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On April 09 2011 11:50 mpupu wrote:
Some people may think it's wrong because they've not been exposed to the alternatives. If you know about the other conventions but choose to ignore them, more power to you. Although in that case, I wouldn't call other people's opinion "wrong" but "different".
But it IS wrong if they said 2, or 1/(2*x).
because the OP did not post it in a logical way of thinking. Since he left out parenthesis, means whoever ASSUMED them, is WRONG, not just different.
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On April 09 2011 11:39 Keitzer wrote:
It saddens me to see people not understand that they actually got it wrong.
The order of the problem:
First parenthesis, thus you get 48/2*12
Next:
Division and multiplication are on the same Order of Operations. Any 8th grader can tell you that.
Thus, you MUST do 48/2 since it comes first... you MUST. If you wish that the 2*12 come first, you must group them into their own so you'd have 48/(2*12).
Finally:
Since all you have left is 24*12, the obvious answer is 288.
I am currently a 12th grader enrolled in AP Calculus AB and am plan on majoring in Computer Science so Math is kind of my strong point.
I am also a very logical person (which helps make me better at Math), and when I see people laugh at those who guessed the right answer, I become very upset.
It saddens me that you don't know what the actual argument is about 
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By the way, this is a good example of how the forums could be improved. In this thread, people keep reiterating the same arguments and when they get buried with other posts many pages later, the cycle starts all over again. A solution to this is using a system like Reddit's where posts are moderated and ordered by relevance. However, other threads (like LR) may benefit more from a chronological order so I guess one size doesn't fit all.
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48÷2(9+3)
=48÷2(12)
=48÷24
=2
or
![[image loading]](http://imgur.com/P1NvC.gif)
=2
Im still standing by the answer 2.
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On April 09 2011 11:55 mints wrote:48÷2(9+3) =48÷2(12) =48÷24 =2 or =2 Im still standing by the answer 2.
Nononono... you're assuming 48 / ( 2 (9 + 3))
when in reality there are NO parenthesis after the " / ". Thus, your argument is invalid.
edit: thats like assuming 3 + 3 * 5 = 30. Now you're saying "how are they related?" well, if i ASSUME parenthesis here: (3 +3) * 5, then ya, i get 30... HOWEVER! THATS NOT HOW IT'S WRITTEN! The actual answer is 18
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Got it right, and didn't take a single math class in my undergrad career. Take that, suckas. I'm a product designer, I let Solidworks do the math after my eyes do the calculus to determine if something looks beautiful.
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United States5162 Posts
On April 09 2011 11:55 mints wrote:48÷2(9+3) =48÷2(12) =48÷24 =2 or =2 Im still standing by the answer 2.
Multiplication and division have the same order of operation, so you do whichever comes first when reading left to right.
Thus you would do the parenthesis first like you did, but then do the division of 48/2 since it comes before multiplying the 2*12.
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Found my cheap year 5 calculator
According to it 48÷2(9+3)=2
but 48÷2*(9+3)=288
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On April 09 2011 12:00 Ferocious Falcon wrote:
Found my cheap year 5 calculator
According to it 48÷2(9+3)=2
but 48÷2*(9+3)=288
Does it not recognize the parenthesis next to a constant as multiplication and on the same level as division? if not, then it's a shitty calculator. However, it IS 5 years old, so no worries there.
On the other end, if that's what people used to come up with 2, then dear god, i might just move to Argentina with my cousin.
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no, it assumed a parenthesis here: 48 / ( 2 (9+3) )
which is NOT how it was written in the OP, gg.
are you guys even looking @ the picture it shows?
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On April 09 2011 12:02 Keitzer wrote:Show nested quote +On April 09 2011 12:00 Ferocious Falcon wrote:
Found my cheap year 5 calculator
According to it 48÷2(9+3)=2
but 48÷2*(9+3)=288 Does it not recognize the parenthesis next to a constant as multiplication and on the same level as division? if not, then it's a shitty calculator. However, it IS 5 years old, so no worries there. On the other end, if that's what people used to come up with 2, then dear god, i might just move to Argentina with my cousin.
You missed this post on page 84 of this thread:
On April 09 2011 05:23 MasterOfChaos wrote:
At least one reputable source, namely the American Mathematical Society used high priority for omitted multiplication signs in their publications.
We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display $${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$ ![[image loading]](http://latex.codecogs.com/gif.latex?$${1%5Cover{2%5Cpi%20i}}%5Cint_%5CGamma%20{f(t)%5Cover%20(t-z)}dt$$) is likely to be converted to $(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$ ![[image loading]](http://latex.codecogs.com/gif.latex?$(1/2%5Cpi%20i)%5Cint_%5CGamma%20f(t)(t-z)^{-1}dt$) in our production process.
http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html
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On April 09 2011 11:53 Keitzer wrote:Show nested quote +On April 09 2011 11:50 mpupu wrote:
Some people may think it's wrong because they've not been exposed to the alternatives. If you know about the other conventions but choose to ignore them, more power to you. Although in that case, I wouldn't call other people's opinion "wrong" but "different". But it IS wrong if they said 2, or 1/(2*x). because the OP did not post it in a logical way of thinking. Since he left out parenthesis, means whoever ASSUMED them, is WRONG, not just different.
you're wrong in assuming left associative conventions can be used to argue correctness when they aren't explicitly stated. You have a wide audience from many countries here. Many people have been taught to resolve ambiguities with parentheses; that way you don't have to worry about associativity when precedence is the same. If you can show me an authoritative source that says arithmetic expressions must use left associative operator resolution, I will concede. Note the word must in the previous sentence.
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I used a "÷" symbol instead of "/" not sure why that made this difference though...
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On April 09 2011 09:42 FindMeInKenya wrote:
The thing is, if you consider multiplication by juxtaposition to have priority, you are treating real numbers as not being a field, which we know they are. In this case, multiplication and division happens at the same time.
Beside, programing code are often flawed, why use their logic and train of thought into a math question?
Hmm, you wrote that you are studying math or something, so I will write somewhat more. In your argument you are assuming that we are already in the "math part" of the problem and not still in the parsing part. But that is not the case. In considering multiplication by juxtaposition to have precedence over "normal" multiplication and division (you can even extend it to have priority over Exponent) we are adding new operator, but it is only virtual notational one.
To show that this is the case I will show how for every expression in standard notation you can get expression in new one (NV) and vice versa.
Transformation
a) standard X -> NV Y
1) if X is atomic -> Y=X
2) if X is in the form of AB (implicit multiplication) -> Y = (A)(B)
3) if X is in the form A+B,A-B,.... -> apply transformation on all subexpressions
b) NV Y -> standard X
1) if Y is atomic -> X = Y
2) if Y is AB -> X = (AB)
3) if Y is in the form A+B,A-B,.... -> apply transformation on all subexpressions
Note that I ignored Exponent issue here, I did that for simplicity's sake, but I hope it is clear how it would be dealt with.
So from the above I hope it is clear that we only introduced a notational operator or maybe better name would be shortcut operator for lazy people  . It does not affect in any way the fact that we are working with a field.
I tried to point that out in my previous response that notation is just a way of graphical representation and is not set in stone and has no effect on the "real" math and its theorems.
Anyway to save this thread and make it worth reading further I suggest that everyone who wants to post something here should also post interesting math fact, problem, proof, ...
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On April 09 2011 12:00 Myles wrote:Show nested quote +On April 09 2011 11:55 mints wrote:48÷2(9+3) =48÷2(12) =48÷24 =2 or =2 Im still standing by the answer 2. Multiplication and division have the same order of operation, so you do whichever comes first when reading left to right. Thus you would do the parenthesis first like you did, but then do the division of 48/2 since it comes before multiplying the 2*12.
No...when you add (9+3) ... its then 48÷2(12), the parenthesis does not disappear..so you would distribute the 2 then divide. Thus 48÷24=2
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On April 09 2011 12:03 Ropid wrote:Show nested quote +On April 09 2011 12:02 Keitzer wrote:On April 09 2011 12:00 Ferocious Falcon wrote:
Found my cheap year 5 calculator
According to it 48÷2(9+3)=2
but 48÷2*(9+3)=288 Does it not recognize the parenthesis next to a constant as multiplication and on the same level as division? if not, then it's a shitty calculator. However, it IS 5 years old, so no worries there. On the other end, if that's what people used to come up with 2, then dear god, i might just move to Argentina with my cousin. You missed this post on I think page 82 of this thread: On April 09 2011 05:23 MasterOfChaos wrote:At least one reputable source, namely the American Mathematical Society used high priority for omitted multiplication signs in their publications. Show nested quote +We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display $${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$ is likely to be converted to $(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$ in our production process. http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html
Well I don't see how that makes any sense, as 1/2pi i = 1 / (2pi i)... as the first can be(and is TECHNICALLY) written as (pi i) / 2... which in ALL cases =/= 1/ (2pi i)
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On April 09 2011 12:03 Ropid wrote:Show nested quote +On April 09 2011 12:02 Keitzer wrote:On April 09 2011 12:00 Ferocious Falcon wrote:
Found my cheap year 5 calculator
According to it 48÷2(9+3)=2
but 48÷2*(9+3)=288 Does it not recognize the parenthesis next to a constant as multiplication and on the same level as division? if not, then it's a shitty calculator. However, it IS 5 years old, so no worries there. On the other end, if that's what people used to come up with 2, then dear god, i might just move to Argentina with my cousin. You missed this post on page 84 of this thread: On April 09 2011 05:23 MasterOfChaos wrote:At least one reputable source, namely the American Mathematical Society used high priority for omitted multiplication signs in their publications. Show nested quote +We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display $${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$ is likely to be converted to $(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$ in our production process. http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html
The only problem with that as evidence is that AMS encloses the entire expression in parentheses so as to suggest a fraction which is different than the OP.
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EPT
