There's this question going around, that reads "6÷2(1+2)=?"

The possible answers are one (1) and nine (9). What do you guys get?

I got one, as per the Distribution Property & PEMDAS. The most common answer is nine at the moment.

It comes down to how you interpret the implicit multiplication. If implied multiplication is higher precedence than explicit division, then you get 1. Otherwise, strictly following OOP (expanding the implied multiplication) you get 9.

It's a math troll, really.

Related: 48/2(9+3)=?

The answer is 9

Is it? Aren't you suppose to distribute first, so 6/2(1+2) would be 2+4 then it'd be 6/6 which is one; that's how my computer interprets it as well.

souvik, what value does your computer return? Also, Google gives nine as well.

To repeat everyone else, it comes down to whether you interpret it as 6/2*(1+2) (which equals 9) or 6/[2*(1+2)] (which equals 1).
Implicit multiplication, according to what I've been taught, has no more or less precedence than explicit multiplication. Hence, 9.

This is actually really interesting. Isn't there a real-world example that could be used to verify one answer as correct?

No, it could be (6/2)*(1+2) or 6/(2*(1+2)).

In general though...multiplication and division have the same precedence, as do addition and subtraction. To resolve precedence equality you should read left to right. Any programming language that I know of will tell you the answer is 9.

I've always read PEMDAS as:

Parentheses,
Exponents,
Multiplication and Division (either one as encountered when scanning from left to right), and
Addition and Subtraction (same as above).

If you want your colleague to understand that by writing a/b*c, you actually mean a/(b*c), then that's why parenthesization has been made a convention. Or perhaps I should up make a new rule English in where the reader is expected to know to place the after preposition the word which precedes it thought in, which about makes much as sense. I'm sure I screwed that up. The point remains.

Edit: "Or perhaps I should up make a new in rule English where the reader is expected to know to place the before preposition the word which precedes in it thought, which as about makes much sense." Nailed it.

"distribute" is not a math operation, so no, you would not distribute first.

http://en.wikipedia.org/wiki/Order_of_operations


Implicit or explicit, it is still multiplication and has the same precedence as division.

The answer is thus unambiguously 9. Anyone who thinks it is 1 is simply wrong.

PEMDAS. Parentheses first, so 6/2(3). Implicit multiplication is multiplication. 6/6. It's 1.

multiplication and division have the same precedence, so you operate right to left. 6/2(3) = 6/2*3 = 3*3 = 9

Been a while since you took a math class or what?

Since when do multiplication and division have the same precedence? It's PEMDAS, not PE(MD)(AS)...

Since always. Mnemonics != rule. Go read *any* math textbook and you'll see mult & div have same precedence.

Seriously been a *looong* time since you've done basic math, huh?

http://www.wolframalpha.com/input/?i=6%2F2%281%2B2%29

Souvik made the excellent point that multiplication and division are in some sense the same thing, which for a odd reason did the trick for me. Of course it's been a long time since I've done basic math requiring proper interpretation of grouping of multiplication and division to yield a correct answer; everything is either simple everyday math or something I plug into Matlab / my calculator.

This has been amusing. "6÷2(1+2)=?"
6/2(3)
6/6
=1
The problem seems to be that there is multiplication and division but the parenthesis are always first. The individual probably sees the 6/2 before they recognize the 2(1+2) as having precedence. I would assume that this is supposed to be a trick of the mind.
I do not think that you are right and if there is some proof of this I would like to see it. 6/2(1+2) is the same as 6/2x. Solve for X=(1+2)=3. So 6 would be divided by 6. I do not see how you could look at this any other way.

the point is that 6/2*3 is ambiguous, and these guys are claiming that because multiplication and division have the same precedence, that you evaluation left to right, hence first 6/2 = 3, then 3*3 = 9.

Yes, and I would agree that 6/2*3 is 9.

But you wouldn't agree that 6/2(3) is 9, then? You don't agree that implicit multiplication is the same as explicit multiplication?

Basicman: put 6/2(3) in your calculator. What does it say?