Percentage change compares the difference between a new value and an original value with the original value. Keeping that original base explicit is the main step.
Calculate the change
A quantity rises from 80 to 100. The increase is 20, so the percentage increase is 20 ÷ 80 × 100 = 25%.
If it falls from 100 to 80, the decrease is still 20, but the original base is now 100. The percentage decrease is 20%. Reversing the journey changes the denominator.
Equal percentages do not usually cancel
Start with 200. A 10% increase gives 220. A subsequent 10% decrease subtracts 22, leaving 198.
The two operations use different bases. You can combine their multipliers: 1.10 × 0.90 = 0.99, which is 99% of the starting amount. This explains the final 1% decrease without handling each subtraction separately.
Recover an original value
After a 20% reduction, a value is 72. That means 72 represents 80% of the original, so the original is 72 ÷ 0.80 = 90.
Adding 20% of 72 gives 86.4, not 90, because it uses the reduced base. Reverse-percentage questions require dividing by the remaining proportion.
Handle a zero starting value carefully
The usual percentage-change formula divides by the original value. If that value is zero, the ordinary relative percentage change is undefined. Report the absolute change instead of inventing a finite percentage.
A quick checking routine
Write old value, new value and difference. Confirm which one is the base. Predict whether the result should be positive or negative, then compute. If several changes occur, use each stage's actual value or multiply the corresponding factors. This keeps the arithmetic aligned with the story rather than a memorized shortcut used in the wrong direction.