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## 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 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?
oil changes

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

## Want to join the conversation?

• Who else finds math confusing? TwT
(142 votes)
• I see it as a little confusing but once you figure it out then its really straight forward from there.
(7 votes)
• 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?
(52 votes)
• 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
(8 votes)
• like if you hate math
(28 votes)
• I guess ur getting a like fro me :|
(1 vote)
• how can i find rates easier
(17 votes)
• maybe work on dividing skills? i think. it seems like finding rates is similar to division in a sense
(0 votes)
• Help pls I don’t understand rates but ratios I do
(12 votes)
• 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
(1 vote)
• here's a quick tip
Divide
Multiply
and Subtract
Bring it on down then bring it on back

that's all a Dividing method
(10 votes)
• Divide
Subtract
Multiply
Bring down
Repeat
(2 votes)
• how do ya'll like math. It is unbearably hard, and I'm basically failing in it.
(7 votes)
• So i'm kind of confused and I know this isn't a part of this thing but technically fractions are ratios so why do we use them as parts of things??
(6 votes)
• Ratios are not the same as fractions. Ratios compare two numbers. For example if a bus goes 10 miles every 2 hours, it could be expressed as 10 miles:2 hours. You could also say that the bus is going 5 miles every hour, 5 miles:1 hour. In this case you divided both sides by 2. This is one way fractions and ratios are similar. However they are not the same, because a fraction is simply some number divided by another number. A ratio is a relationship between two numbers.
(0 votes)
• how can you do rate problems
(6 votes)
• i need help i dont understand this rates
(5 votes)
• Rates just tell you that how one quantity relates to another quantity.For example- i read 20 pages in 5 minutes(if i am reading at a constant rate) and this can be represented as 20pages/5minutes which can be simlified to give 4pages/1minute.
(1 vote)