This popped up in my Facebook today.
6-1X0+2/2=?
Half of the answers say the correct answer is 7 as you do the order of operations with multiplication and division first giving you:
6-(1X0)+(2/2)
6-0+1=7

The other half of the people say that sans brackets or parentheses you go left to right.
(6-1)X0+2/2=1
My algebra classes were a loooong time ago, and I’m flat not sure of the correct answer. My first thought was the the latter of the two methods was correct working left to right, but I am not sure.
So mathematical dopers, what is the correct answer?

The usual order of operations is BODMAS (in the UK) or PEDMAS (in the US):
Brackets, Orders, Division, Multiplication, Addition, Subtraction
Parantheses, Exponents, as above.

So 6 - (1 x 0) + (2 / 2) is right, which gives you 7.

Yep, 7. Not having parentheses doesn’t mean you throw out all the other order of operations, just that you start with exponents. Not having exponents doesn’t mean you throw out all the other order of operations, just that you start with multiplication.

I’ve always wondered this about these threads: Are you guys just abbreviating for the Internet, or do you actually pronounce the word “Pedmas” in your head when you do math? I mean, was there actually a teacher somewhere in your lives that was like “Remember, kids, always follow pedmas when you work out arithmetic.”?

Because I of course learned O.o.O. in grade school, but until last years I’d never once heard of “PEDMAS” or “BODMAS” or any of these words.

I say “pedmas”. I learned that mnemonic trick only recently on this forum. I don’t remember learning such a trick in school. I say “pedmas” because I can easily remember it by thinking of a pedophile Christmas. The absurdity and offensiveness makes it stick in my head.

I’ve heard PEMDAS, not PEDMAS. You know, “Please excuse my dear aunt Sally” or similar.

But really, it doesn’t matter, as some have hinted. The order is P E (MD) (AS). Meaning you don’t distinguish between * and / or + and -, they are treated the same, left to right. In what system would the answer be 1? I understand some calculators do some funky things.

Yeah sqrt(4) = 4^0.5, so radicals aren’t very necessary to note.

o.O or O.o is Internet speak for a sort of befuddled or surprised expression. Therefore, 0.o.0 is obviously a triclops.

Radicals written with the usual notation don’t need any special indication for order of operations, any more than fractions written vertically or cosines or binomial coefficients or the power (though not the base) in exponentiation or other such things… They explicitly indicate where their arguments start and stop (for radicals, the one argument is under the top line of the radical sign, the other is slightly raised and to the left of it); there’s nothing left for “order of operations” to do.

For what it’s worth, even though it is of course manifestly reasonable to call this a “math question”, it still (unreasonably) irks me to do so… It’s not really about mathematics, per se. Order of operations is a purely notational ambiguity, and it’s only because we happen to have chosen this infix notation for + and * and so on that we have to bother with it. Had we chosen different ways of putting marks on paper to express our ideas, none of this would have come up in the first place. It has nothing to do with the mathematical content it is introduced in connection with; it is just syntactic parsing.

I’ve never heard of any of these acronyms (PEDMAS, etc.), but they do accurately represent what I was always taught many moons ago.

As for the alternate approach, just going left to right: there is nothing inherently wrong with that, other than the fact that it is different than the accepted standard. If left-to-right *had *been the standard all along, everything would work out just fine. As long as the person writing the equation and the person reading the equation had used the same standard.

Oh, geez—when you mentioned the order of operations and Facebook, I thought you were going to be asking about the problem that spawned this multipage thread!

If you enter this into a basic, “four-function” calculator (i.e. the simplest and cheapest kind), it’ll simply do all the operations from left to right, giving an answer of 1. If you enter it into a scientific calculator (or a graphing calculator), it’ll know about the rule for the order of operations and will do the multiplcation and division before the subtraction and addition, giving you an answer of 7.