Percentage change vs percentage points
Going from 10% to 15% is a 5 percentage-point rise but a 50% relative increase. Mixing the two is the most common percentage mistake in reports and news headlines.
Reverse percentages
If a price is 240 after a 20% increase, the original is 240 ÷ 1.2 = 200 — not 240 − 20%. Divide by (1 + rate) to undo an increase, and by (1 − rate) to undo a discount.