# 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.

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