1
Order of Operations and the Use of Calculators Exercise
Goals:
 To review the order of operations rules from algebra
 To understand how order of operations rules are used by
calculators
Order of Operations Rules:
Given a mathematical expression to solve perform operations on the
expression in the following order:
1st.
Simplify all expressions within parentheses (following the
rules below!)
2nd.
Perform all exponentiation
3rd.
Perform multiplication and division as these expressions
appear from left to right
4th.
Perform addition and subtraction as these expressions
appear from left to right
Example:
(4 X 33 – 8) + 10 – 3 = ?
53 – 7 X 2
Look at the numerator:
First simplify parentheses, following order of operations:
(4 X 33 – 8) + 10 – 3 =
exponentiation first
3
5 –7X2
(4 X 27 – 8) + 10 – 3 =
53 – 7 X 2
multiplication next
(108 – 8) + 10 – 3 =
53 – 7 X 2
finally subtraction
100 + 10 – 3 =
53 – 7 X 2
finish the top
107
2
Now look at the denominator:
___107__
53 – 7 X 2
=
exponentiation first
____107___ =
125 – 7 X 2
multiplication next
__107____ =
125 – 14
subtraction last
__107_=
111
Now divide: The answer is 0.96
Why do we care about this????
CALCULATORS USE ORDER OF OPERATIONS!!!
Put this expression directly into your calculator:
6 X 6 – 3 The correct answer is 1.65
4X5
If you enter this directly without any parentheses, your calculator will give
you the answer:
32.25 if you never hit = until the end
41.25 if you hit = after putting in the top
3
Why?
If you never hit = at all until the end you tell the calculator to do this:
6X6–3/4X5
Order of operations says do all multiplication and division left to right first:
36 – 0.75 X 5 = 36 – 3.75 = 32.25
If instead you hit = after the top:
6 X 6 – 3 = 33, so okay so far but then you tell the calculator to do:
33 / 4 X 5 = 8.25 X 5 = 41.25
So remember, use parentheses where appropriate!!!