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the number next to the parenthesis, 2(1+2), is an implicit way of writing 2*(1+2) , which would behave according to the standard order of operations. people may be confused because they remember the distributive property from algebra, which says that x(1+2) = 1x+2x ; but if you apply the distributive property to this equation as written (6÷2(1+2)) you are violating the order of operations (which are the social construct). In order for the distributive property to apply you would need another set of parentheses: 6÷(2(1+2)).
the "/" does make it more ambiguous from a computer text standpoint. with pencil and paper you can clearly draw the numerator/denominator. On the computer, most mathe programming languages (matlab, python) require explicit mathmatical operators. if I typed 6/2(1+2) into matlab, I get an error. if I type 6/2*(1+2) I get 9.
I could get 1 is if you have 6/(2*(1+2).
as written though, it may be tricky, but the answer unambiguously 9 if you know how to apply your order of operations.
My argument is that when you use the obelus, it delineates what follows as the entire denominator, and is an implicit way of writing 6/(2(1+2))
My argument is that when you use the obelus, it delineates what follows as the entire denominator, and is an implicit way of writing 6/(2(1+2))
Can you provide some documentation that says an obelus is equivalent to a fraction bar? All I can find is that ISO standards say not to use an obelus at all.
My argument is that when you use the obelus, it delineates what follows as the entire denominator, and is an implicit way of writing 6/(2(1+2))
but by that view, 6÷4+2+3 = 6/(4+2+3)
Maybe! Although there’s much less ambiguity about what the component parts of the fraction are in that example. It seems far more likely that your example is supposed to be read as 6/4+2+3.
But! 6÷4*2*3 could very reasonably be read as 6/(4*2*3) imo
He said this after I said my friends were debating the answer:
"ONE Katy
u were probably the right one
: )"
Now I feel like an ass considering I was firmly on team 9
I went down a bit of a rabbit hole yesterday, and found a brief paper that addresses the situation a bit (here - though I dunno if that link will work because I needed to use my ASU libray account for access). but the source is "relating to the order of operation in Algebra" by N.J. Lennes, in The American Mathematical Monthly, 2, Feb, 1917, pg. 93-95.
Important excerpts:
In the case of signs of multiplication and division occur with no signs of addition and subtraction intervening, and in case no symbols og aggregation are used, then it is likewise agreed (in the theoretical development in the books) that each symbol applies only to the face (or divisor) immediately following it, and that the operations are to be performed in order from left to right. Thus, 8 ÷ 2 X 4 = (8 ÷ 2) X 4 = 16, and not 8 ÷ (2 X 4) =1. As in the case of addition and subtraction, it results from this agreement that the commutative law applies to the operations of multiplication and division, while the associative law does not apply, except when teh sign X precedes the group in question. That is, 8 ÷ 2 X 4 = 8 X 2 ÷ 4, but 8 ÷ 4 X 2 is not equal to 8 ÷ (4 X 2). As remarked by Crystal, under these conventions, the associative and commutative laws for addition and subtraction are formally identical with these laws for multiplication and division.( Text Book of Algebra, Part I, page 17.)
Despite laying our these rules, the author then goes on to note that the standard order of operations as we know them is taught and accepted, but in practice "the rule requiring the operations of multiplication and division to be carried out from left to right in all cases, is not followed by anyone." Notably, the ÷ symbol creates the ambiguity, where some people take the whole product following the symbol to be the divisor and there is a distinct lack of consistency in how expressions were written. "In [the aforementioned] Crystal, ÷ u X v is sometimes used to mean (÷ u)v. In such cases, however, the notation ÷ u X v and not ÷ uv is used...he overcomes the difficulty [of ambiguity] by never using the sign ÷ with a product after it. The followers of Chrystal have too often blindly copied his theory, but have not taken pains, as he did, to avoid the inconsistency in usage."
When a mode of expression has become wide-spread, one may not change it at will. It is the business of the lexicographer and grammarian to record, not what he may think an expression should mean (no matter how far-fetched the usual or idiomatic usage may seem), but what it is actually understood to mean by those who use it. The language of algebra contains certain idioms and in formulation the grammar of this language we must note them. for example, that 9a2 ÷ 3a is understood to mean 3a and not 3a3 is such an idiom. The matter is not logical but historical.
so, just like "literally" not longer means "without exaggeration" anymore because of common usage, the strict mathematical interpretation of the ÷ symbol changed because of widespread careless usage. Very string mathematical parsing would give the answer as 9. widespread historical (mis)usage created the ambiguity.
In modern usage though, I think it is very hard to argue that the answer is 1. the ÷ symbol is obsolete (ISO 80000-2). It has been replaced by the "/" symbol. so in the original equation 6÷2(1+2), without a clear designation that 2(1+2) is the denominator, the implicit X would mean the expression is interpreted as 6/2X(1+2). the first step following the standard order of operations would yield 6/2(3). Computers would parse this as 6 / 2 X 3 = 9. Pencil and paper, following the order of operations that says multiplication/division goes Left to Right, the answer would be 9 and not 1. Using the same logic above re: widespread adoption of the meaning of ÷, in the age of digital computation and the widespread conventions adopted by computer programmers/scientists, 6/2(1+2) is (should be) understood to be 9.
This is pretty fucked up and random. I’ve heard my best friend is black, but your fucking dog? Damn. I don’t like judging people, but when they make it this easy...
I put on my favorite band of all time on Youtube tonight, RHCP, and played all of their official videos in order... an hour or 2 in, we get to the Californication album and "Scar Tissue" comes on and I see John Frusciante's return and I was like... This makes me so happy...
I can’t trust someone who doesn’t use any kind of moisture agent (mayo, mustard, oil/vinegar, etc) on their sandwiches. A dry turkey sandwich may be the saddest single food item I can think of.
Post by 10goldbees on May 11, 2019 10:36:21 GMT -5
This week I didn't realize I was out of cheese until I made a sandwich before work. A turkey and honey mustard sandwich on wheat was the definition of... fine.
I left work early that day to go to the grocery store.
I put on my favorite band of all time on Youtube tonight, RHCP, and played all of their official videos in order... an hour or 2 in, we get to the Californication album and "Scar Tissue" comes on and I see John Frusciante's return and I was like... This makes me so happy...
I can't do RHCP often anymore... but "By the Way" or gtfo
I can’t trust someone who doesn’t use any kind of moisture agent (mayo, mustard, oil/vinegar, etc) on their sandwiches. A dry turkey sandwich may be the saddest single food item I can think of.