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### Course: 6th grade (Illustrative Mathematics)>Unit 3

Lesson 4: Lesson 9: Solving rate problems

# 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 $1$ unit of the second quantity.
Examples of unit rates:
There are $60$ minutes in $1$ hour.
Jen types $42$ words in $1$ 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.
$765÷3=255$
The plane flew at a rate of $255$ kilometers per hour. We can also write the unit rate as .

## Using unit rates to solve rate problems

Let's look at an example.
Mark can make $42$ birthday cakes in $7$ days.
How many birthday cakes can Mark make in $5$ days?
First, we find the unit rate.
DaysCakes
$7$$42$
$↓÷7$$↓÷7$
$1$$6$
Mark makes cakes at a unit rate of $6$ cakes for every $1$ day.
Now, we can use the unit rate to find how many cakes Mark makes in $5$ days.
DaysCakes
$7$$42$
$1$$6$
$↓×5$$↓×5$
$5$$30$
In $5$ days, Mark can make $30$ cakes.

## Practice

Problem 1
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.

## Want to join the conversation?

• Who else finds math confusing? TwT
• I see it as a little confusing but once you figure it out then its really straight forward from there.
• If I have 5 goldfish, and my grandma eats one, then I go fishing and somehow find 10 in a river, then my sister takes 2 of them and practices animal CPR on them, I go back to the pet store and buy 53 more, then buy 89 more. How much do i spend if each goldfish is 67 cents?
• I think the cost is 257.18 dollars from getting all the goldfish and multiplying it by 1.67 I do not know if this is correct though
• like if you hate math
• Looks like u got a like from meh :>
• What are ratios?
• A ratio is comparing two unlike things. They are a different form of fractions.
• how can i find rates easier
• maybe work on dividing skills? i think. it seems like finding rates is similar to division in a sense
• Help pls I don’t understand rates but ratios I do
• Are you confused about the unit rate section? If so then the unit rate is when you try to find out how much it would be for only one item. This is credited to my teacher since I completely forgot lol
• here's a quick tip
Divide
Multiply
and Subtract
Bring it on down then bring it on back

that's all a Dividing method
• Divide
Subtract
Multiply
Bring down
Repeat