Transcript Section 2A - Hollins University

Chapter 2
Approaches to Problem Solving
Section 2A
The Problem Solving Power of 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 multiple or divide
numbers – we’ll just create new units.
Units
• Do NOT disregard units.
• ALWAYS pay attention to units.
• Units are your FRIENDS!
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 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
1 inch
1 square inch
1 inch
1 inch
1 inch 1 cubic inch
1 inch
2-A
Operation
Key word or
symbol
Example
Division
per
Read miles  hours as “miles
per hour”
Raising to a second
power
square
Raising to a third
power
cube or cubic
Read ft  ft, or ft2, as
“square feet” or “feet
squared”
Read ft  ft  ft or ft3, as
“cubic feet” or “feet cubed”
Multiplication
hyphen
Read kilowatts  hours as
“kilowatt-hours.”
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  r
where r is the radius of the circle measured in centimeters.
- square centimeters = cm2
2
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
2-A
Unit Conversions
converting one set of units to another
• Trick = multiply by “1”.
1
1=
=
1
8

8
1
4
1
4
12 inches = 1 foot
12 inches
1=
1 foot
1 ft
1=
12 in
1 week = 7 days
1week
1=
7 days
7days
1=
1week
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!)
(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???
2-A
Currency Conversions
(www.xe.com)
Currency
(September 2008):
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
108.7510
Mexican peso
0.09653
10.3593
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?
Problem Solving with Units
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?
2-A
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.
Homework
Pages 97-99: #1-93
TURN IN:
38,44,52,56,60,66,70,76,78,84
Show all steps in your solutions