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
Grouping
symbols are
listed
below.
Return
To
"Top
of
Page"
click
here
Vertical
Lines
(Absolute Value
Bars)

The absolute
value symbol
tells you to
determine the
magniture of
the number
between the
vertical lines,
without regard
to its
sign.
If the number
is negative,
the negative
sign is
ignored. Only
the magniture
of the number
(always
positive) is
returned.
The following
examples
compare and
contrast the
use of
parentheses and
vertical lines
as grouping
symbols.
versus

comparison
of Math
Symbols
Grouping
Symbols 
Comparing
Parentheses and
Vertical Lines
(Absolute
Value) when
evaluatiing the
following
expressions:
versus
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
"P"
(15+5)
"P"
15+5
(20)
20
20
20
E:
no
exponents
to
evaluate
E:
no
exponents
to
evaluate
"M"
3 x
20
"M"
3 x
20
60
The
Same
60
D:
no
division
to
evaluate
D:
no
division
to
evaluate
A:
no
addition
to
evaluate
A:
no
adddition
to
evaluate
S:
no
subtraction
to
evaluate
S:
no
subtraction
to
evaluate
FINAL
ANSWER:
3(15+5) =
FINAL
ANSWER:
315+5
=
Both
answers are
exactly the
same.
Both the
parentheses and
the vertical
line groupings
can be replaced
with the same
number:
a positive 20.
This is shown
on the third
line under
"P"
(above).
versus

comparison
of Math
Symbols
Grouping
Symbols 
Comparing
Parentheses and
Vertical Lines
(Absolute
Value) when
evaluatiing the
following
expressions:
3(515)
versus
3515
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
3(515)
3515
"P"
(515)
"P"
515
(10)
10
10
Different
+10
Note:
Vertical
Line
Groupings
(absolute
value)
always
result in
a positive
number
E:
no
exponents
to
evaluate
E:
no
exponents
to
evaluate
"M"
3 x
(10)
"M"
3 x
(10)
30
Different
+30
D:
no
division
to
evaluate
D:
no
division
to
evaluate
A:
no
addition
to
evaluate
A:
no
adddition
to
evaluate
S:
no
subtraction
to
evaluate
S:
no
subtraction
to
evaluate
FINAL
ANSWER:
3(515) =
FINAL
ANSWER:
3515
=
Both
answers are
not the
same.
Both the
parentheses and
the vertical
line groupings
can
not be
replaced with
the same
number:
the parentheses
grouping is
replaced by a
10, but the
vertical line
grouping is
replaced by a
+10. This is
shown on the
third line
under
"P"
(above).