DM 2A

Transcription

DM 2A

Approaches to Problem Solving
Copyright © 2011 Pearson Education, Inc.
Unit 2A
The Problem-Solving
Power of Units
Slide 2-3
Global Melting
Slide 2-4
The Power of Units

There is no single best approach to solving
quantitative problem.

You will learn some strategies and guidelines to
help you solve problems.
Slide 2-5
2-A
Units
The units of a quantity describe what is being
measured or counted.
Operation
Key word or
symbol
Division
per
Read miles  hours as “miles
per hour.”
Raising to second
power
square
Read ft  ft, or ft2, as
“square feet” or “feet squared.”
Raising to 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.”
Example
Slide 2-6
2-A
Problems to try




Your average speed on a long walk, found by
dividing distance traveled in miles by time elapsed
in hours.
The unit price of oranges, found by dividing the
price in dollars by the weight in pounds.
The cost of a piece of carpet, found by dividing its
price in dollars by its area in square yards.
The flow rate of a river in which 5000 cubic feet of
water flow past a particular location every second.
Slide 2-7
2-A
Unit Conversions
Convert a distance of 9 feet into inches.
Slide 2-8
2-A
Everyday Problems

Everyday problems can be solved with unit
conversion.

There are many different ways to write the
conversion of 1.

The KEY is to use the correct form.
Slide 2-9
2-A
Conversion Factors
A conversion factor is a statement of equality that
is used to convert between units.
Some conversion factors:
12 in.  1 ft
24 hr  1 day
or
or
12 in.
1
1 ft
24 hr
1
1 day
or
or
1 ft
1
12 in.
1 day
1
24 hr
Slide 2-10
2-A
Example 2: Feet to Inches

Convert a distance of 7 feet into inches (p.85)

Convert 24 feet to inches

Convert 24 feet to yards
Slide 2-11
2-A
Example 3: Inches to Feet

Convert a length of 102 inches to feet (p.85)

Now try Minutes to Seconds

Convert 25 minutes to seconds

Convert 2.5 hours to seconds
Slide 2-12
2-A
Using a Chain of Conversions
Slide 2-13
2-A
Conversions with Units Raised to Powers
1 yd = 3 ft
1 yd2 = 1 yd × 1 yd
= 3 ft × 3 ft
= 9 ft2
Slide 2-14
2-A
Hint

We take special care when converting units raised
to powers.

We may not know the conversion factor between
square yards, but we know that 1 yard = 3 ft, so
we can replace it to say
1 yd x 1yd = 1 square yard,
so 3 ft x 3 ft = 9 square feet


Slide 2-15
2-A
Cubic Units
How many cubic yards of soil are needed to fill a
planter that is 20 feet long by 3 feet wide by 4 feet
tall?
The volume is 20 ft × 3 ft × 4 ft = 240 ft3
1 yd = 3 ft, so (1 yd)3 = (3 ft)3 = 27 ft3
Slide 2-16
2-A
Hint

Follow the same idea with cubic yards as you do
square yards.

1yd x 1 yd x 1 yd = 1 cubic yard, so
3ft x 3ft x 3ft = 27 cubic feet.

Slide 2-17
2-A
Currency Conversions
You return from a trip to Europe with 120 euros. How many
dollars do you have?
$1.256
120 euros 
 $150.72
1 euro
Slide 2-18
2-A
Let’s try

You arrive in London with $400. How many
pounds can you buy?

As you leave Paris, you convert 4500 euros to
dollars. How many dollars do you receive?

You return from Mexico with 3000 pesos. How
much are they worth in U.S. dollars?
Slide 2-19
2-A
Exchange Rates

Current exchange rates are constantly changing,
but you can always get current rates by typing
“exchange rates” into any search engine.

Find the reciprocals of the numbers in the Dollars
per Foreign column of Table 2.1.

FYI: Banks offer better rates, some places charge
fees.
Slide 2-20
2-A
Problem Solving with Units

Units can help us decide HOW to solve

Same units – use addition and subtraction ONLY

Different units – usae multiplication and division.
Slide 2-21
2-A
1. Identify the units involved in the problem. Use
them to


decide how to approach the problem;
and determine what units to expect in the answer.
2. Perform any operations on both the numbers
and their associated units.



Numbers with different units cannot be added or
subtracted.
Combine different units through multiplication,
division, or raising to powers.
Replace division with multiplication by the reciprocal.
3. Make sure your answer is in the units you
expected.
Slide 2-22
2-A
Using units to Check Answers

Checking answers is one of the most important
reasons for using units.

You should always check your method and your
calculations as well as your units!!!
Slide 2-23
2-A
Distance Time and Speed

Speed in miles per hour is distance / time

You can always rearrange the equation…


distance = speed x time
time = distance / speed
Slide 2-24
2-A
Let’s try

A car is traveling 25 miles every half-hour. How
fast is it going? (p.90)

An airliner travels 45 miles in 5 minutes. What is
its speed in miles per hour?
Competition speed skydivers have reached record
speeds of 614 miles per hour. At this speed, how
many feet would you fall every second?
Slide 2-25
2-A
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 the acreage
by the cost per acre:
$12,500
50 acres 
 $625, 000
1 acre
Slide 2-26
2-A
Example 10: Buying Farm Land

You are buying 30 acres of farm land at $12,000
per acre. What is the total cost? (p.90)

* an acre was originally defined as the amount of
land a pair of oxen could plow in a day.
Slide 2-27
2-A
Use unit conversions to answer

An airline travels 45 miles in 5 minutes. What is its
speed in miles per hour?

What is the total cost of 1.2 cubic yards of soil if it
sells for $245 per cubic yard?

A hose fills a hot tub at a rate of 3.2 gallons per
minutes. How many hours will it take to fill a 300
gallon-hot tub?
Slide 2-28
2-A
More unit conversions

Suppose you earn $8.50 per hour and work 24
eight-hour days in a month. How much do you
earn in that month?

The median salary for the New York Yankees in
2008 was $1,875,00. Assuming a 160-game
season, express this salary in dollars per game.

If you sleep an average of 8 hours each night,
how many hours do you sleep in a year?
Slide 2-29
2-A
Analyzing Problems

Start analyzing a problem by looking at its units.

Gas Mileage (p.91)
Your destination is 90 miles away and your fuel
gauge shows that your gas tank is only onequarter full. You know that your tank holds 12
gallons of gas and that your car averages about
25 miles per gallon. Do you need to stop for gas?

Slide 2-30
2-A
Let’s try




You plan to take a 2000 mile trip in your car,
which averages 32 miles per gallon.
How many gallons of gasoline should you expect
to use?
Would a car that has only half the gas mileage(16
miles per gallon) require twice as much gasoline
for the same trip?
Explain
Slide 2-31
2-A
Melting Ice
We can find the
correct answer
simply by
working with
units.
Slide 2-32
2-A
Homework

Quick Quiz

P.92: 1-12; 19-85 odd; 1 web 1 world
Slide 2-33

DM 2A

Transcription

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