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.
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Nested
Groupings
(nested
Brackets)
-
If there are
three levels of
grouping in a
nested
expression,
generally
parentheses
are used in the
inner most
groupings.
Square
brackets
are used in the
next higher
level grouping,
and
braces are
used in the
most outer
groupings.
All
mathematical
expressions
must be
evaluated
in
PEMDAS
order
to arrive at
the correct
answer.
If there are
several nested
parentheses,
begin by
evaluating the
innermost
parentheses
first -
before you do
anything else.
After
evaluating the
innermost
parentheses,
evaluate the
next innermost
parentheses,
and so on -
until there are
no parentheses
left.
If there are
several
non-nested
parentheses,
evaluate every
one of them
separately -
before you do
anything
else.
Evaluate
the
following
expression:
{[3(15 +
5) + 27]/3}
Note the
arrangement of
the nested
brackets:
Will be
evaluated
first
:
Expression
inside
Inner
Brackets -
Parentheses
(shown in
blue):
{[3
(
15 + 5
)
+ 27]/3}
Will be
evaluated
second
:
Unevaluated
portion of
expression
inside
Middle
Brackets -
Square
Bracket
Symbols
(shown in
brown):
{
[
3(15 + 5) + 27
]
/3}
Will be
evaluated
third
:
Unevaluated
portion of
expression
inside
Outer
Brackets -
Curly
Bracket
Symbols
(shown in
purple):
{
[3(15 + 5) +
27]/3
}
first
: evaluation of
the expression
inside the
inner most
brackets .
. .
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
{[3
(
15 + 5
)
+ 27]/3}
"P" -
The parentheses
are the math
symbols which
represent the
innermost
bracket
grouping. There
are no
additional
bracket
groupings to
evaluate inside
the
parentheses.
"E" -
no exponents to
evaluate inside
the
parentheses.
"M" -
no
multiplication
to evaluate
inside the
parentheses.
"D" -
no division to
evaluate inside
the
parentheses.
"A" -
( 15+5
)
(
20 )
20
"S" -
no subtraction
to evaluate
inside the
parentheses.
The expression
within the
inner most
parentheses can
be replaced by
the number
20:
{[3
(
15 + 5
)
+ 27]/3}
{[3
(
20
)
+ 27]/3}
{[3
x
20 +
27]/3}
second
: evaluation of
the expression
inside the
middle
brackets .
. .
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
{
[
3 x 20 + 27
]
/3}
"P" -
The square
brackets are
the math
symbols which
represent the
middle bracket
grouping.
"E" -
no exponents to
evaluate inside
the middle
bracket
grouping.
"M" -
3 x
20
60
"D" -
no division to
evaluate inside
the middle
backet
grouping.
"A" -
[ 60+27
]
[
87 ]
87
"S" -
no subtraction
to evaluate
inside the
parentheses.
The expression
within the
square brackets
can be replaced
by the number
87:
{
[
3 x 20 + 27
]
/3}
{
[
60 + 27
]
/3}
{
[
87
]
/3}
{ 87
/3}
third
: evaluation of
the expression
inside the
outer
brackets .
. .
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
{
87/3
}
"P" -
The curly
brackets are
the math
symbols which
represent the
outer bracket
grouping.
"E" -
no exponents to
evaluate inside
the outer
bracket
grouping.
"M" -
no
multiplication
to evaluate
inside the
outer backet
grouping.
"D" -
{ 87/3
}
{
29 }
29
"A" -
no addition to
evaluate within
the outer
backet
grouping.
"S" -
no subtraction
to evaluate
inside the
parentheses.
The expression
within the
outer brackets
can be replaced
by the number
29:
{
87/3
}
{
29
}
29
-
FINAL
ANSWER:
{[3(15 +
5) +
27]/3} =
29
