When a quantity grows (gets bigger), then we can compute its PERCENT INCREASE. Show When a quantity shrinks (gets smaller), then we can compute its PERCENT DECREASE. These concepts are thoroughly explored on this page.
EXAMPLES: Question: A price rose from \$5 to \$7. What percent increase is this? Solution: Which is the original price? Answer: \$5 $\displaystyle\text{% increase} \ =\ \frac{(7-5)}{5} \ =\ \frac{2}{5} \ =\ 0.40 \ =\ 40\text{%}$ OR $\displaystyle\text{% increase} \ =\ \frac{(7-5)}{5}\cdot 100\% \ =\ \frac{2}{5}\cdot 100\% \ =\ 2\cdot\frac{100}{5}\% \ =\ 2\cdot 20\% \ =\ 40\text{%}$ Notes:
Question: A quantity decreased from 90 to 75. What percent decrease is this? Solution: Which is the original quantity? Answer: 90 $\displaystyle\text{% decrease} \ =\ \frac{(90-75)}{90} \ =\ \frac{15}{90} \ \approx\ 0.1667 \ =\ 16.67\text{%}$ 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 $\displaystyle\text{% decrease} \ =\ \frac{(16-13)}{16} \ =\ 0.1875 \ =\ 18.75\text{%}$ How do you find the percent of decrease?To calculate a percentage decrease, first work out the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100. The result expresses the change as a percentage—i.e., the percentage change.
How do I calculate a percentage increase?Calculating Percent Increase. Step 1: Find the difference of the values by subtracting the starting value from the final value.. Step 2: Divide the difference by the starting number.. Step 3: Multiply by 100.. Final Answer: 50% Increase.. |