Grade 11 Math — Functions & Applications · Percent change
Compared with what?
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Compared with what?

Every later lesson leans on this one skill, so it goes first. c=xnewxoldxoldc = \dfrac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}} — read aloud, c equals new minus old, over old. The top is the change; the bottom is what you are comparing it WITH. A $20 rise on an $80 drill is a big deal; the same $20 on a $2000 mower is a rounding error. Same change, different story, and the denominator is the whole difference between them.

Two habits keep you out of trouble. First, the old value always sits underneath — percent change measures from where you STARTED, never from where you ended. Second, let the sign do its job: a negative cc is a drop and should be reported as one, not quietly turned positive. And a check you will use all chapter: the answer comes out as a bare ratio, so multiply by 100 only at the very end, when it puts on its percent sign to go outside.