1. Chapter 2 Approaches to Problem Solving

2. Section 2A
Units
Pages 84-95

3. 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.

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

5. 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

6. 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

7. 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

8. 2-A
Unit Conversions
Trick = multiply by “1”.

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

10. 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.

11. 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)

12. 2-A
Unit Conversions
A car is driving 70 mile per hour. What is its speed in miles per second?

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

14. 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:

15. 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:

16. 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?

17. Currency Conversions (Feb. 5, 2007) www.xe.com :
2-A
Currency Conversions (Feb. 5, 2007) :
Currency
Dollars per foreign
Foreign per Dollar
British pound
$1.9597
Canadian dollar $
European euro $
Japanese yen $
Mexican peso $

18. 2-A
Buying currency
Which is worth more today – 1 British pound or 1 dollar? Explain.

19. 2-A
Buying currency
You return from a trip with 2500 Mexican pesos. How much are your pesos worth in US $?

20. 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?

21. 2-A
Buying currency
How many Canadian dollars can you buy for $100?

22. 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

23. 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

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