Properties
and
Order
of
Operations
PROPERTIES
x
=
multiplication
+
=
addition
‐
=
subtraction
÷ =
division
Distributive=
the
distributive
property
is
a
property
that
simplifies
a
problem
or
expands
a
problem.
The
problem
then
becomes
easier
to
solve.
Example:
2
x
(4
+
4)
=
16
and
2
x
4
+
2
x
4
=
16
4
x
(3+2)
=
20
and
4
x
3
+
4
x
2
=
20
Commutative=the
commutative
property
is
a
property
that
makes
it
possible
to
switch
a
problem
around
and
make
it
come
out
as
the
same
exact
answer.
Example:
4
x
2
=
8
and
2
x
4
=
8
5
+
2
=
7
and
2
+
5
=
7
Fact
family:
a
fact
family
is
a
family
of
four
equations
either
addition
and
subtraction
or
multiplication
and
division
that
comes
up
with
an
answer
that
is
a
number
in
the
problem.
Example:
Another
example
4
+
8
=
12,
8
+
4
=
12,
12
–
4
=
8,
12
–
8
=
4
7
x
4
=
28,
4
x
8
=
28,
28
÷ 7
=
4,
28
÷ 4=
7
Associative
property.
Changing
the
parenthesis
place
but
it
doesn’t
change
the
answer.
Example:
(2+2)
–
2
=
2+(2‐2)
(1
–
1)
+
3
=
(
3
+
1)
‐
1
ORDER
OF
OPERATION
PARENTHESIS=
(
)
EXPONENT
MULTIPLCATION/
DIVISION
ADDITION/
SUBTRACTION
Parenthesis
always
goes
first
even
if
they
are
last
in
the
problem
Exponents
are
always
second.
If
there
are
exponents
in
a
problem,
do
them
first
before
doing
any
actual
solving
of
the
problem.
After
exponents,
you
should
have
all
whole
numbers,
and
then
you
do
Multiplication/division
from
left
to
right.
If
division
comes
left
to
right
before
multiplication
you
do
division
first.
Do
left
to
right.
The
same
thing
happens
with
addition/subtraction.
If
addition
comes
first
then
you
add
first
and
if
subtraction
comes
first
you
subtract.
Do
left
to
right.
EXAMPLES:
5
x
2
+
(3
x
44)
–
4
+
7
ANSWER
5
x
2
+
(3
x
1,024)
–
4
+7
=
5
x
2
+
(3,072)
–
4
+
7
=
10
+
3,072
–
4
+
7
=
3,082
–
4+7=
3,078+7=3,085