Transcript Section 2A
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. 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 2-A Operation Key word or symbol Example Division per Read miles hours as “miles per hour” Raising to a second power square Raising to a third power cube or cubic Read ft ft, or ft2, as “square feet” or “feet squared” Read ft ft ft or ft3, as “cubic feet” or “feet cubed” Multiplication hyphen Read kilowatts hours as “kilowatt-hours.” 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 r where r is the radius of the circle measured in centimeters. - square centimeters = cm2 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/c3 = 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 2-A Unit Conversions converting one set of units to another • Trick = multiply by “1”. 1 1= = 1 8 8 1 4 1 4 12 inches = 1 foot 12 inches 1= 1 foot 1 ft 1= 12 in 1 week = 7 days 1week 1= 7 days 7days 1= 1week 2-A Unit Conversions 30/97 Convert a distance of 18 yards into inches. 33/97 Convert a lot size of 1/5 acre to square feet.(1 acre = 43560 square feet) 38/97 A car is driving at 100 kilometers per hour. What is its speed in kilometers per second? 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!) 2-A Currency Conversions Currency British pound (www.xe.com on 8/29/06): dollars per foreign foreign per Dollar 1.89198 0.528548 0.899786 1.11138 European euro 1.27605 0.783671 Japanese yen 0.00855457 116.897 Mexican peso 0.0917226 10.9024 Canadian dollar 2-A Currency Conversions 49/97 Which is worth more today – 1 British pound or 1 dollar? Explain. 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? Problem Solving with Units 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? 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 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. 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