The Mathematics of Ratios: Comprehensive Percentage Theory
Percentage of a value calculation
What is 20% of $60?
20% is 20/100 multiplied by $60:
$$20\% \times \$60 = \frac{20}{100} \times \$60 = 0.2 \times \$60 = \$12$$
Percentage calculation
$12 is what percent of $60?
$12 is divided by $60 and multiplied by 100%:
$$\frac{\$12}{\$60} \times 100\% = 20\%$$
Whole value calculation
$12 is 20% of what?
$12 is divided by 20%:
$$\frac{\$12}{20\%} = \frac{\$12}{20} \times 100 = \$60$$
Percentage change calculation
What is the percentage change from $40 to $50?
The difference between $50 and $40 is divided by $40 and multiplied by 100%:
$$\frac{\$50 - \$40}{\$40} \times 100\% = 0.25 \times 100\% = 25\%$$