Unit Rates and Ratios
Rates/ratios
• Can be written three different ways
a to b
a:b
a
b
• Because ratios are fractions, they must
always be reduced to simplest form
• A proportion is when two ratios (fractions)
are equivalent.
Example
1 2

3 6
The two ratios are proportional (equal)
Example
• On average, a baseball team scores 3
runs to every 7 hits. Write a ratio for the
situation
Example
• On average, a baseball team scores 3
runs to every 7 hits. Write a ratio for the
situation
3 to 7
3:7
3
7
Using the ratio
• If the number of hits and runs is
proportional, how many hits did the team
have if they scored 6 runs?
3 6

7
Finding a value in a proportion
Just like making an equivalent fraction.
What you do to the top you must do to the bottom
2 6

5
You
1

6 18
You
3 12

7
Example
• Tell whether the ratios are proportional
9
6

51 34
9  34  51 6
306  306
You Try
12 32

20 50
600  640
Using Cross Products to Find a Missing Value
2
5
= x
3
Using Cross Products to Find a Missing Value
6
x
=
8 12
Using Cross Products to Find a Missing Value
9
x
= 10
4
You
12
8
= x
10
You
6
8
= x
8
You
1.5 x
= 10
5
You
0.5 5
= x
4
How many students in here are
left handed?
• If our school has 1,000 students, how
many would we expect to be left handed
based off of our classroom data and
assuming the relationship is proportional?
Unit Rates
This is the value per unit.
You use these all the time:
At the grocery store
For cars
At your job
Speed
Unit Rates
• The denominator must be 1
• How much for 1?
• How long for 1?
Example
• What is the unit rate: $15 for a 5oz
package of cashews. (how much per oz)
$15
5oz
You
• A car can go 270 miles on 9 gallons of
gas. What is the unit rate?
You
• Jim can type 500 words in 10 minutes.
What is the unit rate?
You
• A plane can fly 480 miles per hour. What
is the rate in minutes?
Think Pair Share
• Value-Mart is advertising a Back-to-School
sale on pencils. A pack of 30 sells for
$7.97 whereas a 12-pack of the same
• brand cost for $ 4.77. Which is the better
buy? How do you know?
Pack of 30
Ratio:
Rate:
Unit Rate:
Unit of Measure:
Pack of 12
Pack of 30
Ratio:
Pack of 12
$7.97 for every 30 $4.77 for every 12
pencils
pencils
$15.94 for every
60 pencils
$23.85 for every
60 pencils
Rate:
7.97/30, or
approx. 0.27
dollars per pencil
4.77/12, or
approx. 0.40
dollars per pencil
Unit Rate:
0.27
0.40
Unit of Measure:
dollars per pencil
dollars per pencil
• How is finding an associated rate or unit
rate helpful when making comparisons
between quantities?
Video
Exit Ticket
• 1. At the conclusion of the video, your classmate takes
out his calculator and says, “Wow that was amazing!
That means the dog went about 5 meters in 1 second!”
Is your classmate correct and how do you know?
• 2. After seeing this video, another dog owner trained his
dog, Lightning, to try to break Tillman’s skateboarding
record.
• Lightning’s fastest recorded time was on a 75-meter
stretch where it took him 15.5 seconds. Based on this
data, did Lightning break Tillman’s record for fastest
dog? Explain how you know.