Rates and Unit Rates
Advanced Math Textbook Pages 404-408
Objectives
• I can write rates, equivalent rates, and unit
rates.
• I can use rate, equivalent rates, and unit rates
to compare quantities
Writing a rate!
• Rate: a comparison of two quantities that have
different units
• A rate is written just like one of the way we write
a ratio.
• The fraction bar, slash, and per mean “for every”
• It is written in fraction form.
• Quantity
Quantity
• I want everyone to find their pulse.
• When I say begin, count how many times your
heart beats, when I say stop record what you
found. (10 second)
• Can you write that in a ratio.
• What did you get (student answers)
• Since they both have different units you just
wrote a rate.
Rate
•
•
•
•
•
Chris drove 108 miles in two hours.
What are the quantities?
108 miles and two hours
Can we display this as a rate? Why?
108 miles
2 hours
Because they have two different units.
Try
• A communications satellite orbits the earth at
an average rate of 24 miles in 4 seconds.
Write a rate.
• 24 miles
4 seconds
You biked 68 miles in 4 days. Write rate.
68 miles
4 days
Unit Rates
• Unit Rate= is a rate in which the second quantity
(denominator) is one unit.
• Sadie pays $90 for 6 yoga classes. What is her cost per class?
• First write this as a rate:
• $90
6 classes
In order to find the unit rate divide both quantities by the same
number so the denominator is 1. In this case we should divide
by what?
Divide both by 6.
$90
6
$15
6 classes
6
1 class
Sadie spends $15 per class.
Unit Rates in other areas
• If you know the distanced traveled and the
travel time for a moving object, you can find
the “average speed” or “average rate”.
• Average rate = distance/time
• Isn’t this what you discovered in science.
• If I traveled 180 miles in 3 hours. Find my unit
rate.
• Is there another idea from science that would
involve unit rates.
• Density is the ratio of its mass to its volume.
Try one!
• The cost of 2 cartons of milk is $5.50. What is
the unit price(unit rate)?
• $5.50
2 cartons
Divide both quantities by 2.
$2.75 per carton
Try some more
• Write the rate in fraction form. The find the
unit rate.
• 20 words in 5 minutes
• 48 students 24 computers
• 160 miles in 4 hours
Using Unit Rates
• Lets look at a ruler.
• There are 2.54 centimeters in 1 inch. How many centimeters
in 3 inches?
• Write an equivalent rate to help you solve.
• 7.62 centimeters.
2.54 x 3
• 2.54 cm
1 inch
7.62 cm
3 inches
1x3
Comparing Unit Rates
• On average, a Ruby-throated Hummingbird beats its wings
about 300 times in 60 seconds. A Giant Hummingbird beats
its wings about 108 times in 15 seconds.
• Write the rate for the Ruby-throated hummingbird.
• 3000 beats/60 seconds
• Find the unit rate. (divide the rate)
• 50 beats/second
• Write the rate for the Giant Hummingbird.
• 180 beats/15 seconds
• Find the Unit Rate (divide the rate)
• 12 beats/second
• Which bird beats its wings faster?
• The ruby throated
Compare some more!
•
•
•
•
•
Tell which unit rate is better:
32 calories in 2 hours or 64 calories in 4 hours
Equivalent
8 pounds for $4 or 12 pounds for $3
8 pounds for $4
In conclusion
• Equivalent fractions, ratios and rates are all
found the same way by multiplying or
dividing.
• A rate compares two amounts that have
different units.
• A unit rate you must divide to find it.
Practice tonight
• Workbook pages 101-102