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On April 09 2011 04:48 Sluggy wrote:Show nested quote +On April 09 2011 04:37 Shadowcloak wrote:
why does it ask math at university lvl this is high school material order of operations is elementary school material. The interest of the poll is how people studying math at a high level can overlook the standard way of evaluating expressions. It doesn't say anything about the ability of these people to understand elementary school concepts, but it does serve as a reminder that there are ambiguities in the way things can be evaluated and that is why standardized conventions exist in the first place.
Meh, it's not very standard, because obviously a lot of people don't do it. A group of mathematicians might say: "This is the standard way", but that's just cause that's what they say, doesn't necessarily mean it's right or wrong. The real standardized convention is to use parentheses (brackets) to make your equations clear, not to assume that people will do things left to right or right to left when they're feeling lazy.
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United States24772 Posts
On April 09 2011 04:57 mpupu wrote:Show nested quote +On April 09 2011 04:54 micronesia wrote:On April 09 2011 04:23 chonkyfire wrote:On April 09 2011 04:20 Ace wrote:On April 09 2011 04:16 chonkyfire wrote:On April 09 2011 04:14 Ace wrote:
Even if there is implied multiplication - you can't distribute the 2 because you have to do whats inside parenthesis first.
Pretty simple math here. how is distributing not doing the parenthesis? 2(9+3) = 24 (2*9+2*3) = 24 because there is an expression on the left of it. If it was just what you wrote then sure it works because there is nothing else there. However you have 48 ÷ sitting to the left of it. PEMDAS/Order of Operations tells you that you have to go left to right when dealing with equal precedence. Even if you wanted to distribute this is what you'd get: 48 ÷ 2(9+3) 24(9+3) 216 + 72 288  No now you're not doing the brackets first. If you distribute you do that brackets first. If you did the brackets first you get 48/24 Distributing is not a bracket/parentheses operation... it is multiplication. Thus, you can only distribute if you are allowed to multiply the 2 by the the expression in the brackets. You can not multiply the 2 by the (9+3) yet. Multiplication and Division have equal weight and occur from left to right in a one-liner mathematical expression. The division must be done before the multiplication according to strict math rules. Thus, it is not acceptable to distribute the 2 into the 9+3 before doing 48/2. The point is that it's possible to distinguish between implicit and explicit multiplication, and assign different weight to both. In that case, implicit multiplication occurs first and the distributive law can be correctly applied.
Er no my point was that the P in PEMDAS does not entitle you to distribute before doing other multiplication/division that occurs to the left of it. I agree with you about the explanation for why you might be permitted to do the multiplication of distribution before doing the division in that example due to the written ambiguity.
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On April 09 2011 04:57 Pufftrees wrote:Show nested quote +On April 09 2011 03:58 levelnoobz wrote:
BTW I really don't see the point of those 81 pages appart from proving that if you write maths like this nobody will understand you. By 'nobody' you mean anyone who doesn't understand how math works I imagine.
No he is right, the way it is written is WRONG, and by that I mean that it will creates missunderstandings for nothing really.
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On April 09 2011 04:58 Sluggy wrote:Show nested quote +On April 09 2011 04:52 Roggay wrote:On April 09 2011 04:48 Sluggy wrote:On April 09 2011 04:37 Shadowcloak wrote:
why does it ask math at university lvl this is high school material order of operations is elementary school material. The interest of the poll is how people studying math at a high level can overlook the standard way of evaluating expressions. It doesn't say anything about the ability of these people to understand elementary school concepts, but it does serve as a reminder that there are ambiguities in the way things can be evaluated and that is why standardized conventions exist in the first place. The standard convention requires parenthesis for such cases, atleast its what they taught me at school here, and its more logic this way. Here standard convention means the accepted way of handling things. The standard at your school could be to parenthesize everything so that no ambiguities can exist, but in general you don't need parenthesis to evaluate it if you follow a convention. The standard convention says division and multiplication have the same precedence so how do you choose? The standard is to then evaluate expressions from left to right if the precedence is the same. Ambiguity is eliminated after that. I could state my own convention that once precedence is established to evaluate from right to left, but it wouldn't be standard.
It is maybe a standard in the US, but it may not in other places. The standard in my country is to put parenthesis to exclude any ambiguity, anything else is false.
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On April 09 2011 04:55 mpupu wrote:Show nested quote +On April 09 2011 04:50 Ace wrote:On April 09 2011 04:31 mpupu wrote:On April 09 2011 04:24 Ace wrote:
I just showed you that the answer is still 288 even if you do distribute. I've got a lot of math exposure since you know I have to take a lot of them for my major. But keep assuming that everyone that disagrees with you is "less qualified". PEMDAS isn't just for beginners - it's there for everyone as a standard guideline for dealing with just this kind of thing. Stop making excuses and trolling the thread. Don't take it personally. I'm not trolling anyone and I never said you were "less qualified" or anything like that. But if the only guideline you know is PEMDAS, you're missing the big picture. And saying you can't apply the distributive property is certainly wrong, that's 100% fact. I'll give you an analogy: let's say you know how the common SOH-CAH-TOA applies to trigonometric functions. Would you dispute it if I told you that sine is a trascendental function defined in terms of infinite series? After all, it's just a relation between the lengths of different sides of a triangle, right? What does that have to do with *anything* here? If you have another method then show us but there is no "big picture" here. It's very simple, basic math. Here let's do it like this: 48 ÷ 2(9+3) Let's rewrite it so there is no division. Remembering that multiplication is the reciprocal of division: 48 ÷ 2(9+3) = 48 * 1/2*(9+3) Notice I'm using the original post by the OP so there is no confusion with the "/" sign. There isn't any advanced version of this stuff any further than this. No matter what you try to do the answer will be 288. You can distribute the 1/2 to the parenthesis and up with 48 x 6 , use PEMDAS and up with with 24 x 12, multiply them in any order - it will always be 288. The "other method" has been mentioned several times in this thread: assigning higher precedence to implicit multiplication. But you seem to think PEMDAS is the only valid approach. If you don't want to change your mind, that's your prerogative. Otherwise, the link provided above is a good reference for what I'm trying to say (http://mathforum.org/library/drmath/view/57021.html).
and I just re-wrote it for you with no division and all multiplication just so we could ignore PEMDAS and implicit multiplication. Just elementary a x b x c. Did you just skip that part?
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On April 09 2011 04:50 Roggay wrote:Show nested quote +On April 09 2011 04:42 ChrisXIV wrote:On April 09 2011 04:32 VisuaL. wrote:
I'm currently in school to be a chemist and i took a math course in fall.
I got 288
and
1/(2*x)
was pretty easy and don't see how it can be 2 :s By reading the first one like you did the second. Because if you want to be consistent it has to be 1) 2 and 1/(2x) or 2) 288 and x/2 otherwise you are contradicting yourself. The "2" in "2x" can be interpreted as the coefficient of x, however there is no x in 48÷2(9+3).
x=12
48÷2(9+3)=48÷2x
Anybody who voted 288, and 1/(2*x) is inconsistent in they thinking.
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http://mathforum.org/library/drmath/view/57021.html actually sums it up quite well.
I think this is far preferable to making detailed rules that are
likely to trick people. Sometimes one rule seems natural, and
sometimes another, so people will forget any rule we choose to teach
in this area. I've heard from too many students whose texts do "give
an example that really puts this rule to the test," but do so by
having them evaluate an expression like:
6/2(3)
that is too ambiguous for any reasonable mathematician ever to write.
And no matter what the rule, we would still constantly see students
write things like "1/2x" meaning half of x, so we'd still have to make
reasonable guesses rather than stick to the rules.
Can we finally at least agree the equation is ambiguous? Of course not.
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On April 09 2011 05:04 Ace wrote:Show nested quote +On April 09 2011 04:55 mpupu wrote:On April 09 2011 04:50 Ace wrote:On April 09 2011 04:31 mpupu wrote:On April 09 2011 04:24 Ace wrote:
I just showed you that the answer is still 288 even if you do distribute. I've got a lot of math exposure since you know I have to take a lot of them for my major. But keep assuming that everyone that disagrees with you is "less qualified". PEMDAS isn't just for beginners - it's there for everyone as a standard guideline for dealing with just this kind of thing. Stop making excuses and trolling the thread. Don't take it personally. I'm not trolling anyone and I never said you were "less qualified" or anything like that. But if the only guideline you know is PEMDAS, you're missing the big picture. And saying you can't apply the distributive property is certainly wrong, that's 100% fact. I'll give you an analogy: let's say you know how the common SOH-CAH-TOA applies to trigonometric functions. Would you dispute it if I told you that sine is a trascendental function defined in terms of infinite series? After all, it's just a relation between the lengths of different sides of a triangle, right? What does that have to do with *anything* here? If you have another method then show us but there is no "big picture" here. It's very simple, basic math. Here let's do it like this: 48 ÷ 2(9+3) Let's rewrite it so there is no division. Remembering that multiplication is the reciprocal of division: 48 ÷ 2(9+3) = 48 * 1/2*(9+3) Notice I'm using the original post by the OP so there is no confusion with the "/" sign. There isn't any advanced version of this stuff any further than this. No matter what you try to do the answer will be 288. You can distribute the 1/2 to the parenthesis and up with 48 x 6 , use PEMDAS and up with with 24 x 12, multiply them in any order - it will always be 288. The "other method" has been mentioned several times in this thread: assigning higher precedence to implicit multiplication. But you seem to think PEMDAS is the only valid approach. If you don't want to change your mind, that's your prerogative. Otherwise, the link provided above is a good reference for what I'm trying to say (http://mathforum.org/library/drmath/view/57021.html). and I just re-wrote it for you with no division and all multiplication just so we could ignore PEMDAS and implicit multiplication. Just elementary a x b x c. Did you just skip that part?
Well, the entire point is that some people re-write it in a different way.
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How would this question have been written if it were on the SATs exactly? I have an idea, but I'm not sure it's right so I don't want to post it.
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On April 09 2011 05:02 Roggay wrote:Show nested quote +On April 09 2011 04:58 Sluggy wrote:On April 09 2011 04:52 Roggay wrote:On April 09 2011 04:48 Sluggy wrote:On April 09 2011 04:37 Shadowcloak wrote:
why does it ask math at university lvl this is high school material order of operations is elementary school material. The interest of the poll is how people studying math at a high level can overlook the standard way of evaluating expressions. It doesn't say anything about the ability of these people to understand elementary school concepts, but it does serve as a reminder that there are ambiguities in the way things can be evaluated and that is why standardized conventions exist in the first place. The standard convention requires parenthesis for such cases, atleast its what they taught me at school here, and its more logic this way. Here standard convention means the accepted way of handling things. The standard at your school could be to parenthesize everything so that no ambiguities can exist, but in general you don't need parenthesis to evaluate it if you follow a convention. The standard convention says division and multiplication have the same precedence so how do you choose? The standard is to then evaluate expressions from left to right if the precedence is the same. Ambiguity is eliminated after that. I could state my own convention that once precedence is established to evaluate from right to left, but it wouldn't be standard. It is maybe a standard in the US, but it may not in other places. The standard in my country is to put parenthesis to exclude any ambiguity, anything else is false.
Is that really the standard in your country? I don't care about trying to say whose standard is more correct, because that doesn't make sense. However, I am interested in any nation's math representative (lol) declaring official conventions for a country. I'm a programmer so I just parenthesize everything anyway just in case whatever compiler I'm using has a different convention for some ungodly reason.
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On April 09 2011 04:29 Perscienter wrote:
I suppose grammar is just for beginners, too. The internet elite apparently doesn't need it.
Yes, in point of fact, strict grammatical adherence IS for beginners. There are circumstances where not using strict grammar is correct for a variety of possible reasons. (Including situations such as fiction writing, in which time is not a factor.)
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The problem in the question from the first post is that when you write a division from left to right instead of from top to bottom, you always also use a multiplication sign between elements. And if there would have been a multiplication sign between the "2" and the "(" in the first post, it would not have been interpreted wrongly.
What I saw in school was either this:
48 / 2 * (9 + 3)
or this:
48
--- (9 + 3)
2
or this:
48
-------------
2 (9 + 3)
Also, the dropped multiplication sign reappears to not confuse the reader with spaces, if there would be two numbers besides each other. Like this:
2 (9 + 3) = 2 * 12
Something like "2 12" would be confusing. If it's without numbers, the multiplication sign can still be dropped, like here:
a (b + c) = a b + a c
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the distribution is multiplication in BEDMAS, not a bracket/parenthesis.
why don't people get that?
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On April 09 2011 05:13 Sluggy wrote:Show nested quote +On April 09 2011 05:02 Roggay wrote:On April 09 2011 04:58 Sluggy wrote:On April 09 2011 04:52 Roggay wrote:On April 09 2011 04:48 Sluggy wrote:On April 09 2011 04:37 Shadowcloak wrote:
why does it ask math at university lvl this is high school material order of operations is elementary school material. The interest of the poll is how people studying math at a high level can overlook the standard way of evaluating expressions. It doesn't say anything about the ability of these people to understand elementary school concepts, but it does serve as a reminder that there are ambiguities in the way things can be evaluated and that is why standardized conventions exist in the first place. The standard convention requires parenthesis for such cases, atleast its what they taught me at school here, and its more logic this way. Here standard convention means the accepted way of handling things. The standard at your school could be to parenthesize everything so that no ambiguities can exist, but in general you don't need parenthesis to evaluate it if you follow a convention. The standard convention says division and multiplication have the same precedence so how do you choose? The standard is to then evaluate expressions from left to right if the precedence is the same. Ambiguity is eliminated after that. I could state my own convention that once precedence is established to evaluate from right to left, but it wouldn't be standard. It is maybe a standard in the US, but it may not in other places. The standard in my country is to put parenthesis to exclude any ambiguity, anything else is false. Is that really the standard in your country? I don't care about trying to say whose standard is more correct, because that doesn't make sense. However, I am interested in any nation's math representative (lol) declaring official conventions for a country. I'm a programmer so I just parenthesize everything anyway just in case whatever compiler I'm using has a different convention for some ungodly reason.
![[image loading]](http://i.imgur.com/aP7Gg.jpg)
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On April 08 2011 05:36 Empyrean wrote:
Multiplication and division are done left to right, since they're in the same tier in the order of operations.
Is this true? :O Wikipedia link where I can learn? When I was a kid we had to learn MIDAS, which in swedish stands for "multiplication before division, addition and subtraction". So I always thought that multiplication had higher priority than division.
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On April 09 2011 05:15 BluePanther wrote:
the distribution is multiplication in BEDMAS, not a bracket/parenthesis.
why don't people get that?
EDIT: Nevermind, there's a possible interpretation of your statement that doesn't require willful ignorance of the discussion.
EDIT2: And it's the correct interpretation of your statement. My bad.
Although your statement is STILL deceptive since it implies that division always takes precedence over multiplication. Not really adding clarity here.
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On April 09 2011 04:58 TallMax wrote:Show nested quote +On April 09 2011 04:48 Sluggy wrote:On April 09 2011 04:37 Shadowcloak wrote:
why does it ask math at university lvl this is high school material order of operations is elementary school material. The interest of the poll is how people studying math at a high level can overlook the standard way of evaluating expressions. It doesn't say anything about the ability of these people to understand elementary school concepts, but it does serve as a reminder that there are ambiguities in the way things can be evaluated and that is why standardized conventions exist in the first place. Meh, it's not very standard, because obviously a lot of people don't do it. A group of mathematicians might say: "This is the standard way", but that's just cause that's what they say, doesn't necessarily mean it's right or wrong. The real standardized convention is to use parentheses (brackets) to make your equations clear, not to assume that people will do things left to right or right to left when they're feeling lazy.
Groups of mathematicians are usually the ones establishing standards for math. I think a good example of separating standard convention from convention is for describing length.
In the US our convention is to use yards/feet/inches to measure something
Basically everywhere else it is meters
The scientific standard units (SI) arbitrarily uses metric and I would be a jackass to try and tell people that feet are a standard unit of measuring length. It is true there is nothing special about SI units other than the fact that they present a common ground for people to communicate numbers in a meaningful way without having to do a bunch of conversions.
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United States24772 Posts
On April 09 2011 05:19 Severedevil wrote:Show nested quote +On April 09 2011 05:15 BluePanther wrote:
the distribution is multiplication in BEDMAS, not a bracket/parenthesis.
why don't people get that? Why don't you read even a small fraction of the fucking thread before shitting in it?
He means the several people who have recently incorrectly associated distribution with the parentheses/bracket level of priority in the order of operations. His post does not really indicate ignorance of the thread.
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On April 09 2011 05:18 chonkyfire wrote:Show nested quote +On April 09 2011 05:13 Sluggy wrote:On April 09 2011 05:02 Roggay wrote:On April 09 2011 04:58 Sluggy wrote:On April 09 2011 04:52 Roggay wrote:On April 09 2011 04:48 Sluggy wrote:On April 09 2011 04:37 Shadowcloak wrote:
why does it ask math at university lvl this is high school material order of operations is elementary school material. The interest of the poll is how people studying math at a high level can overlook the standard way of evaluating expressions. It doesn't say anything about the ability of these people to understand elementary school concepts, but it does serve as a reminder that there are ambiguities in the way things can be evaluated and that is why standardized conventions exist in the first place. The standard convention requires parenthesis for such cases, atleast its what they taught me at school here, and its more logic this way. Here standard convention means the accepted way of handling things. The standard at your school could be to parenthesize everything so that no ambiguities can exist, but in general you don't need parenthesis to evaluate it if you follow a convention. The standard convention says division and multiplication have the same precedence so how do you choose? The standard is to then evaluate expressions from left to right if the precedence is the same. Ambiguity is eliminated after that. I could state my own convention that once precedence is established to evaluate from right to left, but it wouldn't be standard. It is maybe a standard in the US, but it may not in other places. The standard in my country is to put parenthesis to exclude any ambiguity, anything else is false. Is that really the standard in your country? I don't care about trying to say whose standard is more correct, because that doesn't make sense. However, I am interested in any nation's math representative (lol) declaring official conventions for a country. I'm a programmer so I just parenthesize everything anyway just in case whatever compiler I'm using has a different convention for some ungodly reason.
that image is meaningless to me, it is a calculators convention for evaluating expressions and it offers nothing about accepted standards
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Germany2896 Posts
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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EPT
