# 6.S: Percents (Summary)

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### Key Terms

commission | A percentage of total sales as determined by the rate of commission |

discount | A percent off the original price, determined by the discount rate |

mark-up | The amount added to the wholesale price, determined by the mark-up rate |

percent | A ratio whose denominator is 100 |

percent decrease | The percent the amount of decrease is of the original amount |

percent increase | The percent the amount of increase is of the original amount |

proportion | An equation of the form \(\frac{a}{b} = \frac{c}{d}\), where b ≠ 0, d ≠ 0.The proportion states two ratios or rates are equal. The proportion is read “ a is to b, as c is to d”. |

sales tax | A percent of the purchase price |

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. |

### Key Concepts

#### 6.1 - Understand Percent

**Convert a percent to a fraction.**- Write the percent as a ratio with the denominator 100.
- Simplify the fraction if possible.

**Convert a percent to a decimal.**- Write the percent as a ratio with the denominator 100.
- Convert the fraction to a decimal by dividing the numerator by the denominator.

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

**Convert a fraction to a percent.**- Convert the fraction to a decimal.
- Convert the decimal to a percent.

#### 6.2 - Solve General Applications of Percent

**Solve an application.**- Identify what you are asked to find and choose a variable to represent it.
- Write a sentence that gives the information to find it.
- Translate the sentence into an equation.
- Solve the equation using good algebra techniques.
- Write a complete sentence that answers the question.
- Check the answer in the problem and make sure it makes sense.

**Find percent increase.**- Find the amount of increase: increase = new amount − original amount
- Find the percent increase as a percent of the original amount.

**Find percent decrease.**- Find the amount of decrease. decrease = original amount − new amount
- Find the percent decrease as a percent of the original amount.

#### 6.3 - Solve Sales Tax, Commission, and Discount Applications

**Sales Tax**: The sales tax is a percent of the purchase price.- sales tax = tax rate • purchase price
- total cost = purchase price + sales tax

**Commission**: A commission is a percentage of total sales as determined by the rate of commission.- commission = rate of commission • original price

**Discount**: An amount of discount is a percent off the original price, determined by the discount rate.- amount of discount = discount rate • original price
- sale price = original price – discount

**Mark-up**: The mark-up is the amount added to the wholesale price, determined by the mark-up rate.- amount of mark-up = mark-up rate wholesale price
- list price = wholesale price + 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 ≠ 0, d ≠ 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 ≠ 0, its cross products are equal: a • d = b • c.

**Percent Proportion**- The amount is to the base as the percent is to 100. \(\frac{amount}{base} = \frac{percent}{100}\)

### Contributors

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."