Percentages
A percent change scales a value up or down by a fraction of itself. Adjust the original value and the percent change to see how the new value moves.
To increase a value by p%, multiply it by (1 + p/100). To decrease by p%, multiply by (1 − p/100). Thinking in terms of that multiplier — rather than calculating the change and then adding or subtracting it — avoids a lot of arithmetic mistakes.
Successive percent changes don’t add up the way you’d expect. A 20% increase followed by a 20% decrease does not bring you back to the original value, because the second change applies to a different (larger) number than the first. Multiply the two factors together — 1.20 × 0.80 — to find the real combined effect.
Reverse percentage problems give you the final value and ask for the original. The temptation is to just subtract the percent from the final value — but you need to divide by the growth factor instead, since the percent was taken of the original number, not the final one.