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Why do we need the order of operations?

What is the order of operations?

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http://www.mathsisfun.com/operation-order-pemdas.html

many webpages give the reason why, and show how to follow the correct sequence.
Here is one ...
http://www.purplemath.com/modules/orderops.htm

What is the only order of operations that does NOT proceed from the left to the right

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