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Ratios, proportions, and percents

Percent of change

The percent of change is the ratio of the amount of change to the original amount.

• When an amount increases, the percent of change is a percent of increase.
• When the amount decreases, the percent of change is negative. You can also state a negative percent of change as a percent of decrease.

$Percent\;change=\frac{amount\;of\;change}{original\;measurement}x100$

or

$Percent\;change=\frac{New\;Value\;-\;Old\;Value}{Old\;Value}x100$

What is the percent of change from 30 to 24?

 Percent of change = $\frac{New\;Value\;-\;Old\;Value}{Old\;Value}x100$ = $\frac{24-30}{30}x100$ = $\frac{-6}{30}x100$ = -0.2x100 = -20%

The percent of decrease is 20%.

What is the percent of change from 8 to 10?

 Percent of change = $\frac{New\;Value\;-\;Old\;Value}{Old\;Value}x100$ = $\frac{10-8}{8}x100$ = $\frac{2}{8}x100$ = 0.25x100 = 25%

The percent of increase is 25%.

What is the percent of change from 10 to 36?
26 % increase
46 % decrease
260 % increase
260 % decrease