A percentage of a value, plus the increase and decrease, all at once.
A percentage of a number is the number multiplied by the fraction: 15% of 240 is 240 × 0.15 = 36. You turn a percentage into a fraction by dividing it by 100, so 15% becomes 0.15. The same operation works for any rate, including above 100%: 150% of 240 is 240 × 1.5 = 360.
Divide the part by the whole and multiply by 100: 52 correct answers out of 80 is 52 / 80 × 100 = 65%. The thing to get right is which number is the denominator — the divisor is always whatever counts as 100 percent. That mix-up is the most common mistake in percentage arithmetic.
You divide rather than subtract. If 21% has been added to a price, the original is the total divided by 1.21: from 121 euro that is 121 / 1.21 = 100 euro. Subtracting 21% from 121 euro would give 95.59 euro, which is wrong, because the percentage was taken from the smaller number. The higher the rate, the wider the gap.
Because the second step takes its percentage from the already increased number. 100 plus 10% is 110, but 10% of 110 is 11, so the result is 99 rather than 100. Each percentage step applies to whatever base is current at that moment, which is why a percentage change is not undone by the same percentage.