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How do I solve this expression?

I have the following expression:
6a/(2x+8)3+a

My problem is that I don't know if I should solve it as :
        6a                                6a
_____________    or     _______________ * 3+a
  (2x+8)3+a                      (2x+8)

How am I supposed to know which one is correct?
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NevSoFly
Asked:
NevSoFly
1 Solution
 
Dan CraciunIT ConsultantCommented:
Operator precedence. /* comes before +-

HTH,
Dan
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aburrCommented:
I think that neither of your suggestions is correct. The expression is ambiguous.
I would try
   (6a/(6x +24))+a
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NevSoFlyAuthor Commented:
your right there is no way to know with just the straight text.  Thx!
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ThomasMcA2Commented:
There is a way to know "with just the straight text" because every math expression has an order of operations that defines the order that each sub-expression gets processed.

Because of those "ordering rules" your example gets processed like this:
    6a
__________ + a
 (2x+8)3

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NevSoFlyAuthor Commented:
ThomasMcA2,

could you please explain to me exactly how you came up with the expression that you did given the order of operations?
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ThomasMcA2Commented:
In the United States the acronym PEMDAS is a common mnemonic to help remember the order. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Following that order for your problem { 6a/(2x+8)3+a }, the parentheses must be evaluated first. Since there is nothing inside the parentheses that can be simplified, the "times 3" that is outside the parentheses comes next, which simplifies to this: { 6a/(6x+24)+a }.
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NevSoFlyAuthor Commented:
I see where I started to go wrong.  After I couldn't simply what was in the Parentheses I restarted at the beginning of the expression, basically I did PEDMAS instead of PEMDAS.  But how do you determine if it should be :
        6a                                6a
_____________    or     _______________ +a
  (6x+24)+a                      (6x+24)
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ThomasMcA2Commented:
Because addition and subtraction are always last. So when you do the multiplication and division first, you get "something plus 'a'."

In other words, trying to change the problem to "6a over something" is merely adding to the confusion. If you do it in-line, you get this: { 6a/(6x+24)+a } which clearly does not have "+a" in the divisor.
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