exams.
These three forms represent the same value in different ways. Being fluent in converting between them is essential for many GCSE questions.
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.
Increase £240 by 15%
To calculate the percentage change between two values, use the formula: Percentage Change = (Change ÷ Original) × 100.
A jacket costs £80, reduced to £60. Find the percentage decrease.
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.
After a 20% increase, a price is £72. Find the original price.
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.
£500 is invested at 3% compound interest for 4 years. Find the final amount.
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.
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.
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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