### Unit 6: Ratios and Proportions

In this unit, we study ratios and proportions. These are mathematical concepts that we use all the time, probably without even 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.

In this unit, we explore how to write ratios, set up and solve proportions, and apply proportions to real-world scenarios.

**Completing this unit should take you approximately 3 hours.**

Upon successful completion of this unit, you 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 to solve real-world and mathematical problems.

### 5.1: Introduction to Ratios

Before we can begin to solve problems with ratios, we need to understand what ratios are.

Watch this video to learn how ratios work. Ratios are essentially fractions, so you will be applying many of the concepts you learned in Unit 3.

Watch this video on ratios to reinforce what you just learned.

Do this homework assignment, which reviews writing fractions in their reduced forms. You can check your answers at the end of the document.

### 5.2: Finding Unit Rates and Prices

One of the useful applications of ratios is finding unit rates and prices. Imagine going to the grocery store to buy pasta. There are many different brands, each with slightly different prices for slightly different sized packages. How do you decide which box of pasta is the best deal? We use unit prices to determine this. By using ratios, we can find the best deal by determining the price per ounce of pasta for each box.

Watch these videos to see how to determine unit prices and rates.

Do this assessment. If you struggle with any of the problems, you can watch a video or get a hint.

### 5.3: Understanding Proportions

Proportions are a way to compare ratios. Solving proportions uses our knowledge of multiplication and division. They are useful in many applications, as we will see in the next section.

Read this section up to "Solve Applications using Proportions". Be sure to review how to solve for an unknown value in a proportion. Do examples 6.40–6.44 and check your answers.

Watch this video for more examples.

### 5.4: Applications of Proportions

Proportions are used in many everyday applications. You probably use proportions without even realizing it! For example, you may know the sodium content of a frozen meal by what it says on the packaging. But, if you eat two portions instead of one, how much sodium are you consuming? We can find this answer by using a proportion.

Read this section, starting at "Solve Applications using Proportions". This section gives many real-world examples of how proportions are used. Do examples 6.45–6.47 and check your answers.

Watch this video for more examples.

Try this assignment for more word problems about proportions. You can check your answers at the end of the document.