Variables and Expressions
After completing this lesson, you will be able to:
 Evaluate expressions using the order of operations
In mathematics, we use the order of operations to perform
mathematical operations. Always follow this order when performing
operations:
 Simplify within grouping symbols first. Grouping symbols
include braces, \{ \} , brackets,[ ] ,and parentheses ( )
 Evaluate all exponents
 Perform all multiplication and division, left to right
 Perform all addition and subtraction, left to right
A good way to remember this is by the saying
Please Excuse My
Dear Aunt Salley
The first letter of each word stands for:
P  Parentheses
E  Exponents
M  Multiplication
D  Division
A  Addition
S  Subtraction
Example 1
Evaluate
= 



3 Â· 12 Ã· 4 + 9 
Since we have an exponent we do that
first 

36 Ã· 4 + 9 
Since we have multiplication we do that
next ( 3 Â· 12 = 36 ) 

9 + 9 
Since we have division we do that next (
36 Ã· 4 = 9 ) 

18 
Last, we do the addition to achieve the
final answer of 18 
Example 2
Evaluate 8 + 12 Ã· 3
8 + 12 Ã· 3 = 



8 + 4 
(Divide 12 by 3) 

12 
(Add 8 and 4) 
Example 3
Evaluate
= 




Complete the addition within the
parentheses first (2 + 3) 

5(25)  25 
Evaluate the exponent 

125  25 
Complete the multiplication ( 5 Â· 25 ) 

100 
Complete the subtraction 
Example 4





Since we are given values for a and b, we
substitute first 


Complete the addition inside the
parentheses 


Complete the multiplication 2 times 3 and 3 times 1 


Add 6 and 3 


Multiply (This easily done by multiplying 2 times 9and
then dividing by 3) 
Example 5
Evaluate for x = 6





Substitute 6 for each x in the expression 


2 times 6 in the numerator and 6 minus 2
in the denominator 


12 plus 4 

4 
16 divided by 4 
