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On April 09 2011 07:13 Sluggy wrote:Show nested quote +On April 09 2011 07:10 gerundium wrote:On April 09 2011 07:06 Zealot)KT( wrote:
1/2x should always be read like 1 ÷ 2 · x which is (1/2)x. why exactly? i read it as X/2, and there are no clues to the opposite. He is asserting that division and multiplication have the same precedence and that they need to be applied left to right. Again it gets back to using this convention which apparently isn't a standard in all countries. It's just boring semantics and it can't be asserted as correct until an international standard is in place 
But isn't it an international standard to equally prioritize addition and substraction? Why wouldn't it be the same for multiplication and division? As far as I know it's also this way for square roots and exponents.
Edit: clarification
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On April 09 2011 07:19 MasterOfChaos wrote:Show nested quote +On April 09 2011 07:06 Zealot)KT( wrote:
Everyone knows this is 58, and not 34. Now compare it to the problem in the OP:
48 ÷ 2 · (9 + 3) = ? This is not identical to the problem in the OP. The OP omitted the "·". The difference in interpretation hinges exactly on the effect of this omission. Many people give this implicit multiplication a higher priority. Even the publication guidelines of the American Mathematical Society contained that convention, so it's not just people who're too stupid to know maths.
Of course, people are being misled by the notation of the OP. However, I'm arguing that the misleadingness of the OP does not mean the problem is ambiguous. It can be interpreted in multiple ways, but only one of them is right (outcome wise).
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On April 09 2011 07:23 Zealot)KT( wrote:Show nested quote +On April 09 2011 07:13 Sluggy wrote:On April 09 2011 07:10 gerundium wrote:On April 09 2011 07:06 Zealot)KT( wrote:
1/2x should always be read like 1 ÷ 2 · x which is (1/2)x. why exactly? i read it as X/2, and there are no clues to the opposite. He is asserting that division and multiplication have the same precedence and that they need to be applied left to right. Again it gets back to using this convention which apparently isn't a standard in all countries. It's just boring semantics and it can't be asserted as correct until an international standard is in place But isn't it an international standard to equally prioritize addition and substraction? Why isn't it the same for multiplication and division? As far as I know it's also this way for square roots and exponents.
They are equal as in you do not choose which ever you want to do first.
You do the ones that comes first in the equation left to right.
eg. 4 - 3 + 5 = 6 =/= -4
likewise.
4 / 2 * 5 = ( 4/2 )*5 =/= 4/( 2*5 )
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On April 09 2011 07:39 Rtran10 wrote:Show nested quote +On April 09 2011 07:23 Zealot)KT( wrote:On April 09 2011 07:13 Sluggy wrote:On April 09 2011 07:10 gerundium wrote:On April 09 2011 07:06 Zealot)KT( wrote:
1/2x should always be read like 1 ÷ 2 · x which is (1/2)x. why exactly? i read it as X/2, and there are no clues to the opposite. He is asserting that division and multiplication have the same precedence and that they need to be applied left to right. Again it gets back to using this convention which apparently isn't a standard in all countries. It's just boring semantics and it can't be asserted as correct until an international standard is in place But isn't it an international standard to equally prioritize addition and substraction? Why isn't it the same for multiplication and division? As far as I know it's also this way for square roots and exponents. They are equal as in you do not choose which ever you want to do first. You do the ones that comes first in the equation left to right. eg. 4 - 3 + 5 = 6 =/= -4
Yeah, and that's exactly my point.
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I can't tell if people are just trolling now or if they actually still think the answer is 2 
This is mathematics people not philosophy or literature it is open to debate what you think the signs mean or how they work. division and multiplication is on the same level of operations so do it left to right.
288
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It's funny how self-righteous all the people are about how '288' is the definitive and only right answer.
On the other hand, everyone voting '2' is putting forth rational arguments and showing understanding of both sides of the 'debate'.
Meanwhile, '2' is slowly gaining percentile in the vote
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On April 09 2011 07:43 Zealot)KT( wrote:Show nested quote +On April 09 2011 07:39 Rtran10 wrote:On April 09 2011 07:23 Zealot)KT( wrote:On April 09 2011 07:13 Sluggy wrote:On April 09 2011 07:10 gerundium wrote:On April 09 2011 07:06 Zealot)KT( wrote:
1/2x should always be read like 1 ÷ 2 · x which is (1/2)x. why exactly? i read it as X/2, and there are no clues to the opposite. He is asserting that division and multiplication have the same precedence and that they need to be applied left to right. Again it gets back to using this convention which apparently isn't a standard in all countries. It's just boring semantics and it can't be asserted as correct until an international standard is in place But isn't it an international standard to equally prioritize addition and substraction? Why isn't it the same for multiplication and division? As far as I know it's also this way for square roots and exponents. They are equal as in you do not choose which ever you want to do first. You do the ones that comes first in the equation left to right. eg. 4 - 3 + 5 = 6 =/= -4 Yeah, and that's exactly my point.
When you draw your formulas on pen and paper, multiplication and division are naturally completely different looking. It's the same when using typesetting software for math. I mean this:
![[image loading]](http://latex.codecogs.com/gif.latex?$${1\over{2\pi%20i}}$$)
If you don't want your formulas to take up as much vertical space, because you want to use it inside your paragraphs with normal English sentences around it, MasterOfChaos found the example from the AMS guidelines, to typeset the same formula like this:
![[image loading]](http://latex.codecogs.com/gif.latex?$$1/{2\pi%20i}$$)
Link: http://www.teamliquid.net/forum/viewpost.php?post_id=8696719
The multiplication sign in a normal forum post text, where you do not have special typesetting software, should really not be dropped. It's just trying to confuse people. I also never had a calculator that lets you omit the multiplication sign and write stuff like 1/2x instead of 1/2*x.
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Oh boy, this thread needs a liquibet to bet on the winner :D I vote for 288
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Here's the answer. There's no clear answer since it's missing a parenthesis. It depends on what background you have in mathematics. If you prioritize multiplication or dividing. What would lead to a sure answer is either (48/2) * (9+3) or 48/(2(9+3)). It's stupid to argue over but my answer is still 2 since multiplication > dividing is what I've been taught at least.
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48÷2(9+3)=x
log(48÷2(9+3))=logx
log(48)-log(2)+log(12)=log(x)
this clearly shows the relationship between the different parts of the equation.
log(48/2)=log(x/12)
48/2=x/12
288=x
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5 x 10 ^ 5 / 3 x 10 ^ 4
288 people see (5 x 10 ^ 5 / 3)?
T = PV / nR would be (p)(v)/(n)(R) and done left to right?
The only correct answer is that the form 48÷2(9+3) is ambiguous and therefore can equal 2 or 288, depending on how you see it.
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On April 09 2011 08:07 Ropid wrote:Show nested quote +On April 09 2011 07:43 Zealot)KT( wrote:On April 09 2011 07:39 Rtran10 wrote:On April 09 2011 07:23 Zealot)KT( wrote:On April 09 2011 07:13 Sluggy wrote:On April 09 2011 07:10 gerundium wrote:On April 09 2011 07:06 Zealot)KT( wrote:
1/2x should always be read like 1 ÷ 2 · x which is (1/2)x. why exactly? i read it as X/2, and there are no clues to the opposite. He is asserting that division and multiplication have the same precedence and that they need to be applied left to right. Again it gets back to using this convention which apparently isn't a standard in all countries. It's just boring semantics and it can't be asserted as correct until an international standard is in place But isn't it an international standard to equally prioritize addition and substraction? Why isn't it the same for multiplication and division? As far as I know it's also this way for square roots and exponents. They are equal as in you do not choose which ever you want to do first. You do the ones that comes first in the equation left to right. eg. 4 - 3 + 5 = 6 =/= -4 Yeah, and that's exactly my point. When you draw your formulas on pen and paper, multiplication and division are naturally completely different looking. It's the same when using typesetting software for math. I mean this: If you don't want your formulas to take up as much vertical space, because you want to use it inside your paragraphs with normal English sentences around it, MasterOfChaos found the example from the AMS guidelines, to typeset the same formula like this: Link: http://www.teamliquid.net/forum/viewpost.php?post_id=8696719The multiplication sign in a normal forum post text, where you do not have special typesetting software, should really not be dropped. It's just trying to confuse people. I also never had a calculator that lets you omit the multiplication sign and write stuff like 1/2x instead of 1/2*x.
As long as you understand what you write yourself, it doesnt really matter; however, if someone looks at what you write, they might not have the same conventions as you do.
Technically, 1/2x does mean x/2 if you want to be critical. Many people will write 1/(2x) as 1/2x because they just dont care. If someone else looks at it, they might not see it like you do.
In the end, its always better to have the brackets to take away any ambiguity from an expression.
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On April 09 2011 08:13 quiggy wrote:
48÷2(9+3)=x
log(48÷2(9+3))=logx
log(48)-log(2)+log(12)=log(x)
this clearly shows the relationship between the different parts of the equation.
log(48/2)=log(x/12)
48/2=x/12
288=x
Nice. I was almost tempted to ask the poll question on Math Overflow but it would probably just get closed immediately.
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On April 09 2011 08:13 quiggy wrote:
48÷2(9+3)=x
log(48÷2(9+3))=logx
log(48)-log(2)+log(12)=log(x)
this clearly shows the relationship between the different parts of the equation.
log(48/2)=log(x/12)
48/2=x/12
288=x
This is you assuming that 12 isn't a part of what 48 is being divided with. The Logs doesn't change anything my answer is still both and neither of them another parenthesis is needed to draw a conclusion /thread.
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United States7483 Posts
The correct answer is supposed to be 288, but the unclear notation of the author is leading to the confusion.
Fix the notation, and this isn't an issue. All this proves is that unclear notation creates wrong answers.
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On April 09 2011 08:23 Kaonis wrote:
This is why i'm not taking Calculus :<
Thats really sad : (
This isn't what maths is about, this is what you run into in very early maths and when you are finishing typesetting a paper for review (opposite ends of the spectrum). The thread is so long because of the argument between the two groups (which in theory should never meet).
You shouldn't ever take this thread to be indicative of mathematics.
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On April 09 2011 08:30 HaNdFisH wrote:Thats really sad : ( This isn't what maths is about, this is what you run into in very early maths and when you are finishing typesetting a paper for review (opposite ends of the spectrum). The thread is so long because of the argument between the two groups (which in theory should never meet). You shouldn't ever take this thread to be indicative of mathematics.
Calculus is easy as shit as well or well the fundamentals of it there's of course weird shit later on but it's not that bad imo
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I believe proximity trumps symbology. not saying i'm right or wrong, but with this understanding i answered "2" and "1/(2*x)", which are consistent answers.
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On April 09 2011 08:25 simme123 wrote:Show nested quote +On April 09 2011 08:13 quiggy wrote:
48÷2(9+3)=x
log(48÷2(9+3))=logx
log(48)-log(2)+log(12)=log(x)
this clearly shows the relationship between the different parts of the equation.
log(48/2)=log(x/12)
48/2=x/12
288=x
This is you assuming that 12 isn't a part of what 48 is being divided with. The Logs doesn't change anything my answer is still both and neither of them another parenthesis is needed to draw a conclusion /thread.
Going by what is shown in the equation step by step thats the relationship. All the numbers are constants not variables and are not being held in place by addition or subtraction.
1/2x IS very subjective as the 2 and x should be held in place but nothing is keeping them there. However with 1/2x+2, most of us should agree that its 1/(2x)+2 this is because the existence of a variable and the addition. With 48/2(9+3) the non-existence of either a variable or place holding should cause it to be read as two separate groups with equal importance.
We could get into the 0=1 argument eventually and we all know how fun that one is XD
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EPT
