Calculating Unit Rates and Unit Prices

Video Lessons > Calculating Unit Rates and Unit Prices

Introduction and Video

In this video lesson, we will learn strategies for calculating unit rates and unit prices. We'll define what they are and look at examples of how to calculate unit rates and unit prices.

Before beginning this lesson, it's important to understand rates and how to write them.

Lesson Notes for Unit Rates and Unit Prices

Let's look at the details of the video lesson, including definitions and examples of calculating unit rates and prices.

Definition of Unit Rate

A unit rate is a specific type of rate where the second value, also known as the denominator when expressed as a fraction, is the number one. This concept has many practical applications. For instance, the expression "60 miles per 1 hour" or, in fraction form, "60 miles/1 hour" exemplifies a unit rate. With unit rates, it's common to omit the 1 in the second value. So instead of saying "60 miles per 1 hour," we can simply say "60 miles per hour."

Example of Calculating Unit Rate

Ian can type 170 words in five minutes and we want to find his typing speed as a unit rate.

• To find his typing speed as a unit rate (words per minute), we start with the given information: 170 words in five minutes.
• This ratio can be represented as a fraction: 170 words/5 minutes. Since one of the values represents time, it's placed in the denominator. However, this is not yet a unit rate due to the denominator being five instead of one.
• To convert it to a unit rate, we divide the numerator by the denominator (170 divided by 5), resulting in 34. Therefore, Ian can type 34 words per minute, which can also be written as "34 words/minute."

Definition of Unit Price

Unit price is a particular kind of unit rate where the numerator is a measure of money. Similar to unit rates, the second value or denominator is one. For instance, if a box of cookies costs $3, the unit price can be expressed as "$3 per one box," "$3 over one box" in fraction form, or using the front slash symbol "$3/box."

Example of Calculating Unit Price

Shayla bought three boxes of cookies for $12.75 and we want to find the unit price per box of cookies.

• We start with the information given: $12.75 for three boxes, which can be represented as "$12.75 over three boxes" in fraction form.
• Since the second value is not one, we need to modify the fraction. The most straightforward way to accomplish this is to divide the numerator by the denominator.
• By dividing the numerator by the denominator ($12.75 divided by 3), we find the unit price to be $4.25 per box, which can also be represented as $4.25/box.

Summary and Practice

In this video lesson, we learned the definitions of unit rate and unit prices and how to calculate them. Remember, when finding a unit rate or unit price, it's important to first set up the problem based on the provided information, ideally in fraction form. If one of the values involves money, it's placed as the numerator. If there is a unit of time, that value is placed in the denominator. Division is then used to determine the unit rate or unit price. And finally, be sure to include the units in your final answer.

Try this practice activity to see what you learned. 

Related Standard: Common Core 6.RP.A.2