Math Textbook Pages 404408 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 ID: 735768
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Slide1
Rates and Unit Rates
Advanced
Math Textbook Pages
404-408Slide2
Objectives
I can write rates, equivalent rates, and unit rates.
I can use rate, equivalent rates, and unit rates to compare quantitiesSlide3
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
QuantitySlide4
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
.Slide5
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.Slide6
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 daysSlide7
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.Slide8
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.Slide9
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 cartonSlide10
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 hoursSlide11
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
7.62 cm
1 inch 3 inches
1 x 3 Slide12
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 throatedSlide13
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 $4Slide14
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.Slide15
Practice tonight
Workbook pages
101-102