Review the basics of rates and try some practice problems.

What is a rate?

A rate is a ratio that compares two quantities with different units of measure.
Example of a rate:
A plane flew 765765 miles in 55 hours.

Unit rates

A unit rate is a comparison of two measurements where one of the terms (usually, the second term) is 1\goldD1.
Examples of a unit rates:
There are 6060 minutes in 1\goldD1 hour.
Jen types 4242 words in 1\goldD1 minute.
Want to learn more about rates? Check out this video.

Finding unit rates

To find a unit rate, we divide the first quantity in a rate by the second.
A plane flew 765765 miles in 55 hours.
The plane flew at a rate of 153153 miles per hour. We can also write the unit rate as 153 miles:1 hour153\text{ miles}:\goldD1\text{ hour}.
Want to learn more about solving unit rates? Check out this video.

Using unit rates to solve rate problems

Let's look at an example.
Mark can make 42\blueD{42} birthday cakes in 7\redC7 days.
How many birthday cakes can Mark make in 5\purpleD5 days?
First, we find the unit rate.
Mark makes cakes at a unit rate of 66 cakes for every 11 day.
Now, we can use the unit rate to find how many cakes Mark makes in 5\purpleD5 days.
In 5\purpleD{5} days, Mark can make 30\greenD{30} cakes.


Problem 1
Frances can complete 9191 oil changes in 77 days.
How many oil changes can Frances complete in 1111 days?
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
oil changes

Want to try more problems like this? Check out this exercise.