Question 474634: What are the steps of the order of operations? Why is it important that you follow the steps rather than solve the problem from left to right?
Write an expression for your classmates to simplify using at least three of the following:
Groupings: Parenthesis, brackets, or braces
o Exponents
o Multiplication or division
o Addition or subtraction
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Steps are: parentheses, exponents, and other composite functions take precedence over other operations, followed by multiplication/division, followed by addition/subtraction (hence, PEMDAS). It is important so that mathematicians have a clear way of defining each equation, e.g. if 5 x 3 + 7 and 5 x (3 + 7) were both done left to right, then there would be no easy way to define 5 x (3 + 7) (except maybe (3 + 7) x 5) but we don't want to do that for a complicated problem.
I say "other composite functions" because exponents are not the only one (here I will use a factorial as an example of a composite function). Suppose we want to evaluate
 + (2+2)! - 3)
We can still go from left to right, but follow the order of operations. 2^(3+1) is the same as 2^4, or 16. 16 + 4 = 20, 20 times 5 is 100.
Next, we have 2+2 is 4. The exclamation point denotes an operation called a factorial (something you'll learn in combinatorics), in which the factorial of a positive integer is simply the product of it and all other positive integers less than it. So 4! = 4*3*2*1 = 24. 100 + 24 = 124.
We subtract 3, 124 - 3 = 121 to get our final answer.
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