Grade 10 Math · Percent change
Measured from home base
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Measured from home base

Prices move, and percent change is how you say how much in a way that is fair to compare: c=newoldoldc = \dfrac{\text{new} - \text{old}}{\text{old}} — read aloud: c equals new minus old, all over old. Here old is the price before, new is the price after, and cc is the change you are solving for — a fraction of the old price, times 100 to say it as a percent. The subtraction finds the move; the division measures it against where you STARTED. Home base is always the old value — divide by the new one and you get a different (and wrong) answer for the very same price move.

And the sign carries real information: a rise makes cc positive, a drop makes it negative — a price falling from $50 to $45 is a change of −10%, minus sign and all. Keep the sign and the formula runs both directions with one bracket: new=old(1+c)\text{new} = \text{old}\,(1 + c), rises and drops alike. One tool, both doors.