Order of Operations
Think About This…
Mrs. Bee went to the grocery store about bought a roast for $8.70 and 3 pounds of hamburger meat
for $2.50 a pound. The expression $8.70 + 3 × $2.50 represents the total amount she spent on these
items. How much did Mrs. Bee spend?
Juniata says the total is $16.20, but Tom says the total is $29.25. Who is right and why is the other
person wrong?
Why is Order of Operations Important?
Mathematicians agreed on a specific way to simplify expressions so that everyone gets the same
answer. Math problems with 2 or more different operations must be solved using the order of
operations. The order of operation rules have many real-life applications including:

building a fence, a house, or almost any other project

a manager ordering food for a restaurant based on the number of visitors
expected for the day

balancing bank accounts
P
E
M D
A
S
The order in which you perform some mathematical operations makes a difference in the answer you get. We
can use the acronym PEMDAS to help us remember the correct order of operations. PEMDAS stands for:
P
E
M
D
A
S
Keystone Algebra I
Fuller 15 | Page 1
Example 1:
Evaluate:
2 − [24 ÷ 23 + (7 − 2)]
Example 2:
Evaluate:
(6 + 10.8) + 10.4 × 102
Example 3:
Evaluate:
Keystone Algebra I
200 + 6[40⁄(−4)]
Fuller 15 | Page 2
Example 4:
Evaluate:
(4) × (−10) − 10
(−5)2
Example 6:
Evaluate:
(3 × 2)2 − 10 + 9
−7
Example 7:
Evaluate:
Keystone Algebra I
(5 − 3)2 × (−4) − 10 + 18/6
Fuller 15 | Page 3