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.

John

Sep 08, 2013@ 19:35:36Ok. I totally understand everyone’s confusion. Here is what the order of operations says: (my credentials. Master’s in math, several years of teaching and tutoring. I AM NOT WRONG here so do not try to argue any further.)

multiplication and division take the exact same spot in the order of operations (because division is just multiplication by the reciprocal. They are essentially THE SAME OPERATION). and you perform them from left to right. When you do 6/2(1+2) you do what’s in the parentheses first (BTW this is how you spell parentheses) so 6/2(3) The person above (Adrian I think) is right. When you just have a number in parentheses, you really don’t need parentheses anymore. There is no operation occurring within them. Yes. You do need to multiply but this can now be written “6/2*3” going from left to right is 6/2 first, then times 3. The answer is 9.

Drew

Dec 31, 2012@ 17:52:59Sorry, but you guys are making rules up. In the rules of Parentheses, it never mentions you must distribute a number, which is multiplication, you simply use it as multiplication. A single number written next to a parentheses is considered multiplication. In fact, distribution is a subsection of multiplication, so in turn, you are contradicting yourself in your own explanation. The fact that there is a website arguing for the wrong answer and people believe it to be true is the reason that the US is ranked 27th in the world in arithmetic and science. You make my job as a teacher that much more difficult.

Brian J.

Dec 20, 2012@ 16:58:15I agree, the parentheses do not go away and the 2 must then be distributed to eliminate the parentheses with leads to the next order of operation which would be 6 divided by 6.

Brian J.

Dec 20, 2012@ 16:59:46I meant to leave this comment under Brianjohnsondesign

A mathematician.

Aug 09, 2012@ 11:41:32Wolfram and Adrian are right. 9. You are wrong.

David

Apr 28, 2011@ 13:02:22Yup, Brian you got me. 5 Semesters of college math and I forgot to distribute. It makes perfect sense if you change the 2 to an x and try and set the equation equal to 1.

adrian

Apr 28, 2011@ 04:24:23as for sources for such a simple math problem. go nuts.

http://math.about.com/od/algebra/a/distributive.htm

http://www.freemathhelp.com/distributive-property.html

adrian

Apr 28, 2011@ 04:19:30Order of operations = Paranthesis, Exponents, Multiplication and Division(“and” being the key word meaning they have equal priority), Addition and Subtraction.

6/2(1+2)= Break it down with PE(MD)(AS)

Paranthesis: (1+2)= 3. So that turns the equation into 6/2×3

Exponents: There are none in this equation

Multiplication and division: Since multiplication and division share the same level of priority you divide first, this is due to the fact that equations are read left to right. So 6/2=3. This turns the equation to 3×3 which I am sure no one will argue against equaling 9

also you people need to understand the fine line between distribution in ALEGBRA(which has letters acting as variables for UNKNOWN integers) and distribution in ARITHMETIC(which is simple math where all integers are KNOWN and accounted for)

It seems like a lot of people do not understand that if there is no variable you do not HAVE to distribute, especially if the number before the parenthesis is already part of another operation. 6/2(1+2) is not the same thing as 6/(2(1+2)). and even if the equation WAS 6/(2(1+2)), you still would NOT have to distribute since (2×1)+(2×2) is the same shit as 2x(1+2) . That is why 6/2(1+2)=9 and 6/(2(1=2))=1. I really can not think of any clearer way to explain this.

Netmajic Social Media

Apr 28, 2011@ 12:15:54You made one critical mistake.

“6/2(1+2)= Break it down with PE(MD)(AS)

Paranthesis: (1+2)= 3. So that turns the equation into 6/2×3”

You broke down (1+2) into 3. Okay… Where did the parentheses go? You don’t think you need them anymore??? Is that a math law, that you can just get rid of them when you feel like? I don’t think so. The equation does NOT turn into 6/2×3. It turns into 6÷2(3). Oh look, parentheses! There they are. So… We don’t just get rid of important aspects of the equation, huh? They were there the whole time, and you cannot get rid of them.

Thus left to right doesn’t matter, because we haven’t gotten down to multiplication and division. We are still at parentheses.

Brandon Brewer

Oct 10, 2012@ 20:30:18so by what you are saying we are left with 6/2(3) …ok..whats IN the parenthesis …3! so now that is solved parenthesis go away…and you have 6/2*3 ….parenthesis in pemdas only encomopasses what are in the parenthesis…its not parenthesis and everything next to it thats not in parenthesis.

brianjohnsondesign

Oct 10, 2012@ 21:39:07“parenthesis in pemdas only encomopasses what are in the parenthesis”

That’s not accurate. Parenthesis are often used to denote multiplication, often with a single number contained within them at the start of the equation. They still go first, and that’s because they have parenthesis around them. They do not go away once the equation within them is solved, they are still there to indicate that it needs to go first.

Brian J.

Dec 20, 2012@ 18:18:11When parentheses stand alone with nothing in front of them, they still have a number in front of them, 1. So therefore, when they stand alone, without a number in front, they would be solved simply by solving what is inside of the parentheses, but when a number is directly attached to the parentheses, that number becomes part of that expression and the only way to eliminate parentheses is to distribute that number through it. Once this operation is done, then the rest of the operations may be performed. If one is to solve this to get 9, they are rewriting the formula as 6(1+2)/2 because essentially they are separating what is in parentheses from the 2, but what order of operation gives them the ability to do so?