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Order Of Operations in Four Steps

Date: 02/15/98 at 12:24:37
From: Fasil Moghul
Subject: Order Of Operation

I need help figuring out what operation to do first. I have heard of 
Pemadas but I do not know what it means. Can you help?

Date: 02/19/98 at 17:02:18
From: Doctor Schwenoha
Subject: Re: Order Of Operation

Not pemadas, but PEMDAS. We have used this acronym for the order of 
operations for a long time to help remember the key words:  

Parentheses, Exponents, Multiplication, Division, Addition, and 

There is a tendency to just remember the words and not remember some 
groupings that occur, though. I have lately been teaching the order of 
operations as a list of 4 things rather than using pemdas.

1. Parentheses - do everything in parentheses first.  
   Go to the innermost parentheses first if there is more than one set 
   of parentheses in the problem. If there is more than one set but  
   they are isolated from each other, then do them independently. 

   If you are dealing with a fraction you should treat the top as if 
   it were in parentheses and the bottom as if it were in parentheses 
   even if the parentheses weren't written in the original state.  
   That's because the fraction bar means division and we'll get to 
   that after we take care of any parentheses.

2. Exponents - After clearing up any parentheses that you can, you 
   should next go to any exponents. Remember that the exponent goes 
   with the thing it is closest to. If it had been closest to a 
   parenthesis sign then you have already cleared up the parentheses 
   before worrying about the exponent. 

   You can treat any square roots as an exponent (you'll learn why 
   in a later math class).

3. Multiplication AND division as you come to it going from left to 
   right - these two operations need to be seen as a team rather than 
   as separate entities. Using pemdas to remember the words is fine, 
   but you have to see the "md" as a connected word.

4. Addition AND subtraction as you come to it going from left to right 
   - again, see the "as" as a connected word.

So, there is the order of operations. The only thing that makes this 
the correct order is that mathematicians all over the world agreed a 
long time ago to do it this way. So no matter if you speak German and 
another person speaks French, you both speak MATHEMATICS and can 
communicate with each other.

-Doctor Schwenoha,  The Math Forum
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Associated Topics:
Elementary Addition
Elementary Division
Elementary Multiplication
Elementary Subtraction

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