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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
Subtraction.

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

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
Check out our Web site  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Division
Elementary Multiplication
Elementary Subtraction

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