5-2 Ratios, Rates, and Unit Rates
Unit Rate Notes
Thurs/Fri 1/30,31
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Course 3
5-2 Ratios, Rates, and Unit Rates
Vocabulary
rate
unit rate
unit price
Course 3
5-2 Ratios, Rates, and Unit Rates
A rate is a comparison of two quantities
that have different units. It is usually
written as a fraction.
Ratio: 90
3
, 90 : 3 , 90 to 3
Rate: 90 miles
3 hours
Course 3
Read as
“90 miles per 3 hours.”
5-2 Ratios, Rates, and Unit Rates
Unit rates are rates in which the second
quantity is 1. It always needs to be 1 in
the denominator.
The ratio 90 can be simplified by dividing:
3
90 = 30
3
1
unit rate: 30 miles, or 30 mi/h
1 hour
Course 3
5-2 Ratios, Rates, and Unit Rates
Additional Example 1: Finding Unit Rates
1
1
3
1
Jeff hikes 2 mile every 15 minutes, or 4 hour. Lisa hikes
1
mile every 10 minutes, or 6 hour. How far do they each
hike in 1 hour? 2 hours?
Use the bar diagram to help you
determine how many miles Jeff
hikes . How many hours are in
1 hour.
1
4
hour
Distance (mi)
Time (h)
Use the bar diagram to help
you determine how many
miles Jeff hikes . How many
hours are in 1 hour.
1
6
hour
Distance (mi)
Time (h)
Course 3
1
6
1
3
1
2 mile
1
4
2
3 mile
1
3
1
4
hour
1
hour
mile
1
6
1
4
1
6
1
12
mile
1
2
hour
1
1
6
mile
1
2
hour
mile
3
4
hour
1
4
hour
2 miles 4 mile
1
2
1
6
1
6
hour
2 miles 4 mile
1
2
hour
5-2 Ratios, Rates, and Unit Rates
Additional Example 1: Finding Unit Rates
Fred can type 30 words in half a minute. How
many words can he type in 1 minute?
30
1
2
30 ÷
30 ·
1
2
2
1
=
words
min.
60
Write a rate by
making a fraction.
Make a division
problem then solve.
How many words can Fred type in a minute?
Fred can type 60 words a minute
Course 3
5-2 Ratios, Rates, and Unit Rates
Example 2
Penelope can type 90 words in 2 minutes. How
many words can she type in 1 minute?
words
min.
90
2
90 = 45
2
Write a rate by
making a fraction.
Reduce your rate you
made.
How many words can Penelope type in one minute?
Penelope can type 45 words a minute.
Course 3
5-2 Ratios, Rates, and Unit Rates
Unit price is a unit rate used to compare
price per item. When writing as a fraction
the price is always written in the
numerator and the item in the
denominator .
money
item
Course 3
5-2 Ratios, Rates, and Unit Rates
Example 3
Pens can be purchased in a 5-pack for $1.95
or a 15-pack for $6.20. Which is the better
buy?
Money
Items
$1.95 =
5 pens
.39¢
1 pen
Money
Items
$6.20 =
15 pens
.41¢
1 pen
Find the unit price of
the 5-pack by making a
fraction and solving.
Find the unit price of
the 15-pack by making
a fraction and solving.
Which pack of pens is the better buy?
The better buy is 5 pens for $1.95
Course 3