Before you read

Answer first — see what you already know.

At a department store clearance event, a jacket originally priced at $45 is marked 20% off. What is the sale price?

A
$9.00
B
$25.00
C
$36.00
D
$40.00

Check your answer

Answer:

Before you read

Answer first — see what you already know.

The median home price in a neighborhood rose from $250,000 to $290,000 over three years. What was the percent increase?

A
13.8%
B
16.0%
C
18.5%
D
40.0%

Check your answer

Answer:

Theory

Percentage Basics

A percentage is a fraction out of 100:
$p\% = \frac{p}{100}$

25% tax on income

Three types of problems:
1. What is $p\%$ of $N$ ? $\to$ $\frac{p}{100} \times N$
2. $A$ is what percent of $B$ ? $\to$ $\frac{A}{B} \times 100$
3. $A$ is $p\%$ of what? $\to$ $\frac{A}{p/100} = \frac{100A}{p}$

\text{Original: } $80
$\text{Increase: } 15\%$
\text{New} = 80 \times 1.15 = $92multiply by (1 + rate)

Percent increase calculation

Example 1

What is 15% of 240?

$0.15 \times 240 = 36$

Example 2

36 is what percent of 240?

$\frac{36}{240} \times 100 = 15\%$

15%

Theory

Percent Increase and Decrease

Percent change formula:
$\text{Percent change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

Shortcut multipliers:
- Increase by $p\%$ : multiply by $(1 + \frac{p}{100})$
- Decrease by $p\%$ : multiply by $(1 - \frac{p}{100})$

Example: A $200 item after a 25% discount: $200 \times 0.75 = \$150$

Example 1

A stock price goes from $80 to $92. What is the percent increase?

Change $= 92 - 80 = 12$

Percent increase $= \frac{12}{80} \times 100 = 15\%$

15%

Example 2

A population of 50,000 increases by 8% per year for 2 years. What is the final population?

After year 1: $50{,}000 \times 1.08 = 54{,}000$

After year 2: $54{,}000 \times 1.08 = 58{,}320$

58,320

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2 more sections including examples, practice problems, and step-by-step solutions.

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