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Math question (order of operations)
This popped up in my Facebook today.
61X0+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) 60+1=7 The other half of the people say that sans brackets or parentheses you go left to right. (61)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.
(We learned it PEMDAS  Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) Last edited by WhyNot; 09022012 at 01:17 PM. 




To further confuse people, it's BEDMAS in Canada...





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.
What is "0.o.0."? 




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. 




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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. Last edited by Indistinguishable; 09022012 at 05:30 PM. 




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Okay...in the system of people who didn't pay attention in prealgebra class when they were 11. Better? 




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 lefttoright 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!
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They never taught me PEDMAS, and it would've save me a lot of trouble had ever since first grade.
Of course, using the initial letters should have occurred to me by second grade. My very educated mother just served us nine pickles. 




I could adopt any arbitrary order of operations I want but it would be useless for communication if nobody else used it. What order of operations that is actually used by anybody would yield an answer of 1?





Lefttoright order.





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On Google, "BODMAS" returns about 220,000 results, against 17,000 for "BOMDAS" and 6,000 for "BIDMAS" so I suspect "BODMAS" is fairly common. For example: http://mathsisfun.com/operationorderbodmas.html 




At least as far back as Windows 3.1, Windows calculator has had a "Standard Mode," in which it behaves like a basic calculator and uses lefttoright order, and a "Scientific Mode," in which it behaves like a scientific calculator and follows the rules for the algebraic order of operations.










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Some calculators and programming languages. There is a picture going around the tubes showing four calculators giving four different answers to the same problem. When in doubt, use parentheses.





This discussion reminds me of my first math class in college, which was the first class I ever had where we were allowed to use calculators (calculators were forbidden in math classes when I was a lad). On the first day of class the teacher was telling us how to choose a calculator. He said to punch in something like 1 + 2 * 3, and if the answer it gives is 9, don't buy it.
On a side note, he said the reason we were allowed to use them in college was that by the time we graduated high school we should already know how to do basic math by "brute force". 




The OP is not, strictly speaking, a "math question". There is nothing inherently, objectively, "right" about the widely adopted order of mathematical operations, it is a convention, nothing else. It's not "math", it can't be proven. In any case, relying on this, both casually and in stuff like programming, is not a good idea. When I code, I always disambiguate with parentheses.





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Would you mind crossposting your comment to the current thread on mnemonic sentences? Last edited by Leo Bloom; 09032012 at 03:39 PM. 






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The display will show as follows: type 1, display shows [ 1] type +, display shows [ 1 +] type 2, display shows [ 2 +] type +, display shows [ 3 +] type 3, display shows [ 3 +] type =, display shows [ 6] 1 + 2 X 3 = yields this: 1 [ 1] + [ 1 +] 2 [ 2 +] X [ 2 X] 3 [ 3 X] = [ 7] 




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A term (in the sense of elementary algebra) is a product of variables and scalars; this exists as a concept independently of how you choose to notate it. Lefttoright vs. conventional orderofoperations has no bearing on this. Similarly, in left to right order, the equation you intended would instead be written 3 * 2 + 5 = 5 + (2 * 3), expressing the same true fact. Nothing is lost; it's just notated differently. Yes, parentheses would come up, just as they come up when you want to indicate certain things under the current convention. (You can eliminate parentheses altogether if you move away from infix notation [e.g., if we notated addition and multiplication the same way we denote general functions, we'd write +(*(3, 2), 5) = +(5, *(2, 3)), or, just as well, + * 3 2 5 = + 5 * 2 3, as the parentheses and commas would no longer be necessary. Perhaps ideally, we'd write things in their direct tree form, rather than linearizing them...], but if you cling to infix notation, you're stuck with these conflicts of precedence, and whatever convention you pick for deciding them, you will sometimes want to move away from its default) Last edited by Indistinguishable; 09032012 at 06:24 PM. 




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I was told the O of BODMAS stands for "of", and was equivalent to multiplication, but I suppose it is really just there for pronouncability. (At that stage of things, I don't think we had been introduced to the term "exponent" at all, though we probably knew about "powers".) Last edited by njtt; 09032012 at 07:06 PM. 




48,000 Google hits for BEDMAS, which is what I was taught in New Zealand.
The only other order of operations convention that I know of is Polish notation, where the operators are placed to the left of the operands. So 1+2 in conventional notation is expressed as + 1 2. But the equaiton in the OP doesn't make sense in Polish notation. 




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Remember, to create Polish notation, just follow the usual "function(argument1, argument2, etc.)" convention in math, then remove all the (superfluous) parentheses and commas. (Or, in other words, write the expression tree, and then transcribe it in preorder traversal) So the OP's 6(1*0)+(2/2) would become +((6, *(1, 0)), /(2, 2)) = +  6 * 1 0 / 2 2. And the OP's (61)*0+2/2 would become +(*((6, 1), 0), /(2, 2)) = + *  6 1 0 / 2 2. [For reverse Polish notation, you do the same thing, but with function names coming after their arguments (i.e., the expression tree in postorder traversal). This is natural in programming because this reflects how computation actually proceeds: first you evaluate the arguments, then you apply the function to them, eventually evaluating the whole expression this way from the bottomup. So in reverse Polish notation, the OP's 6(1*0)+(2/2) would become 6 1 0 *  2 2 / +, and the OP's (61)*0+2/2 would become 6 1  0 * 2 2 / +] Last edited by Indistinguishable; 09042012 at 01:19 PM. Reason: My favorite convention? Just write the expression tree qua tree, and don't worry about linearizing it... 




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Last edited by lisiate; 09042012 at 05:05 PM. 






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I am guessing that they resolved the multiplication and division: 6  1X0 + 2/2 becomes 6  0 + 1 But then carried forward with addition before subtraction: 6  0 + 1 where the addition resolves to 1, leaving 6  1 = 5. 




Really? OoOps is what? 2nd or 3rd grade? If an adult did not know basic primary school English most people would say that's idiotic





Good to know after 3 years we finally got that conundrum resolved.





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Some pedants will try to claim it's an absolute violation of the laws of English grammar (which don't really exist either, but that's a separate matter) while others will take the more sensible and historically sound argument that sentence ending prepositions occur all the time. As mentioned ad nauseum at this point, there's no "Academy of Mathematics" that determines absolute rules. We have a few rules of thumb, enforced by nobody in particular, to reduce ambiguity in expressions. But ambiguity still exists. The "correct" response to this sort of ambiguity, which is not actually addressed by the usual order of operations lessons and if there is a "correct" response at all, is not to blindly rely on nonexistent rules but to ask for a clarification from the writer and to gently chide them for writing such an ambiguous expression in the first place. An equally acceptable but less predictable course of action is to ask your arithmetic teacher the class policy, because the deliberate use of this type of ambiguity is generally as a lesson to a class  in this particularly case a lesson that is unnecessary as the better lesson is to avoid such ambiguities entirely in actual practice. Last edited by Great Antibob; 03222015 at 12:22 PM. 