Rate

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Rate

• Zigila 2005 Comparing Scaling

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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

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Rate

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

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Unit 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

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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).
• What is your answer?

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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).
• What is your answer?

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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?
• Set up your proportion
• 55 495
• 1 t
• Cross multiply 55t 495
• Divide both sides by 55 to find t
• t ?

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Rates

• 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 ?

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Rates
What does h ? a.) He will work .6 of an
hour b.) He will work 240 hours c.) He will
work 15 hours
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Rates
Check the set up of your proportion. Remember it
is 60 per 3 so it should look like 60 x 3 12

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Rates
b.) He will work 240 hours. You are correct!
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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?

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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?

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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

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Rate of speed
a.) 405 mph Make sure that you are dividing and
not multiplying.
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Rate of speed
b.) 54 mph Look at your answer more carefully!
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Rate of speed
c.) 45 mph You are correct!
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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?

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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

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Population density

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

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Population density

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

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Rate of speed
Notice that the 55 and 495 are on top.
55 495 1 t Also notice that the speed was
55 miles per hour that is why in the proportion
you see 55 over 1.
Miles hours
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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/S1U2L
  3/S1U2L3Pract.html

Where did I get my information?
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Resources

• http//www.nationalgeographic.com/xpeditions/lesso
  ns/01/g912/density.html
• http//www.eduplace.com/math/mathsteps/6/e/
• http//www.math.com/school/subject1/lessons/S1U2L3
  GL.html
• http//www.math.com/school/subject1/lessons/S1U2L3
  EX.html
• http//www.eduplace.com/math/mathsteps/6/e/6.rates
  .ideas.html