the problem solving power of units
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2A. The Problem Solving Power of Units. Basics. Units of quantity describe what is being measured or counted. We can only add values that have the same unit of measure. We can multiply and divide values that have different units. . Examples. - PowerPoint PPT PresentationTRANSCRIPT
THE PROBLEM SOLVING POWER OF UNITS
2A
Basics
Units of quantity describe what is being measured or counted.
We can only add values that have the same unit of measure.
We can multiply and divide values that have
different units.
Examples
It wouldn’t make sense to combine 3 apples with 2 bananas…5 banapples?
If you walk 20 miles in 3 hours, what is your average speed?
Examples
If you drive 60 miles per hour, how far did you travel in 2 hours?
Examples
To find the area of a room we multiply length times width A 10 foot by 8 foot room is 80 square feet or 80 ft2
To find the volume of a box we take length x width x height 2cm x 3cm x 4cm = 24 cm cubed
To find the amount of energy used by a light bulb we multiply its power rating by the length of time it is turned on. 60 kilowatt x 2 hours = 120 kilowatt-hours
Examples
Area and Volume Conversions- Page 97 #48 A warehouse is 40 yards long and 25 yards wide and
piled with cartons to a height of 3 yards. What is the area of the warehouse floor? What is the total volume of the cartons? (Assume there is no space between the cartons)
The bed of a pickup truck is 3.5 feet deep, 12 feet long, and 5 feet wide. What is the area of the bed’s floor? What is the volume of the bed?
A can has a circular base with an area of 6 square inches and is 4 inches tall. What is the total volume?
Reading units
Operation Keyword or Symbol ExampleMiles / hours
Division per “miles per hour”
Raising to a squareft x ft or ft^2 Second power “square feet” or
“feet squared”
Raising to a third power cube or cubic ft x ft x ft or ft^3 “cubic feet” or “feet cubed”
Multiplication hyphen kilowatt x hours“kilowatt-hours”
Example
Identifying UnitsIdentify the units you would expect in each of the
following. State the units in both words and mathematically. The price of fabric, found by dividing its cost in dollars by
its area in square feet. The gas mileage of a car, found by dividing the distance in
miles it travels by the amount of gas in gallons that it uses.
The cost for grass seed when you buy enough to cover 80 square yards at a total price of $160.
The density of a rock, found by dividing its weight in grams by its volume in cubic centimeters.
A car engine torque calculated by multiplying a force in pounds by a distance in feet.
Working with fractions
A fraction represents division
Numerator- top of the fraction
Denominator- bottom of the fraction
Integers can be written as fractions 5 = 5/1
Adding and Subtracting Fractions
Multiplying Fractions
Dividing Fractions
Fraction to Decimal
Decimal to Fraction
ExampleEvaluate each of the following
a
b
c
d
.
.
.
.
145
310
59
49
23
14
12
13
14
e
f
g
h
.
.
.
.
16
611
18
116
35
53
12
13
14
Unit Conversions
The trick is to find a “well chosen 1” Multiplying the numerator and the denominator by
the same number doesn’t change the value of the original fraction.
When the numerator and the denominator are the same value the fraction is equal to 1…hence the name “well chosen 1”
Examples-Well Chosen 1’s
60 seconds 1 minute 1 minute 60 seconds
7 days 1 week 1 week 7 days
1 foot 12 inches12 inches 1 foot
Convert the following
3 feet to inches
108 inches to feet
Chain of Conversions
How many seconds are there in 1 week?
Conversions with Powers
How many square feet in a square yard?
3 ft
3 ft
Example
Convert 150 sq ft to sq yds
Examples
Unit Conversions- Convert a distance of 7 miles into yards; there are
1760 yards in a mile. 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.
Use a chain of conversions with familiar measures of time to convert 4 weeks into minutes
Convert a park size of 3.5 square miles to acres. (1 acre = 1/640 mi2)
A car is driving 100 kilometers per hour. What is its speed in kilometers per second?
Examples
Cubic Units- Find a conversion factor between cubic inches and
cubic feet. Write it in three forms. How many cubic inches are in 3 cubic yards? A cargo container is 50 feet long, 10 feet wide, and 8
feet tall. Find its volume in cubic feet and cubic yards.
Example
Currency Conversions- Use Table 2.1 on page 90
Which is worth more, 1 Mexican peso or 1 Japanese yen? Explain.
How many Canadian dollars can you buy for $100? You return from a trip with 75 British pounds. How
much are your pounds worth in dollars? Apples in Japan sell for about 250 yen each. If you
buy 4 apples, how much have you spent in dollars?
Using Units to Help You Solve Problems
By looking at what kind of answer we are trying to get this can help us determine what operation we need to perform.
Examples
Page 98- #70 You are buying 2.8 kilograms of cherries priced at
$3.50 per kilogram. How much will you pay?
Page 98- #66 An airplane travels 95 miles in 10 minutes. How fast
is it going in miles per hour?
Examples
A 40 acre orchard produces 12,000 apples. What is the yield in apples per acre?
You are buying floor tile to cover a room that measures 20 feet by 25 feet. The tile is priced at $7.50 per square foot. How much will the tile cost?
Examples
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 will the turf cost?
You work 40 hours per week and are paid $13.50 per hour. If you work all 52 weeks in a year, how much will you earn?
Examples
Page 98- #78 An average human heart beats 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?