### Unit 6: Percentages

In this course, you have already studied fractions and decimals. In this unit, you will study the other "fraternal twin" of fractions: percents, which are actually fractions and decimals in disguise. (Perhaps we should call them "fraternal triplets.") Going back to our example with decimals: we established that a dollar is 100 cents, a quarter is 25 cents, and the fraction form would be 25/100, which reduces to 1/4. A percentage is simply a fraction whose denominator is 100. Therefore, 25/100 becomes 25%. Because it is also 0.25, the percent is a fraction which is a decimal, which in turn is a percent. It's the Circle of Math. (Cue music from "The Lion King.")

Percents appear all over the place in life, especially when it comes to buying products. If you are considering whether to buy clothes at one store that has a sale with 65% off or a second store that has a sale with 50% off and an additional 15% discount off the sale price, you might be surprised to learn that the two sales are not the same. For those who follow the stock market, you might see the news talking about how your stock has had an increase of 70%. What does that mean?

In this unit, you will learn the rules of percentages and how to apply them. You will learn to convert percentages to and from fractions and decimals. You will learn about percent increase and decrease, which comes into play when you are out shopping. You will also learn (to the delight of shoppers everywhere) exactly how to calculate sale prices, restaurant tips, and other similar items.

**Completing this unit should take you approximately 13 hours.**

Upon successful completion of this unit, you will be able to:

- identify the basic components of a percent problem;
- convert between percent, decimal, and fraction notation;
- use proportional relationships to solve multi-step percent problems; and
- apply percent concepts in various practical applications.

### 6.1: Percent Basics

### 6.1.1: Describing the Meaning of Percent

Take notes as you watch these videos. Watch the presentations carefully two or three times until you are able understand the basics of percents.

### 6.1.2: Conversions

### 6.1.2.1: Decimal to Percent and Percent to Decimal

Take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to convert a decimal to a percent and a percent to a decimal.

Study the "Changing a Percent to a Decimal" and "Changing a Decimal to a Percent" sections on pages 504 and 505 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Changing a Percent to a Decimal), which will take you directly to the reading. After reading and studying these sections, complete the "You Try It" problems beside Examples 4-7 on pages 504 and 505. This reading contains examples on changing a percent to a decimal and vice versa. Then, complete the odd-numbered exercises for 19-49 on pages 508 and 509 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to change a percent to a decimal and vice versa. The solutions to these problems are located in the "Answers" section on page 510 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Answers").

Complete the assignment. You can review the concepts associated with the questions with the Khan videos in sub-subunit 6.1.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete the assignment. You can review the concepts associated with the questions with the Khan videos in sub-subunit 6.1.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 6.1.2.2: Fraction to Percent and Percent to Fraction

Take notes as you watch these video. View these presentations carefully two or three times until you are able to understand how to convert a fraction to a percent and a percent to a fraction.

Study the "Changing a Percent to a Fraction" section on pages 502-504 of the textbook, stopping at "Changing a Percent to a Decimal." Then, study "Changing a Fraction to a Percent" on pages 506-508 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Changing a Percent to a Fraction"), and (7 Percent, 7.1 Percent, Decimal, Fractions, "Changing a Fraction to a Percent"), which will take you directly to the readings. After reading and studying these sections, complete the "You Try It" problems beside Examples 1-4 on pages 502-504 and Examples 8-10 on pages 506-508. This reading contains examples of changing a percent to a fraction and vice versa.

Then, complete the odd-numbered exercises for 1-17 and 51-79 on pages 508-510 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to change a percent to a decimal and vice versa. The solutions to these problems are located in the "Answers" section on page 510 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Answers").

### 6.2: Percent Problems

### 6.2.1: Find a Given Percent of Another Number

Study "Find a Given Percent of a Given Number" on pages 512-514 of the textbook, stopping at "Find a Percent Given Two Numbers." The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Find a Given Percent of a Given Number), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1-3 on pages 512-514. This reading contains examples of finding a given percent of a given number.

### 6.2.2: Find a Percent Given Two Numbers

Take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find a percent given two numbers.

Study "Find a Percent Given Two Numbers" on pages 514-516 of the textbook, stopping at "Find a Number That Is a Given Percent of Another Number." The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Find a Percent Given Two Numbers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 4 and 5 on pages 514-516. This reading contains examples of finding a percent when given two numbers.

### 6.2.3: Find a Number That Is a Given Percent of Another Number

Study "Find a Number That Is a Given Percent of Another Number" on pages 516 and 517 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Find a Percent Given Two Numbers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 6 and 7 on pages 516 and 517. This material contains examples of finding a number that is a given percent of another number.

Then, complete the odd-numbered exercises for 1-49 on page 518 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to change a percent to a decimal and vice versa. The solutions to these problems are located in the "Answers" section on page 519 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, "Answers").

### 6.3: Applications of Percent

### 6.3.1: General Applications

Study "7.3 General Applications of Percent"on pages 521-524 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1-4 on pages 521-524. This material contains examples of percent applications.

Then, complete the odd-numbered exercises for 1-37 on pages 525-527 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply concepts of percent. This includes determining the percent that you earned on a test, finding the amount of a population who fall under certain criteria, and finding the sales tax on specific items. The solutions to these problems are located in the "Answers" section on page 528 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent, "Answers").

### 6.3.2: Percent Increase or Decrease

Take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find the amount that grows or decreases by a percent.

Study the "7.4 Percent Increase or Decrease" section on pages 529-537 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1-6 on pages 529-537. This material contains applications of percent increase or decrease.

Then, complete the odd-numbered exercises for 1-37 on pages 538-541 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the percent of increase or decrease, which includes how much an item is discounted at the store, the percent of increase in a salary, and finding the new cost of a product. The solutions to these problems are located in the "Answers" section on page 541 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease, "Answers").

Complete this assignment, which tests your knowledge of percent word problems. The assignment incorporates concepts of solving applications of percents. You can review the concepts associated with the questions with the Khan videos in sub-subunit 6.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete this assignment, which tests your knowledge of percent word problems. The assignment incorporates concepts of solving applications of percents. You can review the concepts associated with the questions with the Khan videos in sub-subunit 6.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete this assignment, which tests your knowledge of percent word problems. The assignment incorporates concepts of solving applications of percents. You can review the concepts associated with the questions with the Khan videos in sub-subunit 6.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.