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

2. 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.

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

4. 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 ft 2 (square feet) The room’s height is 12 feet. The volume of the room is 25ft × 30ft × 12ft = 9000 ft 3 = 9000 cubic feet

5. Read kilowatts  hours as “kilowatt-hours.” hyphenMultiplication Read ft  ft  ft or ft 3, as “cubic feet” or “feet cubed” cube or cubicRaising to a third power Read ft  ft, or ft 2, as “square feet” or “feet squared” squareRaising to a second power Read miles  hours as “miles per hour” perDivision ExampleKey word or symbol Operation 2-A

6. Practice – what units? 19/96 The price of apples, found by dividing their total cost in dollars by their total weight in pounds. –dollars per pound = $/lb 1b/85 The area of a circle, found with the formula where r is the radius of the circle measured in centimeters. - square centimeters = cm 2 27/97 The density of a rock, found by dividing its weight in grams by its volume in cubic centimeters. -grams per cubic centimeters = g/c 3 = g/cc 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

7. Unit Conversions converting one set of units to another Trick = multiply by “1”. 2-A 12 inches = 1 foot 1 week = 7 days

8. Unit Conversions 30/97 Convert a distance of 18 yards into inches. 2-A 38/97 A car is driving at 100 kilometers per hour. What is its speed in kilometers per second? 33/97 Convert a lot size of 1/5 acre to square feet.(1 acre = 43560 square feet) 44/97 A football field is 100 yards long and 60 yards wide. Find its area in square yards and square feet. (Careful with square and cubic units!)

9. Currency Conversions (www.xe.com on 8/29/06):www.xe.com 2-A Currencydollars per foreignforeign per Dollar British pound 1.891980.528548 Canadian dollar 0.8997861.11138 European euro 1.276050.783671 Japanese yen 0.00855457116.897 Mexican peso 0.091722610.9024

10. Currency Conversions 49/97 Which is worth more today – 1 British pound or 1 dollar? Explain. 2-A 51/97 You return from a trip with 2500 Mexican pesos. How much are your pesos worth in $? 54/97 How many Canadian dollars can you buy for $100?

11. Problem Solving with Units 57/98 A car travels 14 miles in 15 minutes. How fast is it going in miles per hour? 59/98 You purchased 40 acres of farm land for $200,000. How much did you pay per acre? 61/98 You are buying 4.7 pounds of apples priced at $1.29 per pound. How much do you pay? 66/98 You are buying artificial turf to cover a game field that is 150 feet long and 100 feet wide. The turf costs $7.50 per square yard. How much do you pay? 2-A 56/97 Apples in Japan sell for about 75 yen each. If you buy 4 apples, how much have you spent in dollars?

12. Problem Solving with Units 70/98 A human heart beats about 60 times per minute. If an average human being lives to the age of 75, how many times does the average heart beat in a lifetime? 75/98 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. 2-A

13. Homework Pages 97-99 Part I: #34, 45, 48, 53*, 54* 55*, 58, 62, 65, 68, 76 *use the exchange rates given to you in class. Part II: #58, 60, 62, 65, 68, 76