re: Bizarre Math Question and Answer breaks the internet - Sorry if already posted

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Did anyone else get 27?

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"I Did!"

Cal Berkeley prof. on why there is no single answer

ETA

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A problem that hit the Internet in early 2011 is, "What is the value of  48/2(9+3) ?" 

Depending on whether one interprets the expression as  (48/2)(9+3)  or as  48/(2(9+3))  one gets  288  or  2.  There is no standard convention as to which of these two ways the expression should be interpreted, so, in fact,  48/2(9+3)  is ambiguous.  To render it unambiguous, one should write it either as  (48/2)(9+3)  or  48/(2(9+3)).  This applies, in general, to any expression of the form a/bc :  one needs to insert parentheses to show whether one means  (a/b)c  or  a/(bc). 

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Cal Berkeley prof. on why there is no answer

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well i'm an LSU Alum and I say 2.

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Except for the fact that M and D are on the same playing field and you're supposed to go left to right. Same with A and S.

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I think I shite myself a bit deciphering this.

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Cal Berkeley prof. on why there is no answer

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There is not "no answer." Two answers may be "technically" correct, but 288 is a superior answer to 2.

288


48 /(2(9+3)) = 2

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There is no standard convention as to which of these two ways the expression should be interpreted, so,

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I'd like to see what he's seeing.. As far as I understand it there is absolutely a standard convention used to interpret this and it occurs naturally.

It's the most basic form of arithmetic, addition.

You can literally read this problem from left to right.

The whole purpose of PEMDAS is to simplify and shorten problems from addition. If you break it down left to right, while understanding the reasoning, PEMDAS isn't even needed.

First step:
48÷2 is glorified subtraction, a short and neat way of saying that I have a whole (48) and I want it split into 2 halves (24+24), and one thrown in the garbage ((24+24)-24=[24]). I now have 24.

Second step:
24×(9+3). The parentheses specifically say "don't multiply by 9 and then add 3, add 9 and 3 together first." We've acknowledged the fact that order of operations exist, and we are inserting an exception.

This is the only step in which we have specified that the sum of two specific numbers is a single operand so as to fit our problem.

And so we come to step 3:
24x(9+3), or 24x12, or even more specifically 24+24+24+24+24+24+24+24+24+24+24+24.

Which equals 288.

The entire problem can be rewritten in it's longest form using only addition as 48+(-24)+24+24+24+24+24+24+24+24+24+24+24=288.

The order of operations is naturally ocurring because, simply put, all of PEMDAS aside from parentheses is addition.

5^3 is short for 5x5x5, 5x3 is short for 5+5+5. Division is a form of multiplication and subtraction is a form of addition.

One operation always follows the next unless we specifically create a scenario in which it does not in parentheses.

Arithmetically speaking, the positioning of the operators is what locks the order, but once you properly break it down to addition it doesn't matter if you read it right to left from the bottom up, you're getting 288.

Now I think I'm done with all math for a good while...




tl;dr I may have to disagree

So left to right never comes into play? IYO, 5-2+3=x can be calculated accurately in any direction? Or would you say it's written wrong because it lacks proper notation beyond the fake implicit rule of left to right?

If you use order of operations you easily get 2.