Key Concepts
6.1 Understand Percent
 Convert a percent to a fraction.
 Step 1. Write the percent as a ratio with the denominator 100.
 Step 2. Simplify the fraction if possible.

Convert a percent to a decimal.
 Step 1. Write the percent as a ratio with the denominator 100.
 Step 2. Convert the fraction to a decimal by dividing the numerator by the denominator.

Convert a decimal to a percent.
 Step 1. Write the decimal as a fraction.
 Step 2. If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100.
 Step 3. Write this ratio as a percent.

Convert a fraction to a percent.
 Step 1. Convert the fraction to a decimal.
 Step 2. Convert the decimal to a percent.
6.2 Solve General Applications of Percent
 Solve an application.
 Step 1. Identify what you are asked to find and choose a variable to represent it.
 Step 2. Write a sentence that gives the information to find it.
 Step 3. Translate the sentence into an equation.
 Step 4. Solve the equation using good algebra techniques.
 Step 5. Write a complete sentence that answers the question.
 Step 6. Check the answer in the problem and make sure it makes sense.
 Find percent increase.
 Step 1.
Find the amount of increase:
$\text{increase}=\text{new amount}\text{original amount}$  Step 2. Find the percent increase as a percent of the original amount.
 Step 1.
Find the amount of increase:
 Find percent decrease.
 Step 1.
Find the amount of decrease.
$\text{decrease}=\text{original amount}\text{new amount}$  Step 2. Find the percent decrease as a percent of the original amount.
 Step 1.
Find the amount of decrease.
6.3 Solve Sales Tax, Commission, and Discount Applications
 Sales Tax The sales tax is a percent of the purchase price.
 $\text{sales tax}=\text{tax rate}\cdot \text{purchase price}$
 $\text{total cost}=\text{purchase price}+\text{sales tax}$
 Commission A commission is a percentage of total sales as determined by the rate of commission.
 $\text{commission}=\text{rate of commission}\cdot \text{original price}$
 Discount An amount of discount is a percent off the original price, determined by the discount rate.
 $\text{amount of discount}=\text{discount rate}\cdot \text{original price}$
 $\text{sale price}=\text{original price}\u2013\text{discount}$
 Markup The markup is the amount added to the wholesale price, determined by the markup rate.
 $\text{amount of markup}=\text{markup rate wholesale price}$
 $\text{list price}=\text{wholesale price}+\text{mark up}$
6.4 Solve Simple Interest Applications
 Simple interest
 If an amount of money, $P$, the principal, is invested for a period of $t$ years at an annual interest rate $r$, the amount of interest, $I$, earned is $I=Prt$
 Interest earned according to this formula is called simple interest.
6.5 Solve Proportions and their Applications
 Proportion
 A proportion is an equation of the form $\frac{a}{b}=\frac{c}{d}$, where $b\ne 0$, $d\ne 0$.The proportion states two ratios or rates are equal. The proportion is read “$a$ is to $b$, as $c$ is to $d$”.
 Cross Products of a Proportion
 For any proportion of the form $\frac{a}{b}=\frac{c}{d}$, where $b\ne 0$, its cross products are equal: $a\cdot d=b\cdot c$.
 Percent Proportion
 The amount is to the base as the percent is to 100. $\frac{\text{amount}}{\text{base}}=\frac{\text{percent}}{100}$