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### Rates and Unit Rates

Regular Math Textbook Pages 407-411

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 (unit)

Quantity(different unit)

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 $60 for 6 yoga classes. What is her cost per class?
- First write this as a rate:
- $60

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.

$606 $10

6 classes 6 1 class

Sadie spends $10 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 150 miles in 3 hours. Find my unit rate.

Try one!

- The cost of 2 cartons of milk is $6.00. What is the unit price(unit rate)?
- $6.00

2 cartons

Divide both quantities by 2.

$3.00per carton

Try some more

- Write the rate in fraction form. The find the unit rate.
- 20 words in 5 minutes
- 24students 12computers
- 160 miles in 2 hours

Comparing Unit Rates

- On average, a Ruby-throated Hummingbird beats its wings about 3000 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 103-104

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