Prerequisites
Arithmetic | 12 of 17
Prerequisites: Ratios, Rates, and Proportions. Enables: Algebra.
Percent means per hundred.
$$
p\% = \frac{p}{100}
$$
Examples:
$$
25\% = \frac{25}{100} = 0.25
$$
$$
7\% = \frac{7}{100} = 0.07
$$
$$
125\% = \frac{125}{100} = 1.25
$$
Percent of a number
To find $p\%$ of a number $N$:
$$
\frac{p}{100}N
$$
Example:
$$
20\%\text{ of }80 = 0.20(80)=16
$$
Finding the percent
To find what percent $A$ is of $B$:
$$
\frac{A}{B}\cdot100\%
$$
Example:
$$
18\text{ is what percent of }72?
$$
$$
\frac{18}{72}\cdot100\% = 25\%
$$
Percent increase
Percent increase is:
$$
\frac{\text{new} - \text{old}}{\text{old}}\cdot100\%
$$
Example:
A value changes from $40$ to $50$.
$$
\frac{50-40}{40}\cdot100\%=25\%
$$
Percent decrease
Percent decrease is:
$$
\frac{\text{old} - \text{new}}{\text{old}}\cdot100\%
$$
Example:
A value changes from $80$ to $60$.
$$
\frac{80-60}{80}\cdot100\%=25\%
$$
Simple interest
Simple interest is:
$$
I = Prt
$$
where:
$I$ = interest
$P$ = principal
$r$ = annual interest rate as a decimal
$t$ = time in years
Total amount:
$$
A = P + I
$$
or
$$
A = P(1+rt)
$$
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