Calculating Percent Increase and Decrease

When a quantity grows (gets bigger), then we can compute its PERCENT INCREASE:

$ \text{PERCENT INCREASE} = \frac{\displaystyle{(\text{new amount} - \text{original amount})}} {\displaystyle\text{original amount}} $

When a quantity shrinks (gets smaller), then we can compute its PERCENT DECREASE:

$ \text{PERCENT DECREASE} = \frac{\displaystyle{(\text{original amount} - \text{new amount})}} {\displaystyle\text{original amount}} $

Both formulas have the following pattern:

$ \text{PERCENT INCREASE/DECREASE} = \frac{\displaystyle{\text{change in amount}}} {\displaystyle\text{original amount}} $

Note that when you compute percent increase or decrease,
you always compare how much a quantity has changed to the original amount.

Note also that the numerator in these formulas is always a POSITIVE number
(or zero, if the quantity doesn't change at all).

EXAMPLES:

Question: A price rose from \$5 to \$7. What percent increase is this?

Solution: Which is the original price? Answer: \$5
This will be the denominator.

$\text{% increase} = \frac{(7-5)}{5} = \frac{2}{5} = 0.40 = 40\text{%}$

Note: Be sure to give your answer as a PERCENT.

Question: A quantity decreased from 90 to 75. What percent decrease is this?

Solution: Which is the original quantity? Answer: 90
This will be the denominator.

$\text{% decrease} = \frac{(90-75)}{90} = \frac{15}{90} \approx 0.1667 = 16.67\text{%}$

Note: In the exercises below, if an answer does not come out exact, then it is rounded to two decimal places.

Question: An item went on sale for \$13 from \$16. What percent decrease is this?

Solution: Which is the original price? Answer: \$16
This will be the denominator.

$\text{% decrease} = \frac{(16-13)}{16} = 0.1875 = 18.75\text{%}$

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.

(an even number, please)