Copyright

How to Calculate Unit Rates & Unit Prices

Instructor: Thomas Higginbotham

Tom has taught math / science at secondary & post-secondary, and a K-12 school administrator. He has a B.S. in Biology and a PhD in Curriculum & Instruction.

One of the most common uses of math is to find out whether something is a 'good deal.' Unit prices, a special kind of unit rate, allow us to determine the best deals. In this lesson, learn how to calculate unit rates, including unit prices.

Comparing Things

Some people are all about comparing. My favorite team has won seven championships in 26 seasons, while my buddy's favorite team has won three titles in 13 years. Which is better? I could pay $1.39 for a 5-ounce bag of gummy bears at one store, or $8.99 for a 32-ounce bag at a different store. Which is a better deal?

To help us make comparisons that make sense in the real world, a special type of ratio is helpful: the unit rate. We will learn all about unit rates, but first we'll do a quick review of ratios.

Ratios

Ratios are simply a comparison between two numbers. Those numbers can be just numbers for numbers' sake (e.g., 8/4), they can be two of the same unit (e.g., 6 feet / 4 feet), or they can be different units (e.g., price / ounce). Ratios can be expressed as fractions. When we divide the numerator by the denominator for a ratio of different units, the result is a special kind of ratio called a unit rate.

What Is a Unit Rate?

A unit rate is a ratio between two different units with a denominator of one. When we divide a fraction's numerator by its denominator, the result is a value in decimal form. Examples include 8 / 4 = 2 and 3 / 6 = 0.5. When we write numbers in decimal form, they could always be written as a ratio with one as the denominator. 2 could be written as 2 / 1, and 0.5 could be written as 0.5 / 1. However, that would just be clumsy and in the way, so we usually drop the one. However, it is important to know that it is there, especially with unit rates.

For the above ratios, if we were talking about 8 miles / 4 hours, dividing the two would give us 2 miles / hour. Notice again that we did not write or include the one, but that we did include the unit 'hour.' Miles / hour is familiar, as are unit rates such as revolutions / minute, salary / year, and interest / amount invested. Conversationally, the word 'per' indicates we are using a unit rate.

How Unit Rates Are Calculated

Holy easy, Batman! To get the unit rate, simply divide the two numbers and the result will be your unit rate, for whatever units you are using. It will tell you how many of the units on top you would expect for every one of the units on bottom. Let's go back to our example from the beginning about the sports teams:

My team: 7 champs / 26 seasons = 0.27 champs per season (cps).

My buddy's team: 3 champs / 13 seasons = 0.23 champs / season.

The championship rate for my team (0.27 cps) is greater than the championship rate for my buddy's team (0.23 cps), so I could argue that my team is better.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account
Support