Work backwards from a final value to find what the original amount was before a percentage change.
Original = final ÷ (1 + percentage ÷ 100) for an increase.
Do not simply subtract the same percentage from the final value. Reverse percentages undo the multiplier that created the final value. After a 20% increase, divide by 1.20. After a 20% decrease, divide by 0.80.
This is useful for finding a pre-tax amount, a price before a markup, an original price before a discount, or a starting figure when only the final value and percentage change are known.
Because the 20% increase was calculated from the original value, not the final value. Dividing by 1.20 correctly reverses the original multiplier.
Yes. Divide the final value by 1 minus the percentage written as a decimal.
The original value cannot be recovered from a final value after a 100% decrease because the multiplier is zero.