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Meh I did 2 out of protest. It only confuses people because of the parenthesis and the unfamiliarity of the division symbol in these kind of constructions, and we were always told to treat the 2(9+3) as an individual unit that had to be multiplied out before one could proceed with the problem at school. So, I just picked one cause I didn't know how to resolve the ambiguity 
Is it not ambiguous though?
Could it not be considered as 48/2 * (9+3) = 288 OR 48 / 2(9+3) = 2 based on the system used to teach the student about ordering, because multiplication and division are treated equally?
Like if I were to write it as 48 over 2(9+3) OR 48 over 2 * 9+3 that would give different answers, and we were certainly never taught whether one or the other was incorrect
I guess we just never learned about the intricacies of the division symbol lol. Oh and I guess that if you just resolve the brackets and don't multiply by the 2, so it becomes 48 / 2 * 12, it makes sense but then I just always thought of the numbers outside of the brackets as being part of resolving them, so extra multiplication symbols would remove the ambiguity. Meh, I got a baller maths grade in school so I'm happy 
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On April 08 2011 08:45 AirportSecurity wrote:
LOL so many weak minded people in this thread
I will admit, my brain broke when I thought of this:
A = xy
B/A =/= B/xy
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On April 08 2011 08:39 Zeke50100 wrote:Show nested quote +On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math.
You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)?
How about 1/2(a+b) versus 1/2*(a+b)?
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On April 08 2011 08:47 jdseemoreglass wrote:Show nested quote +On April 08 2011 08:45 AirportSecurity wrote:
LOL so many weak minded people in this thread I will admit, my brain broke when I thought of this: A = xy B/A =/= B/xy
I do believe (if someone can correct me) that if you are SUBSTITUTING, you automatically set parenthesis.
A = xy, B/A = B/(xy)
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X divided by Y(A+B) = X/(YA+YB)
That's my take on it, so 2.
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On April 08 2011 08:47 garbanzo wrote:Show nested quote +On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)?
There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity.
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On April 08 2011 08:44 Zeke50100 wrote:Show nested quote +On April 08 2011 08:40 munchmunch wrote:On April 08 2011 08:18 MandoRelease wrote:On April 08 2011 08:04 munchmunch wrote:On April 08 2011 08:02 Zeke50100 wrote:On April 08 2011 08:01 munchmunch wrote:
[
Not due to laziness at all, actually. Granted, it would be incorrect to omit the parentheses in many contexts, but in any context where it can be expected to be unambiguous to the reader, it would be recommended to any mathematical writer to drop the parentheses for aesthetic reasons.
Being accustomed to the omission of parentheses doesn't make it right  No, but aesthetics can be a good reason. Not in anything that does not involves advanced mathematics. I certainly agree that you sometime need to lower your accuracy when you write advanced mathematical paper in order to make it understandable. It is not the case for basic math like trigonometry and basically anything put on a non mathematical forum. For these, it's only lazyness because adding parentheses here and there would not make it any less clear, so aesthetics is not always a good reason. Ok, I guess I should write a longer post on my thoughts on this subject. Recall that the original subject was about whether something like cos 2x is an incorrect statement for cos(2x). There is no doubt that it is helpful for beginning students to put the brackets in. And every student should understand that there is an unambiguous idea, essentially "perform the multiplication 2 * x and then evaluate the function cos at 2*x", which can be communicated unambiguously by adding the brackets. It would also be nice if people knew that this statement can be made so clear that a computer can understand it, although a computer might require something like "cos(2*x)" or "(cos (* 2 x))". However, none of that means that cos 2x is wrong! My emotion towards people who perpetuate this sentiment is similar to that contained in Stephen Fry's language rant. As long as the notation is understood, it is never wrong to write cos 2x. And it can sometimes be better to write cos 2x. In differential geometry, for example, if you add parentheses everywhere they might be required, the large amount of parentheses can impede readability. This is not to contradict you; no doubt cos(2x) is a better choice for a homework thread on TL, for example. But that just means that other considerations are preeminent in that situation. The problem is that cos2x is NOT equal to cos(2x). It IS wrong. It's not comparable to Fry's language rant at all, because there is a right and a wrong when it comes to math and mathematical notation.
How is cos2x != cos(2x)?
Even my calculus textbook doesn't use parentheses most of the time. How else could you interpret cos2x other than as cos(2x)?
If you wrote cos2*x then it might be somewhat confusing, but cos2x is pretty clear.
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On April 08 2011 08:49 Zeke50100 wrote:Show nested quote +On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity.
If you can find some evidence of this..
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On April 08 2011 08:48 JinDesu wrote:Show nested quote +On April 08 2011 08:47 jdseemoreglass wrote:On April 08 2011 08:45 AirportSecurity wrote:
LOL so many weak minded people in this thread I will admit, my brain broke when I thought of this: A = xy B/A =/= B/xy I do believe (if someone can correct me) that if you are SUBSTITUTING, you automatically set parenthesis. A = xy, B/A = B/(xy)
Yup. The way you wrote it is correct, which is not the same as the one marked incorrect above (which is indeed incorrect unless x = 1). It really shows how important understanding the use of parentheses is.
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On April 08 2011 08:50 Mailing wrote:Show nested quote +On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this..
It's not ambiguous. Google "order of operations."
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Well I learned something about rudimentary math. I always used the acronym PEMDAS. It has failed b/c I though that what it meant was to prioritize multiplication over division, and addition over subtraction. Apparently my thinking is wrong, and multiplication and division are read left to right when parenthesis and exponents are gotten rid of. :/
Would have liked this problem to be on a piece of paper though, as reading it as
48 (9+3)
2
would be easier
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On April 08 2011 07:09 MasterOfChaos wrote:Show nested quote +On April 08 2011 07:02 JinDesu wrote:On April 08 2011 07:01 Retgery wrote:
I see the mistake now, some people see it as (48 )/2 (9+3) and if 48÷2 is seen as a fraction then the answer comes out to 288, but what some (me included) saw was 48÷[2(9+3)] comes out to 2. This question is a bitch...
Yep, it's the assumption that the division sign automatically sets everything to the right in a bracket. Writing it out on a board or paper would help. The division sign does exactly what it's supposed to. Divide the left number by the right number. The question isn't about the division sign IMO. It's about the omitted multiplication sign. I argue that an omitted multiplication sign is different from an explicit multiplication sign.
Can you provide any proof (written down, not some implementation like on a calculator / web program) that this "omitted multiplication sign" is a mathematical operator? Especially one which has different properties from the normal multiplication sign?
Btw, what is the "explicit" multiplication sign? \cdot? x? *?
Is:
(48 )/2 (9+3) different to
(48 )/2 * (9+3) or different to
(48 )/2 x (9+3) or different to
(48 )/2 \cdot (9+3) ?
What's their order?
Afaik there is only one "multiplication" operation in arithmetics.
And if you want to really make shit up: Where does it state that's it Base10? It could be Base11. Or Hex.
You just assume it's Base10, because that's normal. In the same way that there is only one normal multiplication. Trying to bring "ommited multi behaves differently to normal multi" into the discussion is as far stretched as saying it's Hex. Actually, I can easily mention multiple papers where different bases are explained in a mathematical way. As well as defining normal arithmetics on those bodys (like addition, substraction, multiplication, division). You dont define "ommited multiplication" on those bodies.
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That Mathway thing someone linked a screenshot of earlier is odd.
48÷2(9+3) is evaluated as 48/(2*(9+3))
48÷2*(9+3) as (48/2)*(9+3)
48/2(9+3) as (48/2)*(9+3)
48/2*(9+3) as (48/2)*(9+3)
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On April 08 2011 08:50 Mailing wrote:Show nested quote +On April 08 2011 08:49 Zeke50100 wrote:On April 08 2011 08:47 garbanzo wrote:On April 08 2011 08:39 Zeke50100 wrote:On April 08 2011 08:38 Entropic wrote:
lol what a shittily written and ambiguous expression (as many have noted already) It's 0% ambiguous, but 100% a test of your understanding of math. You really don't see how 1/4*(3+2) is less ambiguous than 1/4(3+2)? How about 1/2(a+b) versus 1/2*(a+b)? There is only one correct way to interpret them. No idea how it's ambiguous. Personal lack of knowledge or personal confusion do not equal ambiguity. If you can find some evidence of this..
Yes, I would like some source that it can definitively only be read one way. And you didn't really answer my question. If you were to ask someone a question, and you wanted absolutely no confusion, then would you consider choosing one notation over the other?
I think you're lying to yourself if you say otherwise.
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On April 08 2011 08:49 Alzadar wrote:Show nested quote +On April 08 2011 08:44 Zeke50100 wrote:On April 08 2011 08:40 munchmunch wrote:On April 08 2011 08:18 MandoRelease wrote:On April 08 2011 08:04 munchmunch wrote:On April 08 2011 08:02 Zeke50100 wrote:On April 08 2011 08:01 munchmunch wrote:
[
Not due to laziness at all, actually. Granted, it would be incorrect to omit the parentheses in many contexts, but in any context where it can be expected to be unambiguous to the reader, it would be recommended to any mathematical writer to drop the parentheses for aesthetic reasons.
Being accustomed to the omission of parentheses doesn't make it right No, but aesthetics can be a good reason. Not in anything that does not involves advanced mathematics. I certainly agree that you sometime need to lower your accuracy when you write advanced mathematical paper in order to make it understandable. It is not the case for basic math like trigonometry and basically anything put on a non mathematical forum. For these, it's only lazyness because adding parentheses here and there would not make it any less clear, so aesthetics is not always a good reason. Ok, I guess I should write a longer post on my thoughts on this subject. Recall that the original subject was about whether something like cos 2x is an incorrect statement for cos(2x). There is no doubt that it is helpful for beginning students to put the brackets in. And every student should understand that there is an unambiguous idea, essentially "perform the multiplication 2 * x and then evaluate the function cos at 2*x", which can be communicated unambiguously by adding the brackets. It would also be nice if people knew that this statement can be made so clear that a computer can understand it, although a computer might require something like "cos(2*x)" or "(cos (* 2 x))". However, none of that means that cos 2x is wrong! My emotion towards people who perpetuate this sentiment is similar to that contained in Stephen Fry's language rant. As long as the notation is understood, it is never wrong to write cos 2x. And it can sometimes be better to write cos 2x. In differential geometry, for example, if you add parentheses everywhere they might be required, the large amount of parentheses can impede readability. This is not to contradict you; no doubt cos(2x) is a better choice for a homework thread on TL, for example. But that just means that other considerations are preeminent in that situation. The problem is that cos2x is NOT equal to cos(2x). It IS wrong. It's not comparable to Fry's language rant at all, because there is a right and a wrong when it comes to math and mathematical notation. How is cos2x != cos(2x)? Even my calculus textbook doesn't use parentheses most of the time. How else could you interpret cos2x other than as cos(2x)?
Textbooks generally offset the 2x portion as some way of indicating that they are on the same level, although not always with parentheses (my textbook leaves an awkwardly-sized gap, using parentheses whenever it doesn't).
cos2x = xcos2 = x * cos2 = (cos2) * x
cos(2x) = ...cos(2x)
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On April 08 2011 08:44 Zeke50100 wrote:Show nested quote +On April 08 2011 08:40 munchmunch wrote:On April 08 2011 08:18 MandoRelease wrote:On April 08 2011 08:04 munchmunch wrote:On April 08 2011 08:02 Zeke50100 wrote:On April 08 2011 08:01 munchmunch wrote:
[
Not due to laziness at all, actually. Granted, it would be incorrect to omit the parentheses in many contexts, but in any context where it can be expected to be unambiguous to the reader, it would be recommended to any mathematical writer to drop the parentheses for aesthetic reasons.
Being accustomed to the omission of parentheses doesn't make it right No, but aesthetics can be a good reason. Not in anything that does not involves advanced mathematics. I certainly agree that you sometime need to lower your accuracy when you write advanced mathematical paper in order to make it understandable. It is not the case for basic math like trigonometry and basically anything put on a non mathematical forum. For these, it's only lazyness because adding parentheses here and there would not make it any less clear, so aesthetics is not always a good reason. Ok, I guess I should write a longer post on my thoughts on this subject. Recall that the original subject was about whether something like cos 2x is an incorrect statement for cos(2x). There is no doubt that it is helpful for beginning students to put the brackets in. And every student should understand that there is an unambiguous idea, essentially "perform the multiplication 2 * x and then evaluate the function cos at 2*x", which can be communicated unambiguously by adding the brackets. It would also be nice if people knew that this statement can be made so clear that a computer can understand it, although a computer might require something like "cos(2*x)" or "(cos (* 2 x))". However, none of that means that cos 2x is wrong! My emotion towards people who perpetuate this sentiment is similar to that contained in Stephen Fry's language rant. As long as the notation is understood, it is never wrong to write cos 2x. And it can sometimes be better to write cos 2x. In differential geometry, for example, if you add parentheses everywhere they might be required, the large amount of parentheses can impede readability. This is not to contradict you; no doubt cos(2x) is a better choice for a homework thread on TL, for example. But that just means that other considerations are preeminent in that situation. The problem is that cos2x is NOT equal to cos(2x). It IS wrong. It's not comparable to Fry's language rant at all, because there is a right and a wrong when it comes to math and mathematical notation.
This is exactly the sentiment that I find disgusting. I mean, I agree with you to a point. But the idea that cos 2x is not equal to cos(2*x), when many people use cos 2x without the slightest ambiguity, is perverse to me.
But let's agree to disagree. If we keep arguing, it can only go two ways: into ad hominem, or into a dick showing contest, neither of which is agreeable to me. And I hope you saw my apology for starting on the ad hominem's earlier.
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People saying this is math question are ehmmm crazy. This is a question about convention. If you wrote it (48/2)*(9+3) everyone would do it correctly. This has nothing to do with math, everything to do with mainly arbitrary convention. Yes there probably is a correct answer, but the answer is meaningless from mathematical point of view. Also math is mostly not written in one-line in reality, so even if you study math at university level you are not used to oneline notation and just go with your gut and get it wrong for multiple psychological reasons.
Want a math problem : Is e^(i * pi) + 1 = 0 ? Not really asking seriously just love that equation. But when we are on topic of math, one of my favourite theorem's : GoodsteinSequence converges to 0. Or even stronger GoodsteinsTheorem. What I love about it is that on the first glance you think it has to converge to infinity, but then you can actually find why it goes to 0 without really going into technicalities. The formal proof is not so nice, but still cool.
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this is why you write it downwards not like xxxxxxx
but
xxxx
--------
yyyy
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On April 08 2011 08:42 Blisse wrote:Show nested quote +On April 08 2011 08:39 MajorityofOne wrote:On April 08 2011 08:35 Blisse wrote:On April 08 2011 08:28 MajorityofOne wrote:On April 08 2011 08:25 Tschis wrote:
So funny how majority of people count as 288, then most are studying, and then most see it as 1/(2*x), which is basically the contrary
//tx This is whats confusing me O.O But I think I get it now. The answer is to lose your whole f**king base. Please look at the number of voters, and realize it was a poll added after the original post, and that the same signs are not used in both polls. ECAEKAAA is my Chemistry Organic compounds acronym. I'm not a fan of using acronyms to explain ideas. Fine for memorizing though. So everybody who voted 2 on the original poll came back to vote 1/(2*x), but the entire 288 crowd is absent? ^^ Either that, or people are voting crazy Then you read the second part of my sentence, which says the same signs are not used in both polls. Ugh, read. 1/2x looks different from 1÷2x.
Your comprehension is at least as bad as mine :p
Voting differently because they "look different" is cause enough for "people are voting crazy", no?
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EPT
