Chapter 2 Approaches to Problem Solving

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

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? The price of apples, found by dividing their total cost in dollars by their total weight in pounds. dollars per pound = $/lb The density of a rock, found by dividing its weight in grams by its volume in cubic centimeters. grams per cubic centimeter = g/c3 = g/cc A car engine torque, calculated by multiplying a force in pounds by a distance in feet. foot-pounds = ft-lbs

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

Unit Conversions Convert a distance of 9 feet into inches. How many minutes are in one week?

2-A Unit Conversions Using the fact that there are 1760 yards in a mile and 3 feet in a yard, convert a distance of 3 miles into feet.

Unit Conversions (a) (b) A football field is 100 yards long and 60 yards wide. Find its area in (a) square yards and (b) square feet. (a) (b)

2-A Unit Conversions A car is driving 70 mile per hour. What is its speed in miles per second?

Unit Conversions Recall – this room had an area of 25×30 = 750ft2. Convert the area to in2 (square inches).

Problem Solving with Units 2-A Problem Solving with Units Example: You are buying 50 acres of farm land at a cost of $12,500 per acre. What is the total cost? The answer should be in dollars. We multiply acreage by the cost per acre:

Problem Solving with Units 2-A Problem Solving with Units You take a trip in which you drive 1200 miles in 20 hours. What is your average speed for the trip? The answer should be in mph. We divide miles traveled by time (hours) traveled:

Problem Solving with Units 2-A Problem Solving with Units A human heart beats about 60 times per minute. If an average human being lives to the age of 80, how many times does the average heart beat in a lifetime?

Currency Conversions (Feb. 5, 2007) www.xe.com : 2-A Currency Conversions (Feb. 5, 2007) www.xe.com : Currency Dollars per foreign Foreign per Dollar British pound $1.9597 .510281 Canadian dollar $0.846067 1.18194 European euro $1.29262 0.773624 Japanese yen $0.00830818 120.363 Mexican peso $0.0915788 10.9196

2-A Buying currency Which is worth more today – 1 British pound or 1 dollar? Explain.

2-A Buying currency You return from a trip with 2500 Mexican pesos. How much are your pesos worth in US $?

2-A Buying currency Apples in Japan sell for about 75 yen each. If you buy 4 apples, how much have you spent in dollars?

2-A Buying currency How many Canadian dollars can you buy for $100?

Example – What went wrong? You ride your bike up a steep mountain road at 5 mph. How far do you go in 3 hours? Student solution: Should be 5 miles/hour ×3 hours = 15 miles

Example – What went wrong? 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: Should be: $7.77/lb × .11 lb = $.85

Homework for Monday Pages 97-99 #32, 35, 50*, 53*, 65, 68, 75 *Use the exchange rates given to you in class.