Chapter 2 Approaches to Problem Solving

1. Chapter 2Approaches 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 this floor is 25 feet long • The other side is 30 feet long. • Area of this floor space = 25 ft × 30 ft = 750ft2(square feet) • The room’s height is 12 feet. • The volume of this room is 25ft × 30ft × 12ft = 9000 ft3 = 9000 cubic feet

5. Operation Key word orsymbol Example Division per Read miles  hours as “miles per hour” Raising to a second power square Read ft  ft, or ft2, as “square feet” or “feet squared” Raising to a third power cube or cubic Read ft  ft  ft or ft3, as “cubic feet” or “feet cubed” Multiplication hyphen Read kilowatts  hours as “kilowatt-hours.” 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 20/96 A speed, found by dividing a distance measured in kilometers by a time measured in seconds. • kilometers per second = km/sec 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

7. 2-A Unit Conversions • Trick = multiply by “1”.

8. 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.

9. 2-A Problem Solving with Units 57/61 A car travels 14 miles in 15 minutes. How fast is it going in miles per hour? 61/61 You are buying 4.7 pounds of apples priced at $1.29 per pound. How much do you pay? 66/61 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? 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?

10. 2-A Example – What went wrong? 71/98 A candy store sells chocolate for $7.70 per pound. The piece you want to buy weighs 0.11 lb. How much will it cost, to the nearest cent? (Ignore sales tax.) Student solution: Since 0.11 / 7.70 = 0.014 , the candy will cost 1.4 cents.

11. 2-A Currency Conversions (www.xe.com on 1/26/06):

12. 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? 56/97 Apples in Japan sell for about 75 yen each. If you buy 4 apples, how much have you spent in dollars?

13. Homework Pages 97-99 #34, 48, 53*, 55*, 58, 62, 65, 68, 73, 75 *Use the exchange rates given to you in class.