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Rate review

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 765 kilometers in 3 hours.

Unit rates

A unit rate of two quantities in a ratio is the number of units of the first quantity for every start color #e07d10, 1, end color #e07d10 unit of the second quantity.
Examples of a unit rates:
There are 60 minutes in start color #e07d10, 1, end color #e07d10 hour.
Jen types 42 words in start color #e07d10, 1, end color #e07d10 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.
Example:
A plane flew 765 kilometers in 3 hours.
765, divided by, 3, equals, 255
The plane flew at a rate of 255 kilometers per hour. We can also write the unit rate as 255, start text, space, k, m, end text, colon, start color #e07d10, 1, end color #e07d10, start text, space, h, o, u, r, end text.
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 start color #0c7f99, 42, end color #0c7f99 birthday cakes in start color #bc2612, 7, end color #bc2612 days.
How many birthday cakes can Mark make in start color #543b78, 5, end color #543b78 days?
First, we find the unit rate.
DaysCakes
start color #bc2612, 7, end color #bc2612start color #9e034e, 42, end color #9e034e
\downarrow, divided by, 7\downarrow, divided by, 7
16
Mark makes cakes at a unit rate of 6 cakes for every 1 day.
Now, we can use the unit rate to find how many cakes Mark makes in start color #543b78, 5, end color #543b78 days.
DaysCakes
start color #bc2612, 7, end color #bc2612start color #9e034e, 42, end color #9e034e
16
\downarrow, times, 5\downarrow, times, 5
start color #543b78, 5, end color #543b78start color #a75a05, 30, end color #a75a05
In start color #543b78, 5, end color #543b78 days, Mark can make start color #a75a05, 30, end color #a75a05 cakes.

Practice

Problem 1
Frances can complete 91 oil changes in 7 days.
How many oil changes can Frances complete in 11 days?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
oil changes

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

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