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On April 08 2011 14:59 Beardfish wrote:Show nested quote +On April 08 2011 14:34 Annoying wrote:proof that answer = 2 If you have 48/2(9+3) The 2 is attached to the (9+3), anyone who even got past algebra should remember factoring an equation out. Example: 2(a+b)=2a+2b 2(9+3)=(18+6) From there you get 48/(18+6)=48/24=2 not my work but i don't see how can this be wrong. for proof, check out http://www.purplemath.com/modules/orderops2.htm 5th example. No, the 48/2 "is attached" to the (9+3). 48/2(9+3) = 48/2(9) + 48/2(3) = 24(9) + 24(3) = 216 + 72 = 288. Also, PEMDAS.
pemdas don't help your case when 67% in this thread read / as a fraction line. You just changed the problem to give the answer 2, instead of 288, to 67% in this thread, who also will view your math as wrong - only because of your selection of sign for division operator
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Many people in this thread have made my following point, but I would like to further clarify. If you make (9+3) = x
Compare
1) 48÷2x
and
2) 48÷2*x
The impression you get from equation 1) is this:
48
2x
You divide all of 48 by 2x, your answer is 2
Now for equation 2, you see this:
48 ÷ 2 * x
Each mathematical operation seems to follow sequentially. The dilemma as seen in equation 1), where it appears that 2x must be solved first before continuing the rest of the equation, is averted. Your answer is 288.
This is just a testament of how poor writing of equations will lead to confusions, that's why we have specialized programs for writing equations and such. This test really proves nothing besides traditional typing in straight lines is a awful way of expression equations. The purpose of this test to see if people adhere to the BEDMAS (brackets, exponents, division/multiplication, addition/subtraction) has failed due to other factors. This is why math teachers deduct marks for terrible form when showing your work (at least mine did).
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I haven't done math in so long
isn't this wrong?
48/2(9+3)=
2*9 + 2*3 = 24
48/24 = 2
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On April 08 2011 15:01 Cutlery wrote:Show nested quote +On April 08 2011 14:59 Beardfish wrote:On April 08 2011 14:34 Annoying wrote:proof that answer = 2 If you have 48/2(9+3) The 2 is attached to the (9+3), anyone who even got past algebra should remember factoring an equation out. Example: 2(a+b)=2a+2b 2(9+3)=(18+6) From there you get 48/(18+6)=48/24=2 not my work but i don't see how can this be wrong. for proof, check out http://www.purplemath.com/modules/orderops2.htm 5th example. No, the 48/2 "is attached" to the (9+3). 48/2(9+3) = 48/2(9) + 48/2(3) = 24(9) + 24(3) = 216 + 72 = 288. Also, PEMDAS. pemdas don't help your case when 67% in this thread read / as a fraction line. You just changed the problem to give the answer 2, instead of 288, to 67% in this thread, who also will view your math as wrong - only because of your selection of sign for division operator
What...?
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On April 08 2011 15:04 chonkyfire wrote:
I haven't done math in so long
isn't this wrong?
48/2(9+3)=
2*9 + 2*3 = 24
48/24 = 2
yes it's wrong.
48/2 x (9+3)
24 x 12
288
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On April 08 2011 14:49 Assymptotic wrote:
And now for a pedantic proof:
Since we have 48, 2, 9, and 3, I will assume we're working within the field of real numbers (if we were working in the ring of integers, this problem gets ugly), which I will denote as R.
We know a few things about R.
R is equipped with the binary operations addition and multiplication, + and * respectively. Let a, b, and c be arbitrary elements in R.
The following properties hold:
1) For any a and b within R, a+b is still within R
2) For any a, b, and c in R, a+(b+c)=(a+b)+c
3) For any a in R, there exists a 0, which we will call the additive identity unit, such that a+0=0+a=a
4) For any a in R, there exists an additive inverse element -a, such that a+(-a)=0=(-a)+a
5) For any a and b in R, a+b=b+a
Note: These first five axioms are equivalent to saying that R is an abelian group with respect to addition, denoted as (R,+)
6) For any a and b in R, a*b is still contained in R
7) For any a, b, and c in R, a*(b*c)=(a*b)*c
8) For any nonzero element a in R, there exists a multiplicative inverse element a^(-1), such that a*a^(-1)=1=a^(-1)*a
9) For any a, b in R, a*b=b*a
10) For any a in R, there exists a multiplicative identity element, which we will call 1, such that a*1=1*a
Note: Axioms 6-10 are equivalent to saying that R minus the 0 element is an abelian group with respect to multiplication, denoted (R\{0}, *).
11) For any a, b, and c in R, a*(b+c)=a*c+a*c and (a+b)*c=a*c+b*c. This is called the distributive property.
Note: The notation ÷ is equivalent to multiplying the number to its immediate right by it's inverse.
e.g. a÷b=a*b^(-1)
Additional Note: When multiplying, the * symbol is sometimes removed for convenience.
e.g. a*b=ab or a(b+c)=ab+ac=a*b+a*c=a*(b+c)
48÷2(9+3)
=48*2^(-1)*(9+3)
=24*(9+3)
=24*9+24*3
=216+72
=288
*defines a field*
*Adds a note on how to interpret notation*
- In some cases implicit multiplication is given priority over explicit multiplication/division.
*Gets 2*
Is the process of defining a field meant to bully people into thinking you are right by having a wall of text?
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On April 08 2011 15:05 Beardfish wrote:Show nested quote +On April 08 2011 15:01 Cutlery wrote:On April 08 2011 14:59 Beardfish wrote:On April 08 2011 14:34 Annoying wrote:proof that answer = 2 If you have 48/2(9+3) The 2 is attached to the (9+3), anyone who even got past algebra should remember factoring an equation out. Example: 2(a+b)=2a+2b 2(9+3)=(18+6) From there you get 48/(18+6)=48/24=2 not my work but i don't see how can this be wrong. for proof, check out http://www.purplemath.com/modules/orderops2.htm 5th example. No, the 48/2 "is attached" to the (9+3). 48/2(9+3) = 48/2(9) + 48/2(3) = 24(9) + 24(3) = 216 + 72 = 288. Also, PEMDAS. pemdas don't help your case when 67% in this thread read / as a fraction line. You just changed the problem to give the answer 2, instead of 288, to 67% in this thread, who also will view your math as wrong - only because of your selection of sign for division operator What...?
View the 1/2x part of the poll to realize how most people interpret the / sign
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On April 08 2011 15:07 Zevah wrote:Show nested quote +On April 08 2011 15:04 chonkyfire wrote:
I haven't done math in so long
isn't this wrong?
48/2(9+3)=
2*9 + 2*3 = 24
48/24 = 2
yes it's wrong. 48/2 x (9+3) 24 x 12 288
You still don't escape the fact that you're trying to do math with horribly ambiguous notation.
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On April 08 2011 15:04 chonkyfire wrote:
I haven't done math in so long
isn't this wrong?
48/2(9+3)=
2*9 + 2*3 = 24
48/24 = 2
Someone else mentioned this in the thread and linked a website that discusses the confusion about this and how the way a question is written can be a problem for some.
I don't care if people get this right or wrong; but my God, if courtesy and help flew as freely as insults, any person who got this wrong would know what they did wrong and be better for it with a little assistance.
Instead we've basically got 50+ pages of people assuming anyone who didn't get the right answer is a "total idiot" and cause for all of us to "worry for humanity."
The hyperbole and ego in this thread is wildly entertaining.
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On April 08 2011 14:27 DarkPlasmaBall wrote:Show nested quote +On April 08 2011 14:18 mcc wrote:On April 08 2011 13:39 DarkPlasmaBall wrote:On April 08 2011 13:32 EEhantiming wrote:
i got 2
48÷2(9+3)
48÷2(12)
48÷24=2
Except "48÷2(12) 48÷24=2" is an incorrect step. You do division (48÷2) to get 24 before you do the multiplication. PEMDAS. Multiplication and division are on the same tier, so you whichever one comes first from left to right. And then 24(12) is 288. I think it's embarrassing how over 40% of the people who took the poll got it wrong... But this is not a law, just a notation. There is a bunch of different notations that do not use any of those rules, and it is easy to create notation where 48/2(2+2) = 6. You just define that implicit multiplication has bigger priority than division/explicit multiplication. This is actually used informally and there is no problem with that as long as people agree to interpret it like that. When you want to write something formally you just use parenthesis anyway. Except 48/2(2+2) = 48/2(4) = 24/4 = 6 for the same mathematical laws (PEMDAS) explained previously, not because 48/2(2+2) = 48/2(4) = 48/8 = 6. That's purely coincidence, as was shown in the OP's problem. Your analogous example happens to have the same answer both ways, but math is certainly not up to interpretation of notation. Math is defined and instructed by universal laws. You can't arbitrarily make multiplication have a bigger priority than division... that's not how math works. Unless you insert parentheses to depict priority, it's never assumed that the order of operations after the P in PEMDAS is violated. Ever. (At least, not in basic arithmetic o.O)
Ok that was bad example, I did not notice that it gets the same result in both notations. Let me rephrase I can define consistent notation where 48/2(3+9) = 2.
Other than that it seems that you misunderstand what notation means and what your PEMDAS is. PEMDAS is not a law it is just a way of defining a notation. Let me state :
2 = * / 48 2 + 3 9 in polish notation (PEMDAS is not applicable)
2 = 48/2(3+9) in notation (lets call it NV) that assigns higher priority to implicit multiplication (PEMDAS is not applicable)
2= 16/2(2+2) in your standard notation (PEMDAS applies)
2 = 48/(2(3+9)) in both NV and standard notation
2 = 2 in all mentioned notations
All those strings of characters mean the same thing : 2.
NV is slightly different because it basically adds new operator - the implicit multiplication, but it just a virtual operator that you can easily get rid of by simple transformation using explicit multiplication and parenthesis. All those notations can easily be transformed into each other. Hopefully you can see how that transformation is done. Notations are just different ways to write the same thing, and they have different strengths and weaknesses. For example reason why Polish notation is so cool, is that it does not require parenthesis to make expressions not ambiguous, as it actually does not have them.
Now math is not up to interpretation of notation. All mathematical laws are still in effect. All expressions have the same value, although their graphical representation(notation) might differ. PEMDAS is not a law, it is just a way of parsing an expression in standard notation and makes no sense in other notations. That can be seen especially well in Polish notation.
Note that when I write 2+1=0 in Z3, that is not (just) different notation. In this case I am operating on different entities altogether.
Of course you can create bunch of useless notations that are consistent, but otherwise serve no purpose. You could argue that NV is just such a useless notation (you cannot claim that about Polish notation and some others), that is your right. But as I pointed out it is often informally used, so it has at least some merit.
EDIT: Example for Polish notation is wrong(thanks for noticing Musou) correct one would be for example 2 = * / 48 48 + 1 1
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On April 08 2011 15:08 Cutlery wrote:
View the 1/2x part of the poll to realize how most people interpret the / sign
But both of those choices are equal.
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On April 08 2011 14:33 CustomKal wrote:Show nested quote +On April 08 2011 14:29 ]343[ wrote:On April 08 2011 13:08 xxpack09 wrote:On April 08 2011 12:58 Severedevil wrote:On April 08 2011 12:53 xxpack09 wrote:
PEMDAS/BEDMAS works from left to right. People tend to forget this.
Fourth-grade mnemonics do not reflect the usage of operators in any real mathematical context. You might as well tell me that five divided by two is equal to two remainder one. Except these "fourth-grade mnemonics" are correct in all situations.... They describe how to interpret symbols and operations in the correct manner. So no, that's a bad analogy. "Remainders" are informal whereas the order in which mathematical operations are carried out is as formal as it gets Since we're just pointlessly continuing this thread, might as well keep it going. "Remainder" is NOT an informal term. The concept of "k modulo n" is fundamental in number theory, and the generalized concept of quotients in algebra come with a "remainder": the quotient group G / H is precisely the group of "remainders" when we take all the elements of G and "mod out by" (or cancel) all the elements of H. Anyway I should stop talking since I probably just said something wrong and need to study for my algebra test lol What you said makes sense. Since it applies the most to computer science where % will the return the remainder when dividing integers. Remainders are a part of life if people like it or not. Mathematics has many different interpretations. The only issue is that with the one it uses a / sign which means division, which means we follow order of operation. Using a --- fraction sign gives an entirely different method and messes a lot of people up due to its large use in high school and later math when dealing with variables as opposed to strictly numbers.
No math does not have many interpretations, but different expressions can depending on the notation used. Laws of mathematics do not change, when notation changes, just their graphical form
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On April 08 2011 15:11 Beardfish wrote:Show nested quote +On April 08 2011 15:08 Cutlery wrote:
View the 1/2x part of the poll to realize how most people interpret the / sign But both of those choices are equal.
Then people are either contradicting themselves in the poll, or you don't see the difference between a fraction line and division sign
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On April 08 2011 15:07 HaNdFisH wrote:Show nested quote +On April 08 2011 14:49 Assymptotic wrote:
And now for a pedantic proof:
Since we have 48, 2, 9, and 3, I will assume we're working within the field of real numbers (if we were working in the ring of integers, this problem gets ugly), which I will denote as R.
We know a few things about R.
R is equipped with the binary operations addition and multiplication, + and * respectively. Let a, b, and c be arbitrary elements in R.
The following properties hold:
1) For any a and b within R, a+b is still within R
2) For any a, b, and c in R, a+(b+c)=(a+b)+c
3) For any a in R, there exists a 0, which we will call the additive identity unit, such that a+0=0+a=a
4) For any a in R, there exists an additive inverse element -a, such that a+(-a)=0=(-a)+a
5) For any a and b in R, a+b=b+a
Note: These first five axioms are equivalent to saying that R is an abelian group with respect to addition, denoted as (R,+)
6) For any a and b in R, a*b is still contained in R
7) For any a, b, and c in R, a*(b*c)=(a*b)*c
8) For any nonzero element a in R, there exists a multiplicative inverse element a^(-1), such that a*a^(-1)=1=a^(-1)*a
9) For any a, b in R, a*b=b*a
10) For any a in R, there exists a multiplicative identity element, which we will call 1, such that a*1=1*a
Note: Axioms 6-10 are equivalent to saying that R minus the 0 element is an abelian group with respect to multiplication, denoted (R\{0}, *).
11) For any a, b, and c in R, a*(b+c)=a*c+a*c and (a+b)*c=a*c+b*c. This is called the distributive property.
Note: The notation ÷ is equivalent to multiplying the number to its immediate right by it's inverse.
e.g. a÷b=a*b^(-1)
Additional Note: When multiplying, the * symbol is sometimes removed for convenience.
e.g. a*b=ab or a(b+c)=ab+ac=a*b+a*c=a*(b+c)
48÷2(9+3)
=48*2^(-1)*(9+3)
=24*(9+3)
=24*9+24*3
=216+72
=288
*defines a field* *Adds a note on how to interpret notation* - In some cases implicit multiplication is given priority over explicit multiplication/division. *Gets 2* Is the process of defining a field meant to bully people into thinking you are right by having a wall of text?
No, it's meant to be humorous. When I said the phrase "And now for a pedantic proof," I said the word 'now' in the a higher, somewhat silly tone. Imagine a Disney princess saying it or something.
I was thinking about italicizing that phrase, should I?
I also got the answer '2' when I glanced at the OP. I only arrived at 288 after cranking out that wall of text line for line.
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On April 08 2011 15:08 Cutlery wrote:Show nested quote +On April 08 2011 15:07 Zevah wrote:On April 08 2011 15:04 chonkyfire wrote:
I haven't done math in so long
isn't this wrong?
48/2(9+3)=
2*9 + 2*3 = 24
48/24 = 2
yes it's wrong. 48/2 x (9+3) 24 x 12 288 You still don't escape the fact that you're trying to do math with horribly ambiguous notation.
Well I thought the answer was 288, I'm just looking at other ways to do it. I still think the answer is 288 but some people are pretty advent about 2?
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On April 08 2011 15:11 Beardfish wrote:Show nested quote +On April 08 2011 15:08 Cutlery wrote:
View the 1/2x part of the poll to realize how most people interpret the / sign But both of those choices are equal.
1/2x = 1/(2*x)
By your logic (both of those choices are equal), then would (1/2)*(x) be equal?
(1/2)*(x) = (1/2)*(x/1) = x/2
C'mon. In most cases for people, this is between elementary and middle school stuff...
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On April 08 2011 15:14 chonkyfire wrote:Show nested quote +On April 08 2011 15:08 Cutlery wrote:On April 08 2011 15:07 Zevah wrote:On April 08 2011 15:04 chonkyfire wrote:
I haven't done math in so long
isn't this wrong?
48/2(9+3)=
2*9 + 2*3 = 24
48/24 = 2
yes it's wrong. 48/2 x (9+3) 24 x 12 288 You still don't escape the fact that you're trying to do math with horribly ambiguous notation. Well I thought the answer was 288, I'm just looking at other ways to do it. I still think the answer is 288 but some people are pretty advent about 2?
Well, to leave the space that is math, and enter the tubes that are the internetss, the thread is a troll, and we're digesting bait.
If you wish to see why, take a sheet of paper, and use 2(9+3) as the denominator, and 48 as the numerator. It's equivalent of writing 48/2x where x=9+3. 67% get the answer 2, while when written with the other "division sign" most people get 288. So the change of sign from ÷ to / apparently changes the entire equation for alot of people. Thusly the OP is a poll and not a quiz. To see how people interpret math, not what the correct answers are
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Let (9 + 3) = x
so 48/2(9 + 3) => 48/2x
By the second poll, most people believe this to be 48/(2x) = 2.
So why on earth is 288 leading?
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This is precisely why people should use excessive brackets when writing down things like this.
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On April 08 2011 15:17 Turo wrote:
Let (9 + 3) = x
so 48/2(9 + 3) => 48/2x
By the second poll, most people believe this to be 48/(2x) = 2.
So why on earth is 288 leading?
so its' not 48/2(x)= 288?
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EPT
