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Example Problems  Geometric Sequence
Example Problems  Arithmetic Sequence
Example Problems  Rationalize the Denominator
Example Problems  Quadratic Equations
Example Problems  Work Rate Problems
Example Problems  statistics
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 Math Symbols  The Most Valuable and Important Relation Symbols Used:
"Proportional To"
Background  why math symbols are used. . .
Symbols are a concise way of giving lengthy instructions related to
numbers and logic.
Symbols are an invention, not a discovery. They are a
communication tool. Symbols are used to eliminate
the need to write long, plain language instructions to describe
calculations and other processes.
The most valuable, most frequently used Math Symbols . . .
The most important, most frequently used Relation symbols
are listed below.
Relation Symbols  click symbol
Proportionality Sign (the math symbol which shows one quantity is directly "Proportional To" another)
As you read the examples, please note that there is not enough information given to complete any calculations. There is just an airy sense that somehow, two values are proportional to one another.
This is intentional. Example 2 does not tell you how much the employee is paid per hour. Example 3 does not tell you how long the gardener takes to complete 500 square feet. Example 4 does not tell you how many miles per gallon the car will deliver. Without this kind of specific information, everything seems to be rather vague and incomplete.
It is. The lack of specific detail is the reason the Proportionality Sign is used instead of another math symbol (an Equal Sign, for example). The Proportionality Sign means two quantities are proportional to one another, but you don't know how. If you were given enough information in the examples to allow you to calculate numerical answers, an equation with another math symbol such as a Ratio Colon or Equal Sign would be used instead of a Proportionality Sign.
Example 1:
,
Variables A and B change in direct proportion to each other
Variable "B" is proportional to Variable "A"
Example 2:
,
An employee is paid a flat amount for each hour they work.
(The more hours that person works, the larger their paycheck will be.
If that person works 10 hours, their pay will be double what they would receive if they worked only 5 hours.
If that person works 20 hours, their pay will be double what they would receive if they worked 10 hours.
. . . and, so on . . .)
Their total earnings will change in direct proportion to number of hours they work.
"Total Pay" is proportional to "Total Hours worked"
Example 3:
,
The time it takes a gardener to mow and weed a yard depends on the size of the yard.
(The larger the yard the gardener mows and weeds, the longer it takes.
If one yard is twice as big as another, it takes the gardener twice as long to mow and weed the larger yard as it takes to mow and weed the smaller yard.
If one yard is ten times as big as another, it will take the gardener ten times as long to mow and weed the larger yard as it takes to mow and weed the smaller yard.
. . . and, so on . . .)
The time it takes the gardener to mow and weed a yard will change in direct proportion to the size of the yard.
"Time Required to Mow & Weed" is proportional to "Size of Yard"
Example 4:
,
The volume of gasoline needed to drive a car depends on how far the car is driven.
(The further a car is driven, the greater the quantity of gasoline it requires.
Driving twice as far today as you drove yesterday requires twice the volume of gasoline as you used yesterday.
Driving ten times as far requires ten times the volume of gasoline.
. . . and, so on . . .)
The volume of gasoline needed varies in direct proportion to the distance the car is driven.
"Volume of gasoline needed" is proportional to "Distance Driven"

