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 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

5. 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

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. 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 = 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. Problem Solving with Units
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. 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 = , the candy will cost 1.4 cents.

11. Currency Conversions (www.xe.com on 1/26/06):
2-A
Currency Conversions ( on 1/26/06):
Currency
Dollars per foreign
Foreign per Dollar
British pound $
Canadian dollar $
European euro $
Japanese yen $
Mexican peso $

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.