Correct me if I'm wrong, but if a number is next to a variable isn't it then considered a coefficient? Then it has no relevance to this. This is a simple order of operations problem with natural numbers, no variables or the like.
I got 9. 6/2(1+2). You do the parentheses first. I don't think you can use the distribution property when the thing next to the parentheses is a expression, not a single number. But I could be wrong.
I got 9. The parentheses did throw me off at first but remember, parentheses with one number are shorthand for multiplication. Left to right. LEFT2RITE DERNIT
Coefficients is a term used for a different purpose. (polynomials mostly?) Coefficient - Wikipedia, the free encyclopedia If I am not mistaken, in our equation, 6, 2, 1, 3 are all coefficients and together are called the constant coefficient since they do not affect a variable, or rather we have a polynomial with no variable and a constant coefficient of 1 (or 9). LOL. Multiplication by juxtaposition relates to order of operations because some mathematicians consider it a higher ranking than normal multiplication and division, or as I like to say it: there is an implicit parentheses when you use multiplication by juxtaposition. And you're right in the sense that multiplication by juxtaposition is most frequently used in variables, i.e. 5x, 6xy, xy, etc. However, many would argue that 2(3) is also an expression of multiplication by juxtaposition - as it is simply putting two numbers together to express multiplication. So, to reiterate, 2(1+2) can be considered a multiplication by juxtaposition and can be implicitly interpreted as (2(1+2)).
Here's mah logic. 6/2(1+2) = 6/2(3) = 3(3) = 9 The answer would be 1 if the equation were 6/[2(1+2)] 6/[2(1+2)] = 6/[2(3)] = 6/6 = 1 The parentheses are everything.
I have seen multiple debates rage over this problem, and I'm tired of it. This problem is not worth arguing over because it is intentionally ambiguous. If it were intended to actually test your math skills, it would be written as either "(6÷2)(1+2)" or "6÷(2(1+2))". As it is, it is made only to cause debates like that. Intentional ambiguity has no place in mathematics, and I'm not going to encourage it by using my knowledge of/education in math to debate it.
>>>Intentional ambiguity has no place in mathematics, and I'm not going to encourage it by using my knowledge of/education in math to debate it. But it has EVERY place on social networking sites, where people can draw lines in the sand, proclaim their allegiance to everything and nothing. (Backstreet Boys or N'Sync?), and argue like beta fish in teacup over their position. And that's REALLY what this "mathematical problem" is all about. Lex
^ Exactly. However, I say 9. The rule about implied parenthesis is just a POSSIBILITY. Everything else is fact. Fact > Possibility. 6÷2(1+2) 6÷2(3) 3(3) 9
I think (THINK!) this debate stemmed from the confusion on the ranking of 'multiplication by juxtaposition' (multiplication by putting two numbers together). And it is confusing, because different math books will use different references. And I actually like this debate because it creates awareness that it is ambiguous and would urge people to verify instead of assuming. It can actually be very critical beyond social networking debates. Suppose that 6/2(1+2) was like a critical message given for a rocket launch (use your imagination!). Instead of assuming it to be 9, we would now clarify with the sender as he/she could very well mean 1.
What is a coefficient? "A coefficient is a number in front of a variable." coefficient - definition of coefficient by the Free Online Dictionary, Thesaurus and Encyclopedia. "A number or symbol multiplied with a variable or an unknown quantity in an algebraic term, as 4 in the term 4x, or x in the term x(a + b)." So, yes, if it were 5x the 5 would be a coefficient. As far as I know, yes you would assume to multiply 5 * x anywhere it is located in the equation. But we're getting off-topic with that part, so moving on. After a bit of fun googling, I came across this: Math Forum - Ask Dr. Math tl;dr : Neither of us are correct Though I still like to stick to the results of the C++ program, despite what the guy says at the end of his email.
Yes, that is indeed one of the sources that I gathered my information from and I definitely encourage people to read it if they want a better idea of the topic. And like I mentioned earlier, the crux of this debate should not be to determine if the answer is 1 or 9, it should be to debate if multiplication by juxtaposition has precedence. And as at present, it seems that this is still a debate, and there are no consensus within the mathematics community. Tying back to my VERY FIRST POST (hmm maybe I am a little bitter), "different mathematicians will have a different say on whether the implicit brackets are there when the shorthand (multiplication by juxtaposition) is used", hence the answer can be 1 or 9. Which is why I feel that the moral of this debate is that when encountering such a situation: CLARIFY! VERIFY!
I find it ironic that the entire ambiguity arises from the advent of printed media. The obelus wasn't used for division prior to the mid 17th century. The entire argument should revolve around why, in the age of the internet and sophisticated word processors and printers, we continue not to have easy to use equation editors built into basic text inputs.
We are not concerned with what the Oompa Loompas of science think. (BIG BANG THEORY reference) :icon_bigg http://www.youtube.com/watch?v=owk-zZt1y04
The mathematical symbology or syntax is a universal language that has a standard. Based on the most unambiguous standard, the answer is 9. Now, all those other interpretations of the scope of the denomenator in this equation are based on nonstandard or proprietary symbology, and is thus inferior.
My math classes say it's 9. Google says it's 9. Facebook says it's 9. Since we read left to right, i figure math is probably done the same way. And yeah, multiplication and division are of equal importance,even though the "M" comes first. So.... 6/2(1+2) 6/2(3) 3*3 ****9***** YAY MATH!
There was a similar question going around, where the solutions were either 2 or 288. Although I can't quite remember the actual question. But anyway, it was set out like this: 6 ________ 2 (1 + 2) In which case the second set of brackets isn't actually there, but it is implied. So the answer really would be 1. However, yes, 6÷2(1+2) is different in that there would be only one set of brackets, and so the answer would be 9. There's also the following argument (not my ideas): Although this still comes to 1, it is derived in a slightly different way. I'm assuming that you added the 1 and 2 to give 3. Hence 2(3). This is multiplication written using brackets. However, the above argument states that 2(1+2) is a single, algebraeic statement, and so the 1 and 2 aren't added together. I'm reasonably sure that every instance of this minor language issue won't actually change the final answer, only the final answer is calculated in a rather different. There's probably a formal proof to it somewhere, though. ---------- Post added 5th May 2011 at 10:24 PM ---------- Oh hang on, as I often am in maths, I'm wrong with regards to my second point. Those who consider 2(1+2) to be a single, algebraeic statement that must be broken up with the same priority as brackets, despite essentially using multiplication, will end up with: =6 / (2X2 + 2X1) =6 / 6 =1 On the other hand, those who consider 2(1+2) to require addition of the 1 and 2, and then it is simply multiplication described using brackets, will arrive at the above here. So yes, this difference does matter, I think? It's hardly advanced maths, but I'm really not familiar enough with axioms to come to a conclusion, so I'm on the fence about this. And I've realised that I've just reiterrated things that've already been said, oops.
