Percent Increase

A ticket price goes up from 20 dollars to 25 dollars. By what percent did it rise? First find the change: 25 - 20 is 5 dollars. Then ask what percent the change is of the original price, the one you started from: $\frac{5}{20}\cdot 100$ is 25. The price rose 25%.

On the board, with p for the percentage: $p = \frac{25-20}{20}\cdot 100$, then $p = 25$. The change goes on top and the original goes underneath.

Why the original? A percent change answers 'how much bigger than before?', so it is measured against before. Dividing by the new price, $\frac{5}{25}$, gives 20%, which is the right size of change measured from the wrong place.