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. Units
Do NOT disregard units.
ALWAYS pay attention to units.
Units are your FRIENDS!

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 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

6. 1 inch
1 inch
1 cubic inch
1 square inch
1 inch
1 inch

7. 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

8. Practice – what units?
29/96 The price of apple juice , found by dividing its
total cost in dollars by its volume in ounces.
dollars per ounce = $/oz
1b/85 The area of a circle, found with the formula
where r is the radius of the circle measured in centimeters.
- square centimeters = cm2
35/97 The gas mileage of a car, found by dividing the distance in miles that it travels by the amount of gas in gallons that it uses. -miles per gallon = m/gal = mpg
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

9. Unit Conversions converting one set of units to another
Trick = multiply by “1”.
12 inches = 1 foot
1 week = 7 days

10. Unit Conversions 43/97 Convert 2 weeks to units of minutes.
2-A
Unit Conversions
43/97 Convert 2 weeks to units of minutes.
44*/97 A car is driving at 100 kilometers per hour. What is its speed in kilometers per second?
53/98 A box-shaped water tank measures 12 feet by 8 feet by 4 feet. Find its volume in cubic yards. (Careful with square and cubic units!)

11. (Careful with square and cubic units!)
1 square yard = 9 square feet
1 square foot = 144 square inches
WHY???
1 cubic yard = 27 cubic feet
1 cubic foot = 1728 cubic inches
WHY???

12. Currency Conversions (September 2008): (www.xe.com)
2-A
Currency Conversions (September 2008): (
Currency
dollars per foreign
foreign per dollar
British pound
1.7834
0.5607
Canadian dollar
0.9360
1.0684
European euro
1.4518
0.6888
Japanese yen
0.0092
Mexican peso

13. 2-A
Currency Conversions
57/98 Which is worth more today – 1 Mexican peso or 1 US dollar? Explain.
61/98 How many US dollars can you buy with 12,000 Japanese yen?

14. Problem Solving with Units
2-A
65/98 A car travels 13 miles in 15 minutes. How fast is it going in miles per hour?
69/98 You are buying 4.7 pounds of apples priced at $1.29 per pound. How much do you pay?
77/98 If you sleep an average of 7 hours each night, how many hours do you sleep in a year?

15. Problem Solving with Units
2-A
Problem Solving with Units
83/98 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.

16. Show all steps in your solutions
Homework
Pages 97-99: #1-93
TURN IN: 38,44,52,56,60,66,70,76,78,84
Show all steps in your solutions