The question is not stated clearly, which is the fundamental cause of all our confusion. If you interpret (9+3) to be a term separate from the 2, you get 288. If you interpret (9+3) as attached to the 2, then you get 2.
A Simple Math Problem? - Page 53
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moltenlead
Canada866 Posts
The question is not stated clearly, which is the fundamental cause of all our confusion. If you interpret (9+3) to be a term separate from the 2, you get 288. If you interpret (9+3) as attached to the 2, then you get 2. | ||
xxpack09
United States2160 Posts
On April 08 2011 14:38 moltenlead wrote: I can see this getting to 100 pages since ideas are being recycled every few pages. The question is not stated clearly, which is the fundamental cause of all our confusion. If you interpret (9+3) to be a term separate from the 2, you get 288. If you interpret (9+3) as attached to the 2, then you get 2. No, it's completely clear. It's just that people don't understand basic mathematical conventions | ||
shabinka
United States469 Posts
On April 08 2011 14:29 ]343[ wrote: 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 Z mod n Z , my favorite set of numbers. | ||
Severedevil
United States4796 Posts
On April 08 2011 14:18 mcc wrote: 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. This. It's been repeated throughout the entire thread, but constantly shouted down by PEMDAS BEDMAS PEMDAS BEDMAS REAL MATH IS THIRD GRADE ranting. | ||
chonkyfire
United States451 Posts
2. Accept the answer is 288 | ||
Mista_Masta
Netherlands557 Posts
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shinosai
United States1577 Posts
On April 08 2011 14:41 chonkyfire wrote: 1. put equation in a scientific calculator 2. Accept the answer is 288 Some scientific calculators will answer 2. What now? http://img339.imageshack.us/img339/9549/headasplode.jpg Need a step 3. | ||
Cutlery
Norway565 Posts
On April 08 2011 14:41 chonkyfire wrote: 1. put equation in a scientific calculator 2. Accept the answer is 288 Did you actually do this? Because the answer it would give you could be 2, if you copy the problem exactly. | ||
SchAmToo
United States1141 Posts
I just re-wrote in my head as 48 / 2(9+3) which is wrong, and I understand that, but thats why I got 2. But at the same time, this is more about being a stickler on notation, than saying that everyone is stupid and can't do math. <--- People will flip out and say without notation math doesn't exist, but I feel like this is more of an elitist "grammar nazi"-esque point, than a truly mathematical one. | ||
ChApFoU
France2981 Posts
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Fatalize
France5210 Posts
The symbol ÷ is almost never used in mathematics. We use fractions because it's much more clearer for less parenthesis. Therefore this poll is completely useless. You could get both 2 and 288 just by thinking OP forgot to put parenthesis. This is just to confuse people and it doesn't show anything about intelligence or whatever. And i'm in an engineering school. | ||
Cutlery
Norway565 Posts
On April 08 2011 14:44 ChApFoU wrote: LOL omg I'm really terrible at maths. I didn't know you should do the division first because it's on the left xD. Don't feel bad, most people shouting "pemdas" don't understand fractions. don't be intimidated | ||
N3rV[Green]
United States1935 Posts
48/2(9+3), you can't simply forget about that 48, it still exists. The 2 is in no way shape or form "attached" to the (9+3). This gives 48/2*(9+3) (*** note that 48/2(9+3)=48/2*(9+3) ***) Which in turn leads to the sum of 216+72, and that still equals 288. People are really bad at math..... Guy below me is awesome. Also, the biggest factor in the problems people are facing lies in the flaws of typing out mathematical equations which are normally written out by hand, or using special word processors to place things correctly. | ||
Assymptotic
United States552 Posts
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=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 its 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)=a(b+c)=ab+ac 48÷2(9+3) =48*2^(-1)*(9+3) =24*(9+3) =24*9+24*3 =216+72 =288 | ||
Assymptotic
United States552 Posts
On April 08 2011 14:00 Phaded wrote: Pretty hilarious that both arguments quote PEMDAS or BEDMAS, but the people that argue for the answer to be 2 are applying it incorrectly. I believe the original OP used the / notation. Just checked the OP, the question is: 48÷2(9+3)=? | ||
Severedevil
United States4796 Posts
On April 08 2011 14:43 Schamus wrote: ...I answered two. I'm also a computer engineer, so... I just re-wrote in my head as 48 / 2(9+3) which is wrong, and I understand that, but thats why I got 2. But at the same time, this is more about being a stickler on notation, than saying that everyone is stupid and can't do math. <--- People will flip out and say without notation math doesn't exist, but I feel like this is more of an elitist "grammar nazi"-esque point, than a truly mathematical one. It is NOT about being a stickler on notation. It is about a fundamental disagreement on notation. (Of course, it's only a problem because we're using division signs, which no one does because they're shitty.) Notation #1) Multiplication by juxtaposition is the same as multiplication with a times sign. So 48/2(9+3) = 48 / 2 * (9 + 3) and order of operations yadda yadda 288. Notation #2) Multiplication by juxtaposition tags its parts together, taking precedence over other multiplications/divisions. So 48/2(9+3) = 48 / (2(9+3)) = 2. Unsurprisingly, the majority reads '2x' as 'two ex' even in the expression 1/2x, probably because the majority have taken algebra. | ||
Moody
United States750 Posts
On April 08 2011 14:49 Assymptotic wrote: And now, for a pedantic proof: + Show Spoiler + 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 identity unit, such that a+0=0+a=a 4) For any a in R, there exists an 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 an 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 an 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 But... But.. But.. We should just ask Day[9]. I heard he's pretty good at math. | ||
MajorityofOne
Canada2506 Posts
On April 08 2011 14:55 Moody wrote: But... But.. But.. We should just ask Day[9]. I heard he's pretty good at math. The only explanation is there was one helluva improvement from TI85 to TI86. A mathematical revolution, even. | ||
chonkyfire
United States451 Posts
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Beardfish
United States525 Posts
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. | ||
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