September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
We already know that grouping
symbols are dealt with before
multiplication, division, addition,
and subtraction.
September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
We also know that multiplication
and division are done before
addition and subtraction.
September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
When multiplication and division
are both in an expression, the
operations are performed from left
to right.
September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
When addition and subtraction are
both in an expression, the operations
are performed from left to right.
September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
There are some other operations,
and they are performed after
grouping symbols but before
multiplication and division.
September 30, 2013
The rules used for simplifying
numerical expressions are called
order of operations.
The most common other operation
involves exponents.
September 30, 2013
There most common other operation
involves exponents.
Here is an example:
42 – 32 • (2 + 1) ÷ 9
September 30, 2013
There most common other operation
is exponents.
Here is an example:
42 – 32 • (2 + 1) ÷ 9
42 – 32 • 3 ÷ 9
September 30, 2013
There most common other operation
is exponents.
Here is an example:
42 – 32 • (2 + 1) ÷ 9
42 – 32 • 3 ÷ 9
42 – 9 • 3 ÷ 9
September 30, 2013
There most common other operation
is exponents.
Here is an example:
42 – 32 • (2 + 1) ÷ 9
42 – 32 • 3 ÷ 9
42 – 9 • 3 ÷ 9
42 – 27 ÷ 9
September 30, 2013
There most common other operation
is exponents.
Here is an example:
42 – 32 • (2 + 1) ÷ 9
42 – 32 • 3 ÷ 9
42 – 9 • 3 ÷ 9
42 – 27 ÷ 9
42 – 3
September 30, 2013
There most common other operation
is exponents.
Here is an example:
42 – 32 • (2 + 1) ÷ 9
42 – 32 • 3 ÷ 9
42 – 9 • 3 ÷ 9
42 – 27 ÷ 9
42 – 3
39
September 30, 2013
That brings is to a well known
mnemonic device:
Please Excuse My Dear Aunt Sally
September 30, 2013
That brings is to a well known
mnemonic device:
Please Excuse My Dear Aunt Sally
or
PEMDAS
September 30, 2013
P
E
M
D
A
S
parentheses
exponents
multiplication
division
addition
subtraction
September 30, 2013
P
E
M
D
A
S
parentheses
exponents
multiplication
division
addition
subtraction
break the tie
by going left to
right
break the tie
by going left to
right
September 30, 2013
(43 + 2) ÷ 3
24 + 2 • 3
September 30, 2013
(43 + 2) ÷ 3
24 + 2 • 3
(64 + 2) ÷ 3
16 + 2 • 3
September 30, 2013
(43 + 2) ÷ 3
24 + 2 • 3
(64 + 2) ÷ 3
16 + 2 • 3
66 ÷ 3
16 + 6
September 30, 2013
(43 + 2) ÷ 3
24 + 2 • 3
(64 + 2) ÷ 3
16 + 2 • 3
66 ÷ 3
16 + 6
22
22
September 30, 2013
(43 + 2) ÷ 3
24 + 2 • 3
(64 + 2) ÷ 3
16 + 2 • 3
66 ÷ 3
16 + 6
22
22
1
September 30, 2013