Order of Operations
By Mr. Walker
The Expression
We need to simplify this expression down to one number (find the answer).
3
25
+(3x5)-2
5
But where do we start?
There is a certain order we need to follow when we simplify
this expression, or we will get the wrong answer. This is called…
Order of Operations
It goes like this…
Going left to right (like when reading)
• Do anything in Parentheses
• Start over and do any Exponents
• Start over and do any Multiplication and Division
• Start over and do any Addition and Subtraction
Definitions
Parentheses are…
3
25
5 +(3x5)-2
( )
Exponents are … Powers and Roots
2
3
16
In this problem 2 has a power of three,
which means you should multiply 2 by itself three times: 2x2x2
Multiplication and Division are …
X
25 is the same as saying 25
5
Addition and Subtraction are…
+
-
5
How Do I Remember All This?
Easy…
Please Excuse My Dear Aunt Sally
Dear Aunt Sally
P had aEvery bad
M day,
D soAplease
S excuse her.
It all started when
shex burnt her
a
u tongue
i
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Then on the way
Whilebshe was
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p her car
l died.
v
d
walking the rest
e of theo way to work
t i a car
i drove
t by and
splattered hernwith mud.
n Wheni she
s finally
t gotr to work her
boss fired her tfor being
e late. Since
p i she idid not
a have a job
anymore she hstarted nwalking home
l o ando found
c a quarter
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but soon
e near a
t tree. ‘Great,’
i n she
n thought
t
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While she
s
c to the sidewalk.
i
was looking down
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e
a a bee stungoher and she
stood up so fast
s that she forgott the tree branch
n right
above her head. BONK! Just then
a 7 year old boy bumped
o
into her because he was reading
n a comic book as he walked.
When he looked up to say ‘Excuse me,’ this is what he saw…
So …
Please Excuse My Dear Aunt Sally
Step by Step ‘P’
3 3
2525
+(3x5)-2
+15-2
55
Please Excuse My Dear Aunt Sally
P
a
r
e
n
t
h
e
s
e
s
(3x5) is 15, so put the 15 in the spot of the (3x5)
You most likely will not have to deal with this step in 4th grade.
Step by Step ‘E’
3
25
+15-8
+15-2
5
Please Excuse My Dear Aunt Sally
E
x
p
o
n
e
n
t
s
3
2 Is the same as 2x2x2
2x2=4 x2 again is 8
3
So replace the 2 with the 8
Step by Step ‘M’ & ‘D’
25
+15-8
5+15-8
5
Please Excuse (My Dear) Aunt Sally
M
u
l
t
i
p
l
i
c
a
t
o
n
D
i Do any multiplication and division as you read left to right
v
i
There is nothing to multiply so do the division.
s
i
25 is the same as saying 25 5
o
5
n
25 divided by 5 is 5.
So replace the 25 with the 5
5
Step by Step ‘A’ & ‘S’
5+15-8
20-8
12
Please Excuse My Dear (Aunt Sally)
A
d
d
i
t
i
o
n
S
u
b
t
r
a
c
t
i
o
n
You are done!
Do any addition and subtraction as you
read left to right
Add the 5+15 to get 20
Take out the 5+15 and put the 20 in that spot
Subtract the 8 from the 20 and get 12
1 10
20
-8
12
borrow
Take away the 20-8 and put the 12
Let’s Try One Together
Remember Please Excuse My Dear Aunt Sally
Simplify this expression
5+(3x4)- 36
Parentheses: (3x4) = 12
6
5+12- 36
6
Exponents: None-Skip
5+12- 36
Multiplication: None-Skip
Division: 36 divided by 6 = 6
Addition: 5+12=17
Subtraction: 17-6=11
6
5+12- 36
6
5+12-6
17-6
11
Try These On Your Own
2+(4x9)- 50
5
Answer
28
56
7 +2x(3x9)-60
Answer
4x(1+7)-24
2
Answer
3
24
3
3 -20+(45 +5)-7
9
Answer
10
For Fun Make Up Your Own Aunt
Sally Story
Please Excuse My Dear Aunt Sally because…