Equivalent Ratios
&
Unit Rates
Vocabulary (
you should already have this written in your
notes – you do not have to copy again!)
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A ratio is the comparison of two numbers written as a
fraction.(division)
A rate is a ratio that compares two quantities measured in
different units.
The unit rate is the rate for one unit of a given quantity. Unit
rates have a denominator of 1.
In a ratio, if the numerator and denominator are measured in
different units then the ratio is called a rate.
Example:
Your school’s basketball team has won 7 games and lost 3 games.
What is the ratio of wins to losses?
Because we are comparing wins to losses the first number in our ratio
should be the number of wins and the second number is the number of
losses.
The ratio is
___________
games won
games lost
=
_______
7 games
3 games
=
__
7
3
Example:
You can travel 120 miles on 6 gallons of gas. What is your fuel
efficiency in miles per gallon?
Rate =
________
120
miles
6 gallons
=
________
20 miles
1 gallon
Your fuel efficiency is 20 miles per gallon.
Examples
Rate:
150 heartbeats
2 minutes
Unit Rate (Divide to get it):
150 ÷ 2 = 75 heartbeats per minute.
Find the Unit Rate
Amy can read 88 pages in 4 hours. What is the
unit rate? (How many pages can she read per
hour?)
88 pages
4 hours
? Pages
1 hour
Writing the units when comparing each unit of a rate is called unit analysis.
You can multiply and divide units just like you would multiply and divide
numbers. When solving problems involving rates, you can use unit
analysis to determine the correct units for the answer.
Example: How many minutes are in 5 hours?
5 hours • 60________
minutes
1 hour
= 300 minutes
To solve this problem we need a unit rate that relates minutes to hours. Because
there are 60 minutes in an hour, the unit rate we choose is 60 minutes per hour.
Example
Joe’s car goes 25 miles per gallon of
gasoline. How far can it go on 8 gallons of
gasoline?
x8
Unit Rate
25 miles
1 gallon
=
8 gallons
x8
25 x 8 = 200. Joe’s car can go 200
miles on 8 gallons of gas.
If the average person lives for 75 years, how long
would that be in seconds?
** I will check your answer tomorrow. Please show
your work and attempt to answer.