Unit 5: 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.
5.1: Introduction to Ratios
Before we can begin to solve problems with ratios, we need to understand what ratios are.
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.
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.
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.