Order of Operations

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September 20, 2005

Dear Student,

The Order of Operations is not one of the hardest, nor is it one of the easiest things that you will have to learn in Algebra and other mathematical classes. To begin in learning the Order of Operations, you must follow the steps, hence the "order" of the operation. To start off, the first step would be to do anything that is inside of grouping symbols ([ ], ( ), { }). Next you would have to do powers from the left to the right (9 squared). Following the Order of Operations, the next phase of a problem would be to do all of the multiplication and division from the left to the right (*, /). The final stage in the Order of Operations is to do all of the addition and subtraction from the left to the right (+, -). Now, you just have to finish by putting it altogether and finding the answer.

Example-
3*6(35-3+5)10squared
1)First do
anything inside3*6*37*10squared
grouping symbols.

2) Next you do powers3*6*37*100
from left to right.

3)Now multiplication 66,600
and division from the
left to the right.

4)Lastly you would do
addition and subtraction
but this problem doesn't
have any.

Above is an example of how the Order of Operations works. It should always be done this way. An example of someone doing it the wrong way is below:

3*6(35-3+5)10squared

1)As you can see18(35-3+5)10squared
this person decided
to go from the left
to the right, ignoring
the steps.

2)They keep going630-3+5*10squared
this way, and calculate622*10squared
the stuff in the
parentheses wrong.

3)They now do the 622*100 =
square of 10, and
multiply it by 622.62,200

As you can see this answer is incorrect, because the Order of Operations was not followed.

I hope my explanation of the Order of Operations will help you understand the basic part of it, but there is much more to come in the future.

Sincerely,
Andy Michaelson
Andy...
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