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Lesson 1: Intro to rates

# 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.

## 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.

## 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
• Current
Frances can complete 91 oil changes in 7 days.
How many oil changes can Frances complete in 11 days?
oil changes

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