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I need to state I am no mathematician, which, by light of the question I'm about to ask should be evident.

A friend of mine recently asked a group of us what we thought the answer to this simple problem is.

6 - 6 * 0 + 6 / 6

A bunch of us gave the answer as 7, though others came up with 1 as the answer. I came to my conclusion using the meagre knowledge I carried from school, from left to right multiply and divide then add and subtract. No problem, I believed I was right.

I posed the question to another friend who is more mathematically minded than I, who told me that you would just work it out left to right, giving the answer 1.

I am now very confused and would like to know what the real answer is!

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up vote 2 down vote accepted
        terms inside parentheses or brackets
        exponents and roots
        multiplication and division
        addition and subtraction

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Which would mean I was correct... thanks for the confirmation. – David Barker Sep 8 '12 at 12:19

You are correct about the problem. Your "mathematically minded" friend is not correct.

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Thanks Cameron, all the confirmation I needed. I will make a point of telling him he's wrong next time I see him. :) – David Barker Sep 8 '12 at 12:19
Well, to be fair, there are a number of "mathematical texts" (read: textbooks for basic algebra courses) that advocate a left-to-right convention of evaluation for order of operations, so I suppose it's entirely possible that your friend has taken far more mathematics courses than you have taken, but is still operating under the (rather clumsy and problematic) left-to-right method. Also, any calculator without any ability to parenthesize (in some fashion) necessarily operates on a left-to-right convention, so again, it's understandable. – Cameron Buie Sep 9 '12 at 4:58

Those are in fact just conventions that allow us to drop parentheses in many cases. With full parethesification(?) yuor expression would be written $(6-(6\cdot 0)) +(6/6)$ and it therefore evaluates to $(6-(6\cdot 0)) +(6/6)=(6-0) +(6/6)=6 +(6/6)=6+1=7$. Ths is different from what you would calculate after instructions like §Take 6, now subtract 6, now multiply by 0, now add 6, now divide by 6", which corresponds to $(((6-6)\cdot 0)+6)/6 = ((0\cdot 0)+6)/6=(0+6)/6=6/6=1$.

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Parenthesification is a great word! Thank you for the explanation, at least I know I'm not as stupid as I was being made to feel! :) – David Barker Sep 8 '12 at 12:25
Parenthesization is the word you're looking for. – Cameron Buie Sep 8 '12 at 13:14

answer is 7.

The priority of solving math expressions is 1st: Multiply or Divide (whichever comes first from right to left) when all operations on multiplication and division are done then move to 2nd priority. 2nd: Add or subtract (whichever comes first from right to left)

6 - 6 * 0 + 6 / 6 6 - 0 + 1 7

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