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Parentheses
Symbols
(also
called round
brackets)
-
Left
"("
parenthesis,
and right
")"
parenthesis are
used as math
symbols
together (as a
pair). They can
be interchanged
with square
brackets or
braces.
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 (see
"Nested
expressions"
for an
example).
Background
. . .
Math
Symbols -
Why
parentheses
are used
in
mathematical
expressions
. . .
All
mathematical
expressions
must be
evaluated
in a
certain
order to
arrive at the
correct
answer.
The sequential
steps used are
summed up in
the acronym
"PEMDAS"
(called the
order of
operations).
"PEMDAS"
tells
you how
to evaluate
every
mathematical
expression by
showing you
which
math symbols to
use in
your
calculations
first,
second, third .
. . and so
on: step
by step, left
to right.
The order
of the
calculations is
what is
important.
The acronym
"PEMDAS"
stands for the
procedure shown
immediately
below. Please
note that the
entire process
of evaluating
mathematical
expressions is
controlled by
using math
symbols in the
correct order
(exactly):
P
- Parentheses:
First -
Evaluate every
part of the
expression
inside every
parentheses -
before you do
anything
else.
The
parentheses
(or bracket)
math symbols
tell you
what to do
first.
That is why
they are used.
(They also make
every
mathematical
expression more
readable.)
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.
E
- Exponent:
Second -
Evaluate every
exponent which
appears in the
expression -
before you do
anything
else.
M -
Multiplication:
Third - Reading
the expression
from left to
right, complete
all
multiplication.
D
- Division:
Fourth -
Reading the
expression from
left to right,
complete all
division.
A
- Addition:
Fifth - Reading
the expression
from left to
right, complete
all
addition.
S
- Subtraction:
Sixth - Reading
the expression
from left to
right, complete
all
subtraction.
Evaluate
the
following
expression:
short
explanation
. . .
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
3
(
15 + 5
)
"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.
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
3
✕
20
"P" -
There are no
additional
expressions
within
parentheses.
"E" -
no exponents to
evaluate.
"M" -
3
✕
20
60
"D" -
no division to
evaluate.
"A" -
no addition to
evaluate.
"S" -
no subtraction
to
evaluate.
FINAL ANSWER:
3(15+5)
=
step by
step
solution
using
PEMDAS
Order of
Operations
evaluate
the
parentheses
add
terms
none
none
none
none
none
none
multiply
numbers
- FINAL
ANSWER: 3(15+5)
= 60
none
none
none
Evaluate
the
following
expression:
short
explanation
. . .
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
3 /
(
15 + 5
)
"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.
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
3
/
20
"P" -
There are no
additional
expressions
within
parentheses.
"E" -
no exponents to
evaluate.
"M" -
no
multiplication
to
evaluate.
"D" -
3
/
20
"A" -
no addition to
evaluate.
"S" -
no subtraction
to
evaluate.
FINAL ANSWER:
3 /
(15+5) =
step by
step
solution
using
PEMDAS
Order of
Operations
evaluate
the
parentheses
add
terms
none
none
none
none
none
none
none
division
- FINAL
ANSWER:
3/(15+5)
=
none
none
Evaluate
the
following
expression:
short
explanation
. . .
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
"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" -
( 15 +
52
)
(
15 +
25
)
"M" -
no
multiplication
to evaluate
inside the
parentheses.
"D" -
no division to
evaluate inside
the
parentheses.
"A" -
( 15 +
25 )
(
40 )
40
"S" -
no subtraction
to evaluate
inside the
parentheses.
"PEMDAS"
Order
(while
reading the
mathematical
expression left
to
right)
3
✕
40
"P" -
There are no
additional
expressions
within
parentheses.
"E" -
no exponents to
evaluate.
"M" -
3
✕
40
120
"D" -
no division to
evaluate.
"A" -
no addition to
evaluate.
"S" -
no subtraction
to
evaluate.
FINAL ANSWER:
3( 15 +
52 )
=
step by
step
solution
using
PEMDAS
Order of
Operations
evaluate
the
parentheses
evaluate
exponent
none
add
terms
none
none
none
none
multiplication
- FINAL
ANSWER:
3/(15+52)
= 120
none
none
none
