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Order of Operations
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Table of Contents
· Introduction to Order of Operations
· Simplify Using Order of Operations
· More Challenging Order of Operations
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Introduction to
Order of Operations
Return to
Table of Contents
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3 + 2(8)
The answer is 40
The answer is 19
Which is right?
19 is correct!
Can you explain why?
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What are operations?
When there exists more than one value, operations
can be any of the following:
· addition
· subtraction
· multiplication
· division
· exponentiation
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What does "Order of Operations" mean?
The Order of Operations is an agreed
upon set of rules that tells us in what
"order" to solve a problem.
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What does P E M/D A/S stand for?
The P stands for Parentheses: Usually represented by ( ). Other
grouping symbols are [ ] and { }. Examples: (5 + 6); [5 + 6]; {5 +
6}/2
The E stands for Exponents: The small raised number next to the
larger number. Exponents mean to the ___ power (2nd, 3rd, 4th,
etc.)
Example: 23 means 2 to the third power or 2(2)(2)
The M/D stands for Multiplication or Division: From left to right.
Example: 4(3) or 12 ÷ 3
The A/S stands for Addition or Subtraction: From left to right.
Example: 4 + 3 or 4 - 3
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How can we remember PEMDAS?
P
E
MD
AS
Please
Excuse
My Dear
Aunt Sally
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Identify the Operation:
(16 - 2)
6(7)
3
12 - 10
54
12 + 4
5
Parentheses
2
234
25
7+6
2
( 2 + 3 + 5)
1+2+4
3
Exponents
8+3
26 - 12
Multiplication
Division
Addition
Subtraction
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Simplify Using
Order of
Operations
Return to
Table of Contents
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6+4÷2
Move the box to find out if you are correct!
8
5
Correct
Incorrect
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Let's take a close look at that problem.
6+4÷2
P
Ask yourself, do I have any parentheses?
No
E
M or D
Whichever occurs 1st from left to right
A or S
Whichever occurs 1st from left to right
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Move onto the next letter
6+4÷2
P
No
E
Ask yourself, do I have any exponents?
M or D
Whichever occurs 1st from left to right
A or S
Whichever occurs 1st from left to right
No
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Move onto the next letters.
6+4÷2
P
No
E
No
M or D
Ask yourself, do I have any multiplication or
division? Yes! Solve from Left to Right.
A or S
Whichever occurs 1st from left to right
It helps if you underline the part of
the problem you are going to solve.
HINT
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Move onto the next letters.
6+4÷2
6+2
P
No
E
No
M or D
Yes! Solve from Left to Right.
A or S
Check to make sure there isn't any more
multiplication or division.
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6+4÷2
6+2
P
No
E
No
M or D
Yes. Is there anymore? No more.
A or S
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Move onto the next letters.
6+4÷2
6+2
P
No
E
No
M or D
Yes. No more.
A or S
Ask yourself, do I have any addition or
subtraction? Yes! Solve from Left to Right.
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We did it!
6+4÷2
6+2
8
P
No
E
No
M or D
Yes. No more.
A or S
Yes.
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Let's try another problem.
3(1 + 9)
P
Do I have any parentheses?
Yes - do the math in the parentheses first.
E
M or D
A or S
Remember to take it one step at a time.
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3(1 + 9)
3(10)
P
Yes! Simplify the parentheses.
E
M or D
A or S
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Move onto the next letter.
3(1 + 9)
3(10)
P
Yes
E
Do I have any exponents? No.
M or D
A or S
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Move onto the next letters.
3(1 + 9)
3(10)
P
Yes. Identify and solve.
E
No.
M or D
Do I have any multiplication or division?
Yes. Solve from left to right.
A or S
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We did it!
3(1 + 9)
3(10)
30
P
Yes. Identify and solve.
E
No.
M or D
Yes. Solve from left to right.
A or S
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Try these!
1
1 + 5(7)
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2
40
5(9)
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3
6-5+2
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4
(4)(3) + 8
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5
9 93
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6
18
9(2)
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7
5(32)
Allison is having a birthday party and is allowed to invite her
friends from school. Of her classmates,
7 girls and 5 boys are allowed to come. Each of Allison's party
favors costs $4 to make.
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Write an expression to help Allison figure out how much money her
party favors will cost. Try to use parentheses to write your
expression.
Expression
(7
+ 5)4
Evaluate your expression.
Pull down
(7 +the
5)4
to see
step
by
(12)4
step
48
solution
8
Make sure to
label your
$48
answer!
Rachel, Ted and Alice are going to the fair.
Together, they were able to buy 75 tickets for
rides. They used 15 of the tickets to ride the
bumper cars. After the ride, they decided to
split the remaining tickets equally. Use
parentheses to write an expression that
represents the number of tickets each friend
will get.
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A
B
C
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9
Erin and Elizabeth went shopping for family
gifts. Together they spent the following: $10,
$20, $8, $13 and $16.
Write an expression to represent the amount
that each of them would spend, if the total were
to be split equally.
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10 Fifteen boys went to the pizza parlor and each
ordered a slice for $2.00, a soda for $1.50 and
garlic bread for $0.75.
Write an expression to represent the total spent
in the pizza parlor.
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11 Mary received a paycheck for $55. She paid
the following debts:
$7.50 each to three friends, a $5 video fee and
$15 for a magazine subscription.
Write an expression to represent the amount
of money Mary has left.
Let's have a quick review of the basics!
8 ÷ (1+3) 52 - 2
Ask yourself, are there any grouping symbols?
Yes - so simplify
8 ÷ (1+3) 52 - 2
8 ÷ 4 52 - 2
Ask yourself, are there any exponents?
Yes - so simplify
8 ÷ 4 52 - 2
8 ÷ 4 25 - 2
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8 ÷ 4 25 - 2
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Is there any multiplication or division?
Yes - so simplify from left to right
8 ÷ 4 25 - 2
2 25 - 2
Is there anymore multiplication or division?
Yes - so simplify from left to right
2 25 - 2
50 - 2
Is there any addition or subtraction?
Yes - so simplify from left to right
50 - 2
48
Let's try a big problem
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32 + 4 6 - 12 (2 + 2) + 8
Are there any grouping symbols?
Simplify them.
32 + 4 6 - 12 (2 + 2) + 8
32 + 4 6 - 12 (4) + 8
Are there any exponents?
Simplify them.
32 + 4 6 - 12 4 + 8
9 + 4 6 - 12 4 + 8
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9 + 4 6 - 12 4 + 8
Is there any multiplication or division?
Simplify from left to right.
9 + 4 6 - 12 4 + 8
9 + 24 - 3 + 8
Is there any addition or subtraction?
Simplify from left to right.
9 + 24 - 3 + 8
33 - 3 + 8
30 + 8
38
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12
2 8+5-3
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13
Let's try an even bigger problem. What happens if
there is more than one set of grouping symbols?
[ 6 - ( 2 8 ) + ( 42 - 9 ) ÷ 7 ] 3
When there are more than 1 set of grouping symbols,
start inside and work out following the Order of
Operations.
[ 6 - ( 2 8 ) + ( 42 - 9 ) ÷ 7 ] 3
[ 6 - ( 16 ) + ( 16 - 9 ) ÷ 7 ] 3
[ 6 - ( 16 ) + ( 7 ) ÷ 7 ] 3
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[ 6 - ( 16 ) + ( 7 ) ÷ 7 ] 3
[ 6 - ( 16 ) + 1 ] 3
[ -10 + 1 ] 3
[ -9 ] 3
-27
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14
[(-3)(2) + (-5)(4)]4 - 1
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15
4 - 2[5 + 3] + 7
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16
42 + 9 - 3[2 - 5]
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17
62
3 + (15 - 7)
Here are a few examples of problems where you
might see the new grouping symbols.
2.4 [ 3.1 + (12 - 6.2) 4 ]
16 ÷ 4
(9)(3)
3 3-8 +6
10 5
-2 { 15 - 4 [ ( 6 + 2 ) - 5 ] - 3 }
Let's simplify these!
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18
52 - (2)(8) + 9
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16 ÷ 4
(9)(3)
Pull
Pull
2.4 [ 3.1 + (12 - 6.2) 4 ]
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2
19 [(2)(4)] - 3(5 + 3)
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Pull
3 3-8 +6
10 5
Pull
-2 { 15 - 4 [ ( 6 + 2 ) - 5 ] - 3 }
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More Challenging Order
of Operations
Return to
Table of Contents
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The same Order of Operations rules apply when a
problem contains negative numbers.
-3 + 5(-2 6) - 9
-3 + 5(-12) - 9
-3 + -60 - 9
-72
The first step in Order of Operations actually includes
all grouping symbols, not just parentheses. Can you
think of any other types of grouping symbols?
Brackets
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Braces
Absolute Value
Division or fraction bar
Order of Operations
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G = Grouping Symbols
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
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20
-4 -3 + -72
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21
5 + -3 - 4(-2)
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22
36 - (-3)(2)
7-52
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23
3(4 - 5) - (-2)3
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24
4 - 3[8 - (5 - 7)]
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25
8 - 16
2
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26
33 2 - 78
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27
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28
8 + 18 - 63 - 7
2-2
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29
4(6 - 11) - (-4)3
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30
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