### Unit 5: Ratios and Proportions

In this unit, we study ratios and proportions – mathematical concepts we use all the time, often without realizing it. For example,

- At the grocery store, have you ever compared unit prices for different packages of the same type of food? That is a ratio.
- When driving 65 mph (miles per hour) on the highway, have you ever determined how long it will take you to get to your destination? That is a proportion.
- In sports, statisticians use proportions to predict an athlete's performance, based on what they have accomplished in the past.

Here we explore how to write ratios, set-up and solve proportions, and apply these skills to real-world experiences.

**Completing this unit should take you approximately 8 hours.**

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

- use ratio concepts to solve problems;
- calculate unit prices and rates;
- apply the processes of solving a proportion; and
- analyze proportional relationships and use them to solve real-world and mathematical problems.

### 5.1: Ratios

### 5.1.1: Introduction to Ratios

Take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand the basics of ratios.

Study the "Introduction to Ratios and Rates" section on pages 449-451 of the textbook, stopping at "Rates." The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1 and 2 on pages 449-451. This material contains examples on ratios. Then, complete the odd-numbered exercises for 1-23 on page 454 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to write and simplify ratios. The solutions to these problems are located in the "Answers" section on page 455 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, "Answers").

### 5.1.2: Finding Unit Rates and Prices

Take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to find unit rates. Watch the second presentation carefully two or three times until you are able to find unit prices.

Study the "Rates" and "Unit Rates" sections on pages 451-453. The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, "Rates"), which will take you directly to the reading. After reading and studying these sections, complete the "You Try It" problems beside Examples 3-6 on pages 451-453. This material contains examples on rates and unit rates. Then, complete the odd-numbered exercises for 23-37 on page 454 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to write and simplify rates, which includes comparing rates to see the better deal on an item. The solutions to these problems are located in the "Answers" section on page 455 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, "Answers").

Complete the assignment that tests your knowledge of ratio word problems. This assignment incorporates concepts of ratios. You can review the concepts associated with the questions with the Khan video in sub-subunit 5.2.1. 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.

### 5.2: Proportions

### 5.2.1: Understanding Proportions

Take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand the basics of proportions.

Study the "Introduction to Ratios and Rates" section on pages 456-459 of the textbook, stopping at "Example 4." The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportions), 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 457-459. This material contains examples on an introduction to proportions. Then, complete the odd-numbered exercises for 1-13, and 17, 19, 23, 27, 29, 31, and 35 on page 463 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportion, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to solve proportions. The solutions to these problems are located in the "Answers" section on page 465 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Proportion, "Answers").

### 5.2.2: Applications of Proportions

Take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand applications of proportions.

Review the "Introduction to Ratios and Rates" section through Example 4 on pages 456-459 of the textbook; note that you already studied this material in sub-subunit 5.2.1. The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportions), which will take you directly to the reading. After reviewing this section, complete the "You Try It" problems beside Example 4 on page 459. This material contains examples on an introduction to proportions. Then, complete the odd-numbered exercises for 37-53 on pages 464 and 465 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportion, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to write and solve proportions, which include finding the cost of an item. The solutions to these problems are located in the "Answers" section on page 465 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Proportion, "Answers").

Read the "Applications of a Proportion" section. Then, complete "Practice Set A," exercises 1-5. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice applications of proportions. Then, complete the odd-numbered problems for 7-25. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to practice applications of proportions.

Complete the assignment that tests your knowledge on proportion word problems. These assignments incorporate concepts of ratios and proportions. You can review the concepts associated with the questions with the Khan video in sub-subunit 5.2.2. 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 the assignment that tests your knowledge on proportion word problems. These assignments incorporate concepts of ratios and proportions. You can review the concepts associated with the questions with the Khan video in sub-subunit 5.2.2. 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.