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 hoursBecause 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 secondsYou biked 68 miles in 4 days. Write rate.68 miles4 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 $156 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 7.62 cm 1 inch 3 inches

1 x 3

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