Percents and Applications

Percent Basics

Percent means "per 100": $25\% = \frac{25}{100} = 0.25$

Converting

| From → To | Method | |-----------|--------| | Percent → Decimal | Divide by 100 ($45\% = 0.45$) | | Decimal → Percent | Multiply by 100 ($0.08 = 8\%$) | | Fraction → Percent | Divide, then multiply by 100 | | Percent → Fraction | Put over 100, simplify ($60\% = \frac{3}{5}$) |

The Percent Equation

$\text{Part} = \text{Percent} \times \text{Whole}$

What is 30% of 80? $x = 0.30 \times 80 = 24$

15 is what percent of 60? $15 = x \times 60 \implies x = 0.25 = 25\%$

Applications

Tax

$\text{Total} = \text{Price} + \text{Price} \times \text{Tax Rate}$ $\text{Total} = \text{Price} \times (1 + \text{Tax Rate})$

Item: \45$, Tax:$8% $$\45 \times 1.08 = $48.60$$

Tip

$\text{Tip} = \text{Bill} \times \text{Tip Rate}$

Discount

$\text{Sale Price} = \text{Original} \times (1 - \text{Discount Rate})$

\80$shirt,$25%$off:$$80 \times 0.75 = $60$

Percent Change

$\text{Percent Change} = \frac{|\text{New} - \text{Original}|}{\text{Original}} \times 100\%$

From 50 to 65: $\frac{|65-50|}{50} \times 100 = 30\%$ increase

Shortcut: "Percent OF" means multiply. "What IS" means equals.