Understanding Order of Operations

The first question I ask every algebra student I work with is "how do you feel about order of operations?"  A thorough understanding of these rules is vital to successful experience in algebra as well as subsequent courses like calculus.  Most of us were taught the mnemonic "please excuse my dear Aunt Sally," or to simply remember "pemdas."  The general interpretation of these mnemonics are in order:  parentheses, exponents, multiplication, division, addition, subtraction.

I ask all of my algebra students to solve the same problem


There are two valid methods for solving this problem for the only correct answer which is x=9.


The first method is to take care of the quantity within the parentheses first


Now the equation reads


The next step is the critical step; you must simplify this equation from left to right


The new equation will then read



The common mistake with this problem is to simplify the quantity within the parentheses first.


The equation then reads


The common mistake in this case is to complete the multiplication before the division


This method is invalid because the simplification must occur from left to right.  In this method the simplification began in the middle of the equation which defies the order of operations.


The second method is to take care of the division first


The new equation then reads


The next step is to simplify the quantity within the parentheses


The equation now reads 3(3)=9 .


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