48÷2(9+3) = ???

[Ibby]

http://knowyourmeme.com/memes/48293

48÷2(9+3) = ? is a math problem that, depending on the order of operations used, leads to two different answers: 2 and 288. It can be a hot topic for debate, and is sometimes used to troll other users because of the argument that can result afterward.

Standard Order of Operations
If one strictly uses the standard order of operations to solve mathematical expressions, the answer to the problem would be 288, which is also the same solution provided by WolframAlpha and Google.
By convention, the order of precedence in a mathematical expression is as follows:
Terms inside of Brackets or Parentheses.
Exponents and Roots.
Multiplication and Division.
Addition and Subtraction.
If there are two or more operations with equal precedence (such as 10÷2÷5 or 7÷2*9), those operations should be done from left to right.
Therefore, the problem “48÷2(9+3) =” would be solved like this:
48 ÷ 2 * (9+3)=
48 ÷ 2 * (12)=
48 ÷ 2 * 12=
24 * 12=
288

However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."
If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).”
But many calculators and textbooks state that a higher value of precedence should be placed on implied multiplication than on explicit multiplication:
Because “5x” is implied to be "5*x," it gets higher priority than "2/5." In this case, "2/5x" would be interpreted as "(2)/(5*x)."
Returning to the original problem, if one utilizes the principles of implied multiplication, then “2(9+3)” gets higher precedence than the explicit “48/2,” and would be solved like this:
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 24=
2
However, there is a lack of consensus on the value of implied multiplication.

[SteveDallas]

Originally Posted by Ibram

Bullshit. Any cites of these calculators and textbooks? I've never heard this.

The root of all this is ambiguous use of the "/" in a single-line context, where properly-typeset multi-line usage would result in either

  2  
----
 5x

or

 2
--- x
 5

Any sensible reinterpretation of one of these into a single line would include appropriate parentheses or other clarification to make it clear how the calculation is carried out. As noted earlier, the entire point of the 48-whatever example is to start an argument.

In fact, I dare say that incorrect interpretation of the fraction bar by bogus separation of terms in numerators and denominators, for example

 x + 5     x     
------- = ---  +  5
   2       2

is a very common student error, and contributes to the misinterpretation of typographical disasters such as we're discussing.