The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Why does PEMDAS work?

Date: 7/9/96 at 14:29:37
From: Anonymous
Subject: Why PEMDAS?

Dear Dr.Math,

I am having trouble with a few problems that involve PEMDAS 
(Parentheses, Exponents, Multiplication, Divison, Addition,
Subtraction). The real question I have is why does this order of 
operations really work?

Thanks a lot, 

Date: 7/9/96 at 17:45:7
From: Doctor Ceeks
Subject: Re: Why PEMDAS?


When you ask "why does this order of operations really work?", you
are asking something which suggests a slight misunderstanding about

The order of operations in which one is to interpret a mathematical
expression such as "2+3 X 5" is a convention. This means that a long 
time ago, people just decided that the order in which operations 
should be performed should be such and so.  It has nothing to do with 
magic or logic.  It's just that some people decided to adopt a way, 
and it has stuck ever since.  It just makes communication a lot 

It's just like asking, "why is it that when I say 'cow', people tend
to conjure up an image of a beast in a field, possibly with spots?"
Well, it's because a long time ago, someone decided to call that beast
a cow. Now, everyone who speaks English knows this and so if you want
to make someone think of the big beast, you just have to say "cow" to efficient! It has nothing to do with the poor little
grass eating just has to do with what people have agreed
upon to make communication with each other a little easier.

So the answer to your question is that it works because you're just
learning how to interpret math formulas the way people have long 
decided to interpret them.

Now, if you're having trouble learning the order of operations, then
you have to remember that you're not having a problem with mathematics
(unless you're getting wrong answers because you're adding 
incorrectly). What you're having trouble with is learning a 
convention, like learning the grammar of a foreign language. Because 
it's just a convention, learning it is just a matter of practice, 
practice, practice. Start slowly and carefully. Eventually you'll 
have it memorized.

-Doctor Ceeks,  The Math Forum
 Check out our web site!   
Associated Topics:
Elementary Number Sense/About Numbers
Middle School Algebra
Middle School Number Sense/About Numbers

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.