By Paula Sims
The origin of the Order of Operations
continues to be a mystery. Evidence shows
that the rule Multiplication precedes
addition and subtraction was developed in
the 1600’s.
The Order of Operation has existed since
the beginning of algebraic notation.
Prior to this, mathematicians used
grammar.
Before we look at the Order of
Operations, does anyone know what the
acronym for it is? How about the
mnemonic?
If you guessed PEMDAS as the
acronym you are correct.
Now let’s look at what the mnemonic
stands for.
Please
() Parentheses
Excuse
n2 Exponents
My
x Multiplication
Dear
/ Division
Aunt
+ Addition
Sally
- Subtraction
Evaluate this algebraic expression
3-5+7x3
Was your answer 15? That is because
most of us normally work from left to
right without the rules to guide us.
When we evaluate the same expression
using PEMDAS we have:
(3-5)+(7x3)
Since the order of operations tells us to
first work inside the parentheses we
may begin with the first part of the
expression:
(3-5)=-2
then we work inside the second part of
the expression:
(7x3)=21
When we combine our answers we get:
-2+21=19
This is different than our original answer
of 15.
Lets Practice using PEMDAS on a few
equations:
1). 3(2+3)-7+8/2=
2). (4+2)/3-8/4+3x2=
3). 5-9/3+3(2+1)=
4). (3+9)/(4-1)-4+(8/2)=
We will work on the first one together.
3(2+3)-7+8/2=
Parentheses (2+3)=5
Multiplication 3(5)=15
Division 8/2=4
Addition 15+4=19
Subtraction 19-7=12
Compare the rest of your answers to mine.
2). 6
3). 11
4). 4
Did we use the same order of operations?
If your answers differ from mine, try again
and see which operation you may have
either left out or completed out of order.
Now try some equations that contain
exponents:
2
1). 3-(4-(7+2)) =
2
2). 2-(3-6) x(-4)=
2
3). 3-(-2) x(-8)+3=
Compare your answers with mine
1). -22
2). 38
3). 38
Are we in agreement? If not that’s alright
because this process will take time to master
and you are off to a great start. So continue
to practice and have fun challenging
yourselves.
Now that you are armed with the
great knowledge of the Order of
Operations go out there and kick
some math!
Work cited
http://en.wikipedia.org/wiki/order_of_operations
http://www.city.directories.us
http://mathforum.org/library/drmath/view/57737
html
http://members.aol.com/jeff570/operations.html
www.Microsoft clip art
Slavin, Steven and Selby, Peter H. “Quick Algebra
Review” 1993 John Wiley & Sons, Inc.