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On April 08 2011 12:20 LloydRays wrote:
The original problem is a kind of "hahaha i got you! trololol" idiotic game that is designed to trap unsuspecting people by phrasing with unreasonably convoluted rules. This is why most people don't learn in school because we don't see the point when there will never be a situation where someone hands you such a problem that is written so poorly considering the division sign isn't used after fractions are introduced.
I guess it makes some unsocial people feel better about how they have wasted their time and make them think that they waste it better than other people who would rather waste time say, playing starcraft, or going for a walk etc.
It is NOT unreasonable rules.
There are three things going on here.
Some people think PEMDAS puts multiplication before division.
Some people start at the parenthesis, and move left, and forget about the left-to-right rule (how is left to right unreasonable?)
Some people replace the division sign with / and automatically assume everything to the right of the division sign is to be solved first.
The third is the trickiest and is the one that most people (or at least should be) are arguing over.
4-2x5+3 = -3 The rules are so simple in solving that, a child can do it.
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On April 08 2011 12:17 Count9 wrote:Show nested quote +On April 08 2011 12:15 SharkSpider wrote:
The correct answer is that real mathematicians don't use the division sign because it's misleading. The actual, official rules behind it are obscure to the extent where someone taking a Math degree doesn't know what they are. For that matter, neither is /. When mathematicians talk online, though, / typically means "big line" unless it's got brackets on it.
So correct or not, the "msn" variety of math syntax recognizes 1/2x as (1/(2x)), at least where I'm from. This is because we always carry through fractions and never write something like (1/2)*x. It would always be x/2 or even 1x/2 if 1 was another number.
For the first one, you do the brackets first, yes, but then you're left with a similar situation. If I used the / sign while asking my prof a question on a message board, then 48/2(9+3) is 2.
Furthermore, the rule of PEMDAS is that multiplication comes before division. Hence, we perform our task as follows:
48÷2(9+3) = 48÷2(12) = 48÷2*12 = 48÷24 = 2
The reason this must be specified is that 48÷2*12 can either be read left to right (a mistake) or by using multiplication first (the correct response).
So yeah, I'm a mathematician and I think it's 2. I was taught the MD in PEMDAS was Multiplication and Division from left to right, just like AS is Addition and Subtraction from left to right. No one would do 1-1+2=-2.
I was taught to do it like that for the multiplication/division. For addition and subtraction, I just treat the messy - signs like +(-) instead, makes it easier.
Either way, this just goes to show that using division symbols and / is a primitive and ineffectual form of communicating mathematics. There's a reason the OP's formula would not be accepted in a paper in math.
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On April 08 2011 12:15 SharkSpider wrote:
The correct answer is that real mathematicians don't use the division sign because it's misleading. The actual, official rules behind it are obscure to the extent where someone taking a Math degree doesn't know what they are. For that matter, neither is /. When mathematicians talk online, though, / typically means "big line" unless it's got brackets on it.
So correct or not, the "msn" variety of math syntax recognizes 1/2x as (1/(2x)), at least where I'm from. This is because we always carry through fractions and never write something like (1/2)*x. It would always be x/2 or even 1x/2 if 1 was another number.
For the first one, you do the brackets first, yes, but then you're left with a similar situation. If I used the / sign while asking my prof a question on a message board, then 48/2(9+3) is 2.
Furthermore, the rule of PEMDAS is that multiplication comes before division. Hence, we perform our task as follows:
48÷2(9+3) = 48÷2(12) = 48÷2*12 = 48÷24 = 2
The reason this must be specified is that 48÷2*12 can either be read left to right (a mistake) or by using multiplication first (the correct response).
So yeah, I'm a mathematician and I think it's 2.
Multiplication NEVER has a precedence over division. They have equal precedence.
48÷2*12 = 48 * 0.5 * 12 = 288 by the associative law.
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Questions like this are why a bunch of people thing the SAT Math section is hard.
Lawl.
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Another way to look at it would be to distribute the 2 into the parentheses first then finish the math.
48/2(3+9) = 48/(6+18) = 48/24 = 2
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This is exactly why I always use gratuitous parenthesis.
Example: ((1/2)x)/5 if I were typing into a calculator, even though 1/2x/5 would get the exact same answer. Helps keep me on track, and I know for sure that it works as intended.
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On April 08 2011 12:25 Fdragon wrote:
Another way to look at it would be to distribute the 2 into the parentheses first then finish the math.
48/2(3+9) = 48/(6+18) = 48/24 = 2
(48 divided by 2 times 3) plus (48 divided by 2 times 9)
You cannot negligently distribute just to get a result that you want. Either fully distribute or don't distribute at all.
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It should honestly look like this: (48÷2)(9+3). Any teacher who wrote the other would get hanged at my school.
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On April 08 2011 12:27 Pigsquirrel wrote:
This is exactly why I always use gratuitous parenthesis.
Example: ((1/2)x)/5 if I were typing into a calculator, even though 1/2x/5 would get the exact same answer. Helps keep me on track, and I know for sure that it works as intended.
I agree with this. Even if I'm doing division in excel or on a calculator, I make sure my denominator has parenthesis.
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basic elementary algebra 
inner braces and/or brackets 1st priority -whatever operations involved. (9+3)= 12
Division and multiplication are equal in priority as addition and subtraction are but division and multiplication are prioritize 1st before addition and subtraction. 48 ÷ 2 (12)
÷ and / are same
*, variable beside a number ie.X9 and any result or number besides a brace are same. 24(12) or 24 x 12 = 288
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On April 08 2011 12:23 SharkSpider wrote:Show nested quote +On April 08 2011 12:17 Count9 wrote:On April 08 2011 12:15 SharkSpider wrote:
The correct answer is that real mathematicians don't use the division sign because it's misleading. The actual, official rules behind it are obscure to the extent where someone taking a Math degree doesn't know what they are. For that matter, neither is /. When mathematicians talk online, though, / typically means "big line" unless it's got brackets on it.
So correct or not, the "msn" variety of math syntax recognizes 1/2x as (1/(2x)), at least where I'm from. This is because we always carry through fractions and never write something like (1/2)*x. It would always be x/2 or even 1x/2 if 1 was another number.
For the first one, you do the brackets first, yes, but then you're left with a similar situation. If I used the / sign while asking my prof a question on a message board, then 48/2(9+3) is 2.
Furthermore, the rule of PEMDAS is that multiplication comes before division. Hence, we perform our task as follows:
48÷2(9+3) = 48÷2(12) = 48÷2*12 = 48÷24 = 2
The reason this must be specified is that 48÷2*12 can either be read left to right (a mistake) or by using multiplication first (the correct response).
So yeah, I'm a mathematician and I think it's 2. I was taught the MD in PEMDAS was Multiplication and Division from left to right, just like AS is Addition and Subtraction from left to right. No one would do 1-1+2=-2. I was taught to do it like that for the multiplication/division. For addition and subtraction, I just treat the messy - signs like +(-) instead, makes it easier. Either way, this just goes to show that using division symbols and / is a primitive and ineffectual form of communicating mathematics. There's a reason the OP's formula would not be accepted in a paper in math.
The same way you can choose to change all subtractions to adding the negative, you can change divisions to multiplying by the reciprocal.
It doesn't matter how you approach the problem, PEMDAS still has multiplication and division on the same tier (and you solve the problem from left to right), and the same goes with addition and subtraction... for the reason I mentioned above. They're pairs of interchangeable operations depending on how you want to manipulate the given problem.
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On April 08 2011 12:23 JinDesu wrote:Show nested quote +On April 08 2011 12:20 LloydRays wrote:
The original problem is a kind of "hahaha i got you! trololol" idiotic game that is designed to trap unsuspecting people by phrasing with unreasonably convoluted rules. This is why most people don't learn in school because we don't see the point when there will never be a situation where someone hands you such a problem that is written so poorly considering the division sign isn't used after fractions are introduced.
I guess it makes some unsocial people feel better about how they have wasted their time and make them think that they waste it better than other people who would rather waste time say, playing starcraft, or going for a walk etc. It is NOT unreasonable rules. There are three things going on here. Some people think PEMDAS puts multiplication before division. Some people start at the parenthesis, and move left, and forget about the left-to-right rule (how is left to right unreasonable?) Some people replace the division sign with / and automatically assume everything to the right of the division sign is to be solved first. The third is the trickiest and is the one that most people (or at least should be) are arguing over. 4-2x5+3 = -3 The rules are so simple in solving that, a child can do it.
so you use the division sign still? People don't like math because of stupid shit like this, if math teachers would focus on helping people understand things by making them clear instead of tricking them into the errors of math, more people would be interested in my opinion
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If the answer to the first question is 2 then:
a + b ÷ c * d ends up being different from a + b * (1/c) ÷ (1/d)
That's a weird idea if I've ever heard one.
I'd have to request clarification for the second question; I don't think it's clear as written.
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What pisses me off is not that people got this wrong on the first go... the question is obviously written in a tricky way. What gets me is that people are actually arguing in favor of the wrong answer after seeing everyone showing why 288 is right.
On April 08 2011 12:25 Fdragon wrote:
Another way to look at it would be to distribute the 2 into the parentheses first then finish the math.
48/2(3+9) = 48/(6+18) = 48/24 = 2
wtf no that is not how algebra works.
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To put matters even more completely right, multiplication is division. Full disclosure: I *am* a mathematician. Anyone who has studied even basic abstract algebra knows that there is nothing called "division" - it's simply multiplying by the inverse. A field (such as the real numbers) has two binary operations - in this case, Addition and Multiplication. Subtraction is really the addition of the additive inverse of whatever you are "subtracting", and division is the multiplication by the multiplicative inverse of whatever you are "dividing" by.
So, in this case, when people say things like "PEDMAS" or any other silly way they had to remember basic order of operations, they are correct in saying that multiplication and division happen at the same level - since they are, in fact, the same operation.
As far as 1/2x, I have no idea if you would mean .5x or (2x)^-1 . Quite simply, if I was given that, I would ask them what it meant - it's unclear. At the very minimum, anyone doing even basic MSN math would write 1/(2x) if that was what they meant, and (1/2)/x, if they didn't want to use one of the many clearer ways of writing that out.
Edit: 1/2x is, technically, .5x. But anyone who writes 1/2x almost certainly meant 1/(2x).
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On April 08 2011 12:30 LloydRays wrote:Show nested quote +On April 08 2011 12:23 JinDesu wrote:On April 08 2011 12:20 LloydRays wrote:
The original problem is a kind of "hahaha i got you! trololol" idiotic game that is designed to trap unsuspecting people by phrasing with unreasonably convoluted rules. This is why most people don't learn in school because we don't see the point when there will never be a situation where someone hands you such a problem that is written so poorly considering the division sign isn't used after fractions are introduced.
I guess it makes some unsocial people feel better about how they have wasted their time and make them think that they waste it better than other people who would rather waste time say, playing starcraft, or going for a walk etc. It is NOT unreasonable rules. There are three things going on here. Some people think PEMDAS puts multiplication before division. Some people start at the parenthesis, and move left, and forget about the left-to-right rule (how is left to right unreasonable?) Some people replace the division sign with / and automatically assume everything to the right of the division sign is to be solved first. The third is the trickiest and is the one that most people (or at least should be) are arguing over. 4-2x5+3 = -3 The rules are so simple in solving that, a child can do it. so you use the division sign still? People don't like math because of stupid shit like this, if math teachers would focus on helping people understand things by making them clear instead of tricking them into the errors of math, more people would be interested in my opinion
Here is the big part. I was never explicitly taught that A/BC when written where the A is above the BC is actually A/(BC). If this was explicitly taught in every school to everyone, a lot fewer people here would be saying 2.
Whether you use the division sign is irrelevant. Using the division sign and using the fraction symbol matters in the way you understand it.
When I first did the thing, I got 2. Then I looked back at it and understood what I did wrong. This thread isn't about calling people stupid. It's about helping people understand what they were taught wasn't completely correct.
Or in the case of people saying PEMDAS and then putting multiplication higher than division, that they were taught completely wrong.
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So, this is 49 pages of people arguing over whether division or multiplication has higher precedence? Neat.
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On April 08 2011 12:34 Bibdy wrote:
So, this is 49 pages of people arguing over whether division or multiplication has higher precedence? Neat.
Maybe if you read those 49 pages, you'd see that division/multiplication priority is the smaller of the two issues.
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On April 08 2011 12:18 Kentor wrote:Show nested quote +On April 08 2011 11:57 -{Cake}- wrote:
math.berkeley.edu/~wu/order5.pdf
^interesting
just sayin nice. thanks for sharing. standardized tests are terrible lol wow he has a lot of other stuff http://math.berkeley.edu/~wu/
Apparently he has something to say about the math problem in the op (quote is slightly edited because certain symbols don't work in TL)
Now one never gets a computation of this type in real life, for several reasons. In
mathematics, the division symbol ÷ basically disappears after grade 7. Once
fractions are taught, it is almost automatic that 6 ÷ 10 would be replaced by
6 * (1/10). Moreover, if anyone wants you to compute 4 + 5 * 6 ÷ 10, he would
certainly make sure that you do what he wants done, and would put parentheses
around 5 * 6 ÷ 10 for emphasis. In a realistic context then, 4 + 5 * 6 ÷ 10
would have appeared either as 4 + (5 * 6 ÷ 10), or 4 + (5 * 6 * (1/10)). The
original problem is therefore a kind of Gotcha! parlor game designed to trap an
unsuspecting person by phrasing it in terms of a set of unreasonably convoluted
rules.
School mathematics education should not engage in enforcing rules for its own
sake, especially if the rules become indefensible. One may teach the Rules for the
Order of Operations in arithmetic in the form (A), but make clear to students
at the same time that these Rules should be applied judiciously and never at the
expense of clarity.
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EPT
