Ups and downs are not symmetric
A 50% fall needs a 100% rise to get back to the start.
Every everyday percentage question in one place: what is 15% of a price, what percent one number is of another, how much something went up, or what your exam marks are as a percentage.
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X% of Y is X ÷ 100 × Y. "X is what percent of Y" is X ÷ Y × 100. Percentage change from an old value to a new one is (new − old) ÷ old × 100, which is why going from 80 to 100 is a 25% increase, but going back from 100 to 80 is only a 20% decrease.
Percentage difference is used when neither value is the "original": it divides the gap by the average of the two. Marks to percentage is simply marks obtained divided by total marks, times 100.
A 50% fall needs a 100% rise to get back to the start.
A rate rising from 10% to 12% is 2 percentage points, but a 20% increase.
Always ask "percent of what?" before comparing figures.
Two 10% increases add up to 21%, not 20%.
Multiply the number by the percentage and divide by 100. For example, 15% of 2,500 is 375.
Subtract the old value from the new value, divide by the old value and multiply by 100.
Divide marks obtained by total marks and multiply by 100. 935 out of 1,100 is 85%.
Change compares a new value with an original one. Difference compares two values with no original, using their average.
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