# Rate - PowerPoint PPT Presentation

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Rate. Zigila 2005 – Comparing & Scaling. Rate. 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. Rate.

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Rate

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## Rate

Zigila 2005 – Comparing & Scaling

### Rate

• 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

### Rate

• 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

### Unit Rate

• 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).

### Unit Rate

• 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).

### Rates

• 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?

55=495

1t

• Cross multiply: 55t = 495

• Divide both sides by 55 to find t

• t = ?

### Rates

• Mike works 60 hours per 3 weeks. At that rate, how many hours will he work in 12 weeks?

• Cross multiply

• Divide both sides by 3 to find h.

• h = ?

### Rates

What does h =?

a.) He will work .6 of an hour

b.) He will work 240 hours

c.) He will work 15 hours

### Rates

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

60=x

312

### Rates

b.) He will work 240 hours.

You are correct!

### Rate of speed

• 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?

### 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?

### 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

### Rate of speed

a.) 405 mph

Make sure that you are dividing and not multiplying.

b.) 54 mph

c.) 45 mph

You are correct!

### Rate practice

• 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?

### Population density

• 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

### Population density

• 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)?

### Population density

• 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)

### Rate of speed

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

### Rate practice

• 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?

### Resources

• 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