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United States5162 Posts
On April 09 2011 12:40 chonkyfire wrote:Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra
It's not 2*9+2*3 because the two is already being affected by the 48. You can't ignore the 48, it goes along with the two in the distribution. If it were 48+2(9+3) then you would distribute only the 2 to the parenthesis and it would be 48+24. But because the 48 is divided by the two, it cant be ignored in the distribution. It goes along too. So it becomes (48/2)*9+(48/2)*3
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On April 09 2011 12:45 chonkyfire wrote:Show nested quote +On April 09 2011 12:41 Keitzer wrote:
yes, you can't just assumed parenthesis left and right.
5 + 5 * 5 =/= 50, NEVER!!!
however, with your, just-assume-em rule, you CAN make it 50... by going (5+5) * 5 = 50
HOWEVER! (and the point i've been making this entire time) is that the ORIGINAL equation is NOT written with assumed parenthesis, and THUS cannot be used in explanation of a wrong answer. that's not a very good source whatever this thread is going no where
yes it is, as it's the EXACT same principle (that assuming parenthesis yields a different result)
edit: posting pic again for those who still are not convinced.... notice the ASSUMED (problem changing) parenthesis in the bottom section.
![[image loading]](http://imgur.com/TTfFT.jpg)
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On April 09 2011 12:45 Myles wrote:Show nested quote +On April 09 2011 12:40 chonkyfire wrote:On April 09 2011 12:36 Keitzer wrote:ok... here we go... Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra It's not 2*9+2*3 because the two is already being affected by the 48. You can't ignore the 48, it goes along with the two in the distribution. If it were 48+2(9+3) then you would distribute only the 2 to the parenthesis and it would be 48+24. But because the 48 is divided by the two, it cant be ignored in the distribution. It goes along too. So it becomes (48/2)*9+(48/2)*3
I would argue the 2 being next to (9+3) is directly effecting (9+3) and that by doing 48/2 first you're ignoring the 24 that actually exists, and from what I keep reading that is the case. I just want a source that says other wise. I'm not asking for much.
On April 09 2011 12:46 Keitzer wrote:Show nested quote +On April 09 2011 12:45 chonkyfire wrote:On April 09 2011 12:41 Keitzer wrote:
yes, you can't just assumed parenthesis left and right.
5 + 5 * 5 =/= 50, NEVER!!!
however, with your, just-assume-em rule, you CAN make it 50... by going (5+5) * 5 = 50
HOWEVER! (and the point i've been making this entire time) is that the ORIGINAL equation is NOT written with assumed parenthesis, and THUS cannot be used in explanation of a wrong answer. that's not a very good source whatever this thread is going no where yes it is, as it's the EXACT same principle (that assuming parenthesis yields a different result) edit: posting pic again for those who still are not convinced.... notice the ASSUMED (problem changing) parenthesis in the bottom section.
Didn't you write that? I'm confused now.
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On April 09 2011 12:33 reprise wrote:Show nested quote +On April 09 2011 12:25 Keitzer wrote:On April 09 2011 12:23 reprise wrote:On April 09 2011 12:15 Keitzer wrote:On April 09 2011 12:13 mints wrote:On April 09 2011 12:08 Keitzer wrote:On April 09 2011 12:05 mints wrote:On April 09 2011 12:00 Myles wrote:On April 09 2011 11:55 mints wrote: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. 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 Distributing = multiplication (notice how you MULTIPLIED the 2 by the 12).. which, in order of operations, states that it's on the same level as division, which means you're still wrong. Yes distribution is the same thing as multiplication no argument there..but you distribute (ie. if there is a parenthesis) before doing multiplication or division. OK, maybe this will convice you... it's what Ace said earlier... 48 / 2 * (9+3) 48 * 1/2 * (9+3) outmath that... since THAT'S WHAT'S IN THE OP! and don't tell me you can just forget about the first multiplication There is no multiplication symbol between the 2 and the (9 + 3), so don't put one there. It changes the format of the question for those who believe multiplication by juxtaposition takes precedence over regular multiplication and division. what the fuck? Sir, to take the high road, I shall first ask... what is your math experience? Because to me, it does not seem higher than a 5th grader who doesn't know what () means in math class. I'm studying math in university. I guess that doesn't compare to your high school AP that you seem to tout around so proudly. Resorting to ad hominem instead of breaking down my argument, classy. Show me an explicitly stated rule where multiplication by juxtaposition does NOT have priority and I will submit. Calculators are not proof, as different calculators have different programming which will result in different answers. MasterofChaos has even nicely linked an instance where it does have priority, but sadly it is not solid proof as it is simply a convention that the AMS uses. Show me God doesn't exist.
All definitions I found of Juxtaposition state that it is used to reduce the size of an equation by removing operators (source: http://en.wiktionary.org/wiki/juxtaposition), although there are a lot more sources for implied multiplication which seems to be the more common name for this event.
The definitions state nothing about priority, it states that it is another way of writing 2 * x (as 2x), it also does not state that the statements are to be grouped together (such as (2 * x) ).
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On April 09 2011 12:40 chonkyfire wrote:Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra
Don't be misled by that AMS quote. That's just the rule describing how documents by AMS should be read. The nothing you see between the 2 and the ( in the OP is still a multiplication, and you have learned in school what to do in that case. It's just weird that the OP omits the multiplication sign but then still uses a division sign.
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On April 09 2011 12:48 chonkyfire wrote:Show nested quote +On April 09 2011 12:45 Myles wrote:On April 09 2011 12:40 chonkyfire wrote:On April 09 2011 12:36 Keitzer wrote:ok... here we go... Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra It's not 2*9+2*3 because the two is already being affected by the 48. You can't ignore the 48, it goes along with the two in the distribution. If it were 48+2(9+3) then you would distribute only the 2 to the parenthesis and it would be 48+24. But because the 48 is divided by the two, it cant be ignored in the distribution. It goes along too. So it becomes (48/2)*9+(48/2)*3 I would argue the 2 being next to (9+3) is directly effecting (9+3) and that by doing 48/2 first you're ignoring the 24 that actually exists, and from what I keep reading that is the case. I just want a source that says other wise. I'm not asking for much. Show nested quote +On April 09 2011 12:46 Keitzer wrote:On April 09 2011 12:45 chonkyfire wrote:On April 09 2011 12:41 Keitzer wrote:
yes, you can't just assumed parenthesis left and right.
5 + 5 * 5 =/= 50, NEVER!!!
however, with your, just-assume-em rule, you CAN make it 50... by going (5+5) * 5 = 50
HOWEVER! (and the point i've been making this entire time) is that the ORIGINAL equation is NOT written with assumed parenthesis, and THUS cannot be used in explanation of a wrong answer. that's not a very good source whatever this thread is going no where yes it is, as it's the EXACT same principle (that assuming parenthesis yields a different result) edit: posting pic again for those who still are not convinced.... notice the ASSUMED (problem changing) parenthesis in the bottom section. Didn't you write that? I'm confused now.
Just find a source yourself, you just need to google the priorities in math. There is no 2 that is afflicting the 12 because 48 said zimzallabim and made it go away.
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On April 09 2011 12:51 Gnax wrote:Show nested quote +On April 09 2011 12:48 chonkyfire wrote:On April 09 2011 12:45 Myles wrote:On April 09 2011 12:40 chonkyfire wrote:On April 09 2011 12:36 Keitzer wrote:ok... here we go... Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra It's not 2*9+2*3 because the two is already being affected by the 48. You can't ignore the 48, it goes along with the two in the distribution. If it were 48+2(9+3) then you would distribute only the 2 to the parenthesis and it would be 48+24. But because the 48 is divided by the two, it cant be ignored in the distribution. It goes along too. So it becomes (48/2)*9+(48/2)*3 I would argue the 2 being next to (9+3) is directly effecting (9+3) and that by doing 48/2 first you're ignoring the 24 that actually exists, and from what I keep reading that is the case. I just want a source that says other wise. I'm not asking for much. On April 09 2011 12:46 Keitzer wrote:On April 09 2011 12:45 chonkyfire wrote:On April 09 2011 12:41 Keitzer wrote:
yes, you can't just assumed parenthesis left and right.
5 + 5 * 5 =/= 50, NEVER!!!
however, with your, just-assume-em rule, you CAN make it 50... by going (5+5) * 5 = 50
HOWEVER! (and the point i've been making this entire time) is that the ORIGINAL equation is NOT written with assumed parenthesis, and THUS cannot be used in explanation of a wrong answer. that's not a very good source whatever this thread is going no where yes it is, as it's the EXACT same principle (that assuming parenthesis yields a different result) edit: posting pic again for those who still are not convinced.... notice the ASSUMED (problem changing) parenthesis in the bottom section. Didn't you write that? I'm confused now. Just find a source yourself, you just need to google the priorities in math. There is no 2 that is afflicting the 12 because 48 said zimzallabim and made it go away.
Do you not read full posts before you respond? I have been looking for sources and all I'm finding are sources saying the opposite, so I'm giving these guys who are so passionate that its 288 a chance to show me some concrete evidence that would lead me to believe the answer is not 2.
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Oh, that shows the problem beautifully. Portable Calculators just do the same whether there's a number or a variable in the parenthesis.
chonkyfire: I'm curious, why don't you just add the 9 and 3 inside the parenthesis? That's the first thing I would do.
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On April 09 2011 12:48 Nysze wrote:Show nested quote +On April 09 2011 12:33 reprise wrote:On April 09 2011 12:25 Keitzer wrote:On April 09 2011 12:23 reprise wrote:On April 09 2011 12:15 Keitzer wrote:On April 09 2011 12:13 mints wrote:On April 09 2011 12:08 Keitzer wrote:On April 09 2011 12:05 mints wrote:On April 09 2011 12:00 Myles wrote: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 Distributing = multiplication (notice how you MULTIPLIED the 2 by the 12).. which, in order of operations, states that it's on the same level as division, which means you're still wrong. Yes distribution is the same thing as multiplication no argument there..but you distribute (ie. if there is a parenthesis) before doing multiplication or division. OK, maybe this will convice you... it's what Ace said earlier... 48 / 2 * (9+3) 48 * 1/2 * (9+3) outmath that... since THAT'S WHAT'S IN THE OP! and don't tell me you can just forget about the first multiplication There is no multiplication symbol between the 2 and the (9 + 3), so don't put one there. It changes the format of the question for those who believe multiplication by juxtaposition takes precedence over regular multiplication and division. what the fuck? Sir, to take the high road, I shall first ask... what is your math experience? Because to me, it does not seem higher than a 5th grader who doesn't know what () means in math class. I'm studying math in university. I guess that doesn't compare to your high school AP that you seem to tout around so proudly. Resorting to ad hominem instead of breaking down my argument, classy. Show me an explicitly stated rule where multiplication by juxtaposition does NOT have priority and I will submit. Calculators are not proof, as different calculators have different programming which will result in different answers. MasterofChaos has even nicely linked an instance where it does have priority, but sadly it is not solid proof as it is simply a convention that the AMS uses. Show me God doesn't exist. All definitions I found of Juxtaposition state that it is used to reduce the size of an equation by removing operators (source: http://en.wiktionary.org/wiki/juxtaposition), although there are a lot more sources for implied multiplication which seems to be the more common name for this event. The definitions state nothing about priority, it states that it is another way of writing 2 * x (as 2x), it also does not state that the statements are to be grouped together (such as (2 * x) ).
You also write division in a vertical fashion instead of from left to right with a division sign. With the question in the OP formulated like that, this fiasco of a thread would never have happened. 
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United States5162 Posts
On April 09 2011 12:48 chonkyfire wrote:Show nested quote +On April 09 2011 12:45 Myles wrote:On April 09 2011 12:40 chonkyfire wrote:On April 09 2011 12:36 Keitzer wrote:ok... here we go... Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra It's not 2*9+2*3 because the two is already being affected by the 48. You can't ignore the 48, it goes along with the two in the distribution. If it were 48+2(9+3) then you would distribute only the 2 to the parenthesis and it would be 48+24. But because the 48 is divided by the two, it cant be ignored in the distribution. It goes along too. So it becomes (48/2)*9+(48/2)*3 I would argue the 2 being next to (9+3) is directly effecting (9+3) and that by doing 48/2 first you're ignoring the 24 that actually exists, and from what I keep reading that is the case. I just want a source that says other wise. I'm not asking for much.
You do the 48/2 first because it is in front of the 2*12. The 12 being in parentheses doesn't mean it takes precedence because it's next the the two. 2(12) is equivalent to 2*12. The problem simplifies into 48/2*12 which will always be 288 when you do the operations left to right.
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On April 09 2011 12:46 Keitzer wrote:Show nested quote +On April 09 2011 12:45 chonkyfire wrote:On April 09 2011 12:41 Keitzer wrote:
yes, you can't just assumed parenthesis left and right.
5 + 5 * 5 =/= 50, NEVER!!!
however, with your, just-assume-em rule, you CAN make it 50... by going (5+5) * 5 = 50
HOWEVER! (and the point i've been making this entire time) is that the ORIGINAL equation is NOT written with assumed parenthesis, and THUS cannot be used in explanation of a wrong answer. that's not a very good source whatever this thread is going no where yes it is, as it's the EXACT same principle (that assuming parenthesis yields a different result) edit: posting pic again for those who still are not convinced.... notice the ASSUMED (problem changing) parenthesis in the bottom section.
What you're doing now is re-posting an image of your own construction pursuant to someone asking for a better source. In the humanities, we don't have even have a phrase for that.
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97 Pages, what the hell, are people really confused that 2(9+3) is 2*(9+3)????
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On April 09 2011 11:44 Ropid wrote:Show nested quote +On April 09 2011 11:27 MaRiNe23 wrote:
I didn't read the thread and I was also scared to post this but I'm pretty sure that "1/2x" question reads as (1/2)x. Mainly nervous cuz so many people voted 1/(2x). What's the correct answer? If a formula stands on its own line on a page and therefore space is of no concern, a mathematician would write something like this in his publication: ![[image loading]](http://latex.codecogs.com/gif.latex?$$\frac{1}{2x}$$) The mathematician would then use something like ![[image loading]](http://latex.codecogs.com/gif.latex?$$1/2x$$) inside his text paragraphs to save vertical space and would mean 1/(2*x), though it would probably be written as ![[image loading]](http://latex.codecogs.com/gif.latex?$$(2x)^{-1}$$) to be clear. Stuff with "/" is generally avoided. Programmers and elementary school kids write stuff like this: "1 / 2 * x" and thus it is clear that it means "(1 / 2) * x". In summary: the OP is a prick.
That makes sense but you should still write it as (1/2)x if you mean x/2. I do many math problems and I can't just type in "1/2x" and expect the TI-83 or 84 to interpret that as 1 divided by 2x unless I explicitely put parenthesis at 2x.
Maybe for a textbook it's understood to be 1/(2x) but in no way is that correct. I'm sure if they had plenty of ink to spare they would "print" that extra parenthesis in between 2x to avoid confusion.
All in all, I understand the reasoning as to why they write it as 1/2x to save vertical space but that is 100% wrong and they really need to put at least put the parenthesis. It would defeinitely fool some kids into putting 1/2x into their TI-84 thinking it will give them 1/(2x) if they didn't know that the author only did that to save vertical space. Lmao what a joke. I didn't know they did that.
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On April 09 2011 13:02 BeJe77 wrote:
97 Pages, what the hell, are people really confused that 2(9+3) is 2*(9+3)????
no, they don't understand order of operations
and even if that's confusing... they don't know how to turn 48 / 2 into 48 * 1/2
to get 48 * 1/2 * 12 = 288, not 2
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On April 09 2011 12:56 DiamondTear wrote: Oh, that shows the problem beautifully. Portable Calculators just do the same whether there's a number or a variable in the parenthesis. chonkyfire: I'm curious, why don't you just add the 9 and 3 inside the parenthesis? That's the first thing I would do.
If you input 1/2(x) instead of 1/2x, the Wolfram Alpha parsing switches from 1/(2*x) to (1/2)*x, so it's not the numbers, but the parenthesis that decide that for Wolfram Alpha. But this also demonstrates that all that left-to-right writing is just not designed for humans, and that's the reason Wolfram Alpha displays a nicely typeset representation, so that you can check you really got what you wanted, before you look at the graphs or whatever it draws from your formula.
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On April 09 2011 13:02 BeJe77 wrote:
97 Pages, what the hell, are people really confused that 2(9+3) is 2*(9+3)????
No, some people think that any number has to get prioritized if it's connected but outside of a parenthis for some reason (don't ask me why). And others just don't know what has priority.
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On April 09 2011 13:04 Keitzer wrote:Show nested quote +On April 09 2011 13:02 BeJe77 wrote:
97 Pages, what the hell, are people really confused that 2(9+3) is 2*(9+3)???? no, they don't understand order of operations and even if that's confusing... they don't know how to turn 48 / 2 into 48 * 1/2 to get 48 * 1/2 * 12 = 288, not 2
Not that you need to do that to get 288.
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On April 09 2011 13:07 Gnax wrote:Show nested quote +On April 09 2011 13:04 Keitzer wrote:On April 09 2011 13:02 BeJe77 wrote:
97 Pages, what the hell, are people really confused that 2(9+3) is 2*(9+3)???? no, they don't understand order of operations and even if that's confusing... they don't know how to turn 48 / 2 into 48 * 1/2 to get 48 * 1/2 * 12 = 288, not 2 Not that you need to do that to get 288.
Yeah, you don't need to make the 2 into 1/2 or whatever... I think people might be hanged up thinking that 2(9+3) is distributive property (if I am using the term properly) or they think that multiplication comes before division, which is not the case sense Multiplication and Division have same priority so you do them left to right in the order they come....
PEDMA
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United States5162 Posts
On April 09 2011 13:02 BeJe77 wrote:
97 Pages, what the hell, are people really confused that 2(9+3) is 2*(9+3)????
It's not just that though. It's 48/2(9+3) which some people are reading as 48/(2(9+3)) when there's nothing to say that the 2 should be distributed by itself. Imo opinion it should be read as (48/2)(9+3)
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On April 09 2011 12:52 chonkyfire wrote:Show nested quote +On April 09 2011 12:51 Gnax wrote:On April 09 2011 12:48 chonkyfire wrote:On April 09 2011 12:45 Myles wrote:On April 09 2011 12:40 chonkyfire wrote:On April 09 2011 12:36 Keitzer wrote:ok... here we go... Yeah, but do you have a reliable source that says you don't assume the 2 goes with (9+3) in this case? Everything I keep reading is that in a situation like this 2(9+3) = (2*9+2*3) If you can give me a source saying otherwise fantastic. I'm looking for it myself. I'm sure you're real smart and great at math, but there has to be a rule written somewhere especially since brackets have their own rules in algebra It's not 2*9+2*3 because the two is already being affected by the 48. You can't ignore the 48, it goes along with the two in the distribution. If it were 48+2(9+3) then you would distribute only the 2 to the parenthesis and it would be 48+24. But because the 48 is divided by the two, it cant be ignored in the distribution. It goes along too. So it becomes (48/2)*9+(48/2)*3 I would argue the 2 being next to (9+3) is directly effecting (9+3) and that by doing 48/2 first you're ignoring the 24 that actually exists, and from what I keep reading that is the case. I just want a source that says other wise. I'm not asking for much. On April 09 2011 12:46 Keitzer wrote:On April 09 2011 12:45 chonkyfire wrote:On April 09 2011 12:41 Keitzer wrote:
yes, you can't just assumed parenthesis left and right.
5 + 5 * 5 =/= 50, NEVER!!!
however, with your, just-assume-em rule, you CAN make it 50... by going (5+5) * 5 = 50
HOWEVER! (and the point i've been making this entire time) is that the ORIGINAL equation is NOT written with assumed parenthesis, and THUS cannot be used in explanation of a wrong answer. that's not a very good source whatever this thread is going no where yes it is, as it's the EXACT same principle (that assuming parenthesis yields a different result) edit: posting pic again for those who still are not convinced.... notice the ASSUMED (problem changing) parenthesis in the bottom section. Didn't you write that? I'm confused now. Just find a source yourself, you just need to google the priorities in math. There is no 2 that is afflicting the 12 because 48 said zimzallabim and made it go away. Do you not read full posts before you respond? I have been looking for sources and all I'm finding are sources saying the opposite, so I'm giving these guys who are so passionate that its 288 a chance to show me some concrete evidence that would lead me to believe the answer is not 2.
Eh, if you are arguing that answer is 2, than the argument should go like this :
Since OP did not specified notation I assumed a notation where implied multiplication has bigger priority than explicit one (that includes division). Ergo answer is 2.
But that is as arbitrary answer as 288, actually even slightly worse.
You also should not argue that there are implied parenthesis, because it is not elegant and leads to problems. Also (I am not sure if you specifically were arguing it) for people arguing that it is 2 or even that expression is ambiguous : Associative and distributive properties have NOTHING to do with it, you cannot argue it based on them. They are properties of mathematical operators and are used after expression is parsed.
So if you parsed OP expression as 48/2*(9+3) = (48/2)*(9+3) so distributive property gives you (48/2)*9 + (48/2)*3 = 288
If you parsed it as 48/(2*(9+3)) than distributive property gives you 48/(2*9 + 2*3).
Note that in the second case those are not hidden parenthesis that I added, but result of transformation from one notation to another , see my reply to FindMeInKenya about that (page 93-94 I think, or somewhere close).
EDIT : added also in last paragraph
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EPT
