A unit rate is a way of demonstrating a process per unit (usually time). For example, if it takes one man 3.5 hours to shovel 7 driveways, we can use the unit rate to calculate how many driveways he shovels per hour.
Unit rates make it easy for us to compare two different processes that may use different quantities. For example, if one car travels 300 miles in 5 hours, and one car travels 130 miles in 2 hours, which car is going faster?
To compare unit rate, you need to calculate the process per unit. In the example in the introduction, we have two cars. The first travels 300 miles in 5 hours. The second car travels 130 miles in 2 hours. To compare which one has traveled faster, we can calculate the unit rate.
The first thing we need to do is divide the distance by the number of hours traveled. This will give us the speed per hour (a unit rate).
For the first car, we divide the distance by the number of hours to get:
Therefore, the first car traveled at 60 miles per hour (mph).
Now, let's repeat those steps with the second car. That traveled 130 miles in 2 hours, so we do:
The second car, therefore, traveled at 65 miles per hour and was therefore faster.
To find the unit rate for any process, work out the most sensible units to use (miles per hour, work per day, etc.) and then use the unit rate to divide the quantity by the number of units.