Symbols are
a **concise
way of giving
lengthy
instructions**
related to
numbers and
logic.

Symbols are
a communication
tool. Symbols
are used to
eliminate the
need to write
long, plain
language
instructions to
describe
calculations
and other
processes.

For example, a
single symbol
stands for the
entire process
for addition.
The familiar
plus sign
eliminates the
need for a long
written
explanation of
what addition
means and how
to accomplish
it.

The same
symbols are
used worldwide
. . .

The *symbols*
used in
mathematics are
*universal*.

The same math
symbols are
used throughout
the civilized
world. In most
cases each
symbol gives
the same clear,
precise meaning
to every
reader,
regardless of
the language
they speak.

The most
valuable,
**most
frequently used
Symbols** in
mathematics . .
.

The most
important, most
frequently used
*
Relation*
symbols are
listed
below.

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.

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 . .
.)

The
employee's
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"