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.
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
2-A
Operation
Key word or
symbol
Example
Division
per
Read miles  hours as “miles
per hour”
Raising to a second
power
square
Read ft  ft, or ft2, as
“square feet” or “feet squared”
Raising to a third
power
cube or cubic
Read ft  ft  ft or ft3, as
“cubic feet” or “feet cubed”
Multiplication
hyphen
Read kilowatts  hours as
“kilowatt-hours.”
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
2-A
Unit Conversions
• Trick = multiply by “1”.
1
1=
=
1
8

8
12 inches
1=
1 foot
1week
1=
7 days
1
4
1
4
1kg
1=
1kg
1 ft
1=
12 in
1year
1=
52 weeks
1=
365 days
1 year
2-A
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 = 43560 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.
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?
2-A
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 = 0.014 , the candy will
cost 1.4 cents.
2-A
Currency Conversions
Currency
(www.xe.com on 1/26/06):
Dollars per foreign Foreign per Dollar
$1.78724
0.559521
$0.866844
1.15361
European euro
$1.22255
0.815830
Japanese yen
$0.00863485
115.789
Mexican peso
$0.0951044
10.5148
British pound
Canadian
dollar
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?
Homework
Pages 97-99
#34, 48, 53*, 55*, 58, 62, 65, 68, 73, 75
*Use the exchange rates given to you in
class.