USING UNITS TO YOUR ADVANTAGE

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USING UNITS TO YOUR ADVANTAGE

• Approaches to Problem Solving

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Cant Add Apples and Oranges

• How many apples do you get when you add 6 apples
  with 7 oranges?
• 6 apples
• The units of a quantity describe what is being
  measured or counted. We can only add like
  quantities (same units).
• You cant add apples and oranges, but you can
  multiply them!!!
• ft. x ft. ft2 kg-m/sec2 kilowatt -hours

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Key words or symbols
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Review of Fractions

• Fractions can be expressed in three ways
• Common fraction - a/b, 1/2
• Decimal form - 0.5
• Percentage - 50
• Adding and subtracting fractions
• MUST HAVE A COMMON DENOMINATOR (otherwise you are
  adding apples and oranges)
• Multiplying Fractions
• Multiply the numerators and the denominators
• Dividing Fractions
• Multiply numerator by the reciprocal of the
  denominator
• What does it mean to divide by a fraction?

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Unit Conversion

• The basic trick of unit conversion is to devise
  an appropriate way of multiplying by 1.

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Conversion Factors

• Convert 7 ft. into inches
• Convert 102 inches to yds.
• How many minutes are there in a week?

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Units raised to powers

• You want to carpet a room that measures 12 ft. by
  15 ft. The carpet is sold in square yards. How
  many square yards of carpet do you need?
• HINTS
• What does a square yard look like?
• How many square feet are in a square yard?
• You want to add a 10 ft. by 20 ft. concrete patio
  to the back of your house. You have read that
  the concrete should be 4 inches thick. How many
  cubic yards of concrete will you need to make
  your patio?
• HINTS
• What does a cubic yard look like?
• How many feet does 4 represent?
• How can you visualize the two dimensional slab
  from the cube of concrete?
• How many cubic feet are in a cubic yard?

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Currency Conversions

• 1 Euro 1.3702 U.S. dollars
• 1 British pound 2.0224 U.S. dollars
• 1 U.S. dollar 11.075669 Mexican pesos
• 1 U.S. dollar 1.05230038 Canadian dollars
• Traveling to Europe, you bring 2000 with you.
  How much money is this in Euros? In British
  Pounds?
• Determine what the conversion is from Euros to
  British Pounds.
• 1 British pound 1.47598891 Euros

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Using Units in problem solving

• Step 1 - Identify the units involved in the
  problem.
• Step 2 - Perform any operations (such as
  multiplication or division) on both the numbers
  and their associated units.
• HINTS
• You cant add or subtract quantities with
  different units (cant add apples and
  oranges!!!), but you can combine units through
  multiplication, division, or raising to powers.
• Step 3 - When you complete your calculations,
  make sure that your answer has the units that you
  expected. If not, you did something wrong.

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Standardized Units

• History
• Based on measurements of body parts!
• Foot was the length of a foot
• Thumb width is about an inch
• Mile was about 1000 paces
• Weird facts
• oz. is used for weight and liquid measure
• Liquid measures are different than dry measures
  (a liquid pint is different than a dry pint!)

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The Metric System

• Basic units of length are
• Meter for length, abbreviated m
• Kilogram for mass, abbreviated kg
• Seconds for time, abbreviated s
• Liter for volume, abbreviated L

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Review of Powers of 10

• What does the power of 10 mean?
• Positive exponent gt places to the right
• Negative exponent gt places to the left
• Adding and Subtracting powers of 10
• Cant add apples and oranges!!!
• Multiplying and Dividing powers of 10
• Raising to powers

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Units of Energy and Power

• Energy is measured in Joules
• Power is the rate at which energy is used -
• A kilowatt-hour is a unit of energy
• 1 kilowatt-hour 3.6 million joules

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Units of Density and Concentration

• Density describes compactness or crowding.
• Material density population density
• Example people / sq. mile
• Blood alcohol content describes the concentration
  of alcohol in a persons body.
• Measured in grams of alcohol / 100 ml of blood

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Example

• An average sized man has about 5 liters (5000 ml)
  of blood, and an average 12 oz can of beer
  contains about 15 grams of alcohol. If all of
  the alcohol was immediately absorbed into the
  bloodstream, what is his blood alcohol content
  (BAC) would we find after an average sized man
  quickly drinks a can of beer?

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Hints and Guidelines for problem solving

• There may be more one answer
• There may be more than one strategy
• Use appropriate tools
• Consider simpler, similar problems
• Consider Equivalent Problems with Simpler
  Solutions
• Approximations can be useful
• Try alternate patterns of thought

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Estimating

• How big are the following
• 4 inches 10 centimeters
• 1 yard 1 meter
• 1 quart 1Liter
• What is the width of a human hair?
• How many miles/hour are you going if the
  speedometer reads 240 km/hour?
• How hot is it if the thermometer reads 45 C?
• How cold is it if the thermometer reads -40 C?