UPDATE 11/10/2011: There is a new problem going around that is as follows: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 – 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 = ? This problem is a whole lot easier and less debatable, and so I am absolutely shocked that the vast majority of respondents are so horribly wrong. It actually makes me sad for humanity. Anyone who took 6th grade algebra knows the order of operations. Multiplication comes first. So the “1 x 0” portion goes first, making it of course 0. Then you add and subtract all the rest, resulting in 14. Basic. SUPER basic. So why exactly are people getting it so wrong? I have absolutely no idea. It is sad.

The answer is 14.

UPDATE: A crushing argument has finally arrived that is seemingly incontrovertible. It was brought up that wolfram would show that the answer is 9, when you plug in the equation. Which is true. It was argued that Wolfram is infallible. But is it really?

The arguer went on further to put the equation a different way. Instead of (1+2), let’s say it is x. So x=1+2. That would make the equation:

6/2x=?

Let’s enter this into Wolfram and assume the answer is 1. We did it here.

What happened? X=3. Wait a second… But 1+2 = 3… Just like in the original equation… But that means… THE ANSWER REALLY IS 1???

Dun Dun Dun… It’s true. Wolfram gives conflicting answers, proving the fallibility of technology in solving ambiguous problems.  As far as I can tell, the program is not using parentheses correctly in the order of operations. They should be as highly ranked or more than variables, but they aren’t. Interestingly, when we do the exact same equation but with the x in parentheses (which should be the same), it gives the answer of 9 . Interesting stuff

The new Facebook feature in which users can post their own questions and have their friends answer has actually begun to pick up lately. Today, I came across a question which over half a MILLION people had answered. It was a math question. And as far as I can tell, most people got it wrong. Here is the question:

6÷2(1+2)=?

Now clearly there is something unusual about this question. It is in a format rarely seen, and with good reason. The order of operations in extremely ambiguous. Most people said the answer was 9. But is it? Lets read about the order of operations. Every operation is ranked, with the highest ranked operations going first, followed by the lower ranked operations. Most people remember “PEMDAS,” which stands for “”Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction””. That is the order in which operations must go.

So according to that order, here is what happens:

6÷2(1+2)=?
6÷2(3)=
6÷6=

1

The answer is one. Parentheses come first, even when they signify a multiplication. Purplemath.com, a popular online math information site,  illustrates this example on this page: http://www.purplemath.com/modules/orderops2.htm. They go through this problem and illustrate the correct method:

    • Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.

16 ÷ 2[8 – 3(4 – 2)] + 1 
= 16 ÷ 2[8 – 3(2)] + 1
 
= 16 ÷ 2[8 – 6] + 1
 
= 16 ÷ 2[2] + 1   
(**) 
    = 16 ÷ 4 + 1 
= 4 + 1
 
5

The ironic thing is that many involved in the discussion are citing “PEMDAS” as the reason why the answer is 9.  One of the highest ranked answers cites this and proof that the answer is 9: http://www.quickmath.com/webMathematica3/quickmath/equations/solve/basic.jsp#v1=6%2F2(a%2B2)%3D9&v2=a

Of course what this girl fails to realize, is that 6/2 is a fraction, which is different than 6÷2. It is calculated differently because a fraction is its own number, not an operation.

Please feel free to share your thoughts about this problem. I don’t think there is any way to show that the answer is 9, but I challenge you to try, and please cite some source as to how that could possibly be correct. 

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