Reverse percentages
Find the original from a percentage-changed value: original = changed ÷ multiplier.
If a value has been increased or decreased by a percentage, divide by the multiplier to find the original. Common GCSE setup: a sale price including VAT, find the pre-VAT amount.
Worked examples
Sale price £240 = 80% of original. Original = 240/0.8 = £300.
Bill £144 includes 20% VAT. Pre-VAT = 144/1.20 = £120.
Population grew 15% to 23,000. Original = 23,000/1.15 = 20,000.
Frequently asked questions
Why ‘reverse’?
Forward: original × multiplier = changed. Reverse: changed ÷ multiplier = original.
Common GCSE trap?
Don't subtract 20% from the gross to find the net. £120 + 20% = £144, but £144 − 20% = £115.20.