Understanding and Writing Rates

Video Lessons > Understanding and Writing Rates

Introduction and Video

Previously, we learned that ratios represent the relationship between quantities. In this lesson, we're going to learn about a special type of ratio called rates. We'll discuss the definition of rate, look at some examples, and learn how to write rates properly.

Before beginning this lesson, you should be familiar with writing ratios.

Lesson Notes

Let's look at the details of the lesson including the definition of rate, examples, and how to write rates.

What is a Rate?

Rate is a type of total-to-total ratio. It describes how one value changes as another value changes. And the two values will be represented with different units of measurement.

As we go through different problems and write rates to represent them, we will need to pay attention to the units. We may see units that represent how much time has passed or how far a car has traveled or even how much money something costs.

Examples of Rates

Imagine that you are riding along in a car and want to keep track of how far you've traveled as time passes. Let's say that you record the following:

• After 1 hour of driving, the car has traveled 60 miles.
• After 2 hours of driving, the car has traveled 120 miles.
• And after 3 hours of driving, the car has traveled 180 miles.

In this example, we have two different values that we're comparing, time and distance. Notice that as time changes, the distance also changes, showing the relationship between time and distance. We can use rates to represent this relationship.

Writing Rates

Here are a few things to keep in mind for writing rates:

• Using Words: We can represent rates with words such as “per,” “for,” or “in.” For example, the car traveled 60 miles in 1 hour, 120 miles in 2 hours, or 180 miles in 3 hours.
• Using Fractions: Just like we could represent ratios as fractions, we can also represent rates as fractions. We could write the rates in our example as 60 miles/1 hour, 120 miles/2 hours, and 180 miles/3 hours.

• Order in Writing Rates: When setting up rates, it's important to consider the order based on the type of measurement. When we have a rate that involves a measurement of time, we place time as the second value or denominator. When writing rates involving money, we place the money value as the first value or numerator.

Summary and Practice

By understanding rates and their representations, you can effectively analyze and compare different types of quantities. Remember that when working with rates, pay extra careful attention to the units involved and how you're placing measurements of time and money.

Try this practice activity to see what you learned. Complete the ratios by dragging each number to its place. Numbers can be used more than once.

Related Standard: Common Core 6.RP.A.1