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Zigila 2005 – Comparing & Scaling

- Ratio that compares two different kinds of numbers
- Unit rate = compares a quantity to its unit of measure
- The word “per” is a clue that you are dealing with a rate.
- The word “per” means to divide

- Important type of ratio used in many real-world scenarios
- Grocery shopping, traveling, medicine, etc.
- Rates of speed
- Heartbeats per minute = heart rate

Unit price is the price for one item

Miles per hour

Miles per gallon

Calories per serving

Dollars per hour

People per square mile

Land per person

Cost/item

Miles/hour

Miles/gallon

Calories/serving size

Dollars/time (hours)

Population/area

Area/population

- To find the unit rate: simply divide the multiple-unit rate by the number of units
- For example: When the 7th grade goes on their perk trip there are 165 students and 3 busses, how many students per bus?
- Divide your multiple-unit rate (165 students) by the number of units (3 busses).
- What is your answer?

- Find the unit price
- If potatoes cost $5.50 for 5 pounds, what does it cost for 1 pound?
- Divide your multiple-unit rate ($5.50) by the number of units (5 lbs).
- What is your answer?

- Rates can be seen in proportions to solve unknown quantities.
- During spring break, the Harlands traveled 495 miles at 55 mph on their motorcycle. How long did the trip take?
- Set up your proportion:
55=495

1t

- Cross multiply: 55t = 495
- Divide both sides by 55 to find t
- t = ?

- Mike works 60 hours per 3 weeks. At that rate, how many hours will he work in 12 weeks?
- Set up your proportion
- Cross multiply
- Divide both sides by 3 to find h.
- h = ?

What does h =?

a.) He will work .6 of an hour

b.) He will work 240 hours

c.) He will work 15 hours

Check the set up of your proportion. Remember it is 60 per 3 so it should look like:

60=x

312

b.) He will work 240 hours.

You are correct!

- If you rode your bike for 2 hours and traveled 24 miles, what is your rate of speed?
- You drove 135 miles for 3 hours, what was your rate of speed?

- Divide your multiple-unit rate (24 miles) by the number of units (2 hours) and that will give you miles per hour.
- What is your rate of speed?

- Divide your multiple-unit rate by the number of units and that gives you miles per hour.
- What is your rate of speed?
a.) 405 mph

b.) 54 mph

c.) 45 mph

a.) 405 mph

Make sure that you are dividing and not multiplying.

b.) 54 mph

Look at your answer more carefully!

c.) 45 mph

You are correct!

- Write a ratio for each and find the unit rate.
1.) 142 heartbeats per 2 minutes

2.) $3.30 for 10 stamps

3.) 1.5 pound for $3.49

4.) One animal can run 60 feet in 4 seconds, while another animal can run 100 feet in 8 seconds. Which animal runs the fastest?

- A term that describes the number of people in an area in relation to the size of that area.
- Divide the number of people by the area they occupy.
- Population density = population/land area

- As of 2000, Michigan’s population was 9,295,297 and its area in square miles is 56,809.2
- What is Michigan’s population density (population per square mile)?

- As of 2000, Crawford County’s population was 12,260 and its area is 558.2 square miles.
- What is the population density for Crawford County? (population per square mile)

Notice that the 55 and 495 are on top.

55=495

1t

Also notice that the speed was 55 miles per hour – that is why in the proportion you see 55 over 1.

Miles

hours

- Go to the website below and do the practice problems. You need to get 10 correct – inform a teacher when you have done so!
- Good luck!
- http://www.math.com/school/subject1/practice/S1U2L3/S1U2L3Pract.html

Where did I get my information?

- http://www.nationalgeographic.com/xpeditions/lessons/01/g912/density.html
- http://www.eduplace.com/math/mathsteps/6/e/
- http://www.math.com/school/subject1/lessons/S1U2L3GL.html
- http://www.math.com/school/subject1/lessons/S1U2L3EX.html
- http://www.eduplace.com/math/mathsteps/6/e/6.rates.ideas.html