Chapter 2 Approaches to Problem Solving Section 2A The Problem Solving Power of Units Pages 84-95

Units The units of a quantity describe what is being measured or counted. We can add or subtract numbers ONLY when they have the same units. We can always multiple or divide numbers – we’ll just create new units.

Units Do NOT disregard units. ALWAYS pay attention to units. Units are your FRIENDS!

For example: Travel 195 miles (distance) Trip took 3 hours (time) Average speed (distance/time) = 195 miles/3 hours = 65 mph (miles per hour)

For example: One side of the floor is 25 feet long The other side is 30 feet long. The area of the floor space = 25 ft × 30 ft = 750 ft2 (square feet) The room’s height is 12 feet. The volume of the room is 25ft × 30ft × 12ft = 9000 ft3 = 9000 cubic feet

1 inch 1 inch 1 cubic inch 1 square inch 1 inch 1 inch

Read kilowatts  hours as “kilowatt-hours.” hyphen Multiplication Read ft  ft  ft or ft3, as “cubic feet” or “feet cubed” cube or cubic Raising to a third power Read ft  ft, or ft2, as “square feet” or “feet squared” square Raising to a second power Read miles  hours as “miles per hour” per Division Example Key word or symbol Operation

Practice – what units? 29/96 The price of apple juice , found by dividing its total cost in dollars by its volume in ounces. dollars per ounce = $/oz 1b/85 The area of a circle, found with the formula where r is the radius of the circle measured in centimeters. - square centimeters = cm2 35/97 The gas mileage of a car, found by dividing the distance in miles that it travels by the amount of gas in gallons that it uses. -miles per gallon = m/gal = mpg pg85 The energy used by a light bulb found by multiplying the power rating in kilowatts by the number of hours it is turned on. - kilowatt X hours = kilowatt-hours

Unit Conversions converting one set of units to another Trick = multiply by “1”. 12 inches = 1 foot 1 week = 7 days

Unit Conversions 43/97 Convert 2 weeks to units of minutes. 2-A Unit Conversions 43/97 Convert 2 weeks to units of minutes. 44*/97 A car is driving at 100 kilometers per hour. What is its speed in kilometers per second? 53/98 A box-shaped water tank measures 12 feet by 8 feet by 4 feet. Find its volume in cubic yards. (Careful with square and cubic units!)

(Careful with square and cubic units!) 1 square yard = 9 square feet 1 square foot = 144 square inches WHY??? 1 cubic yard = 27 cubic feet 1 cubic foot = 1728 cubic inches WHY???

Currency Conversions (September 2008): (www.xe.com) 2-A Currency Conversions (September 2008): (www.xe.com) Currency dollars per foreign foreign per dollar British pound 1.7834 0.5607 Canadian dollar 0.9360 1.0684 European euro 1.4518 0.6888 Japanese yen 0.0092 108.7510 Mexican peso 0.09653 10.3593

2-A Currency Conversions 57/98 Which is worth more today – 1 Mexican peso or 1 US dollar? Explain. 61/98 How many US dollars can you buy with 12,000 Japanese yen?

Problem Solving with Units 2-A 65/98 A car travels 13 miles in 15 minutes. How fast is it going in miles per hour? 69/98 You are buying 4.7 pounds of apples priced at $1.29 per pound. How much do you pay? 77/98 If you sleep an average of 7 hours each night, how many hours do you sleep in a year?

Problem Solving with Units 2-A Problem Solving with Units 83/98 Suppose you drive a car with an average gas mileage of 28 miles per gallon. If you plan to take a 2500-mile cross country trip, how many gallons of gasoline should you expect to use.

Show all steps in your solutions Homework Pages 97-99: #1-93 TURN IN: 38,44,52,56,60,66,70,76,78,84 Show all steps in your solutions