At this point, "2 (12)" is equivalent to "2 x 12" so you really have
I can see how this might seem correct, except that 2(12) is actually just one term, while 2 x 12 is two terms. Not the same.
Well, I simply don't agree. And neither does the WolframAlpha computation engine. [edit ... that link doesn't always resolve correctly, but you can just type in the correct expression]
When you write "2(9+3)", it's inferred that you mean "2 x (9+3)" which is an expression, not a single term.
Perhaps 2(x) is considered a single term, but I think it remains an expression when you're dealing with known values.
Of course, I'm a librarian and not a mathematician. If you teach mathematics at the university level (or you can point to a resource that backs up what you're saying) then I'll be more than happy to sit down and shut up. Otherwise, I'll continue to sit comfortably in the 288 camp.
Interestingly, If you punch in "48??(2(9+3))" at that damned WolframAlpha site, as I suggested earlier, you then get 2 for an answer.
but when you put in 48??2(9+3), which was the original question, it gives you 288. So does google search, btw. I'm converted.
Yeah ... I mentioned that in one of my earlier longwinded dorktastic remedial math posts. So either the Wolfram calculator is flawed or the 2 crowd needs a little more 'merican schoolin'.
So either the Wolfram calculator is flawed or the 2 crowd needs a little more 'merican schoolin'.
calculators don't usually respect the same order of arithmetic operations that compilers follow (compilers are programs used for producing computer code from code written and readable by humans)
If you google this math problem, it has sparked debates all over the internet. 50-pagers and all types of arguing among message boards that aren't even math-related. The equation has ambiguities because it's poorly written.
At this point, "2 (12)" is equivalent to "2 x 12" so you really have
I can see how this might seem correct, except that 2(12) is actually just one term, while 2 x 12 is two terms. Not the same.
Well, I simply don't agree. And neither does the WolframAlpha computation engine. [edit ... that link doesn't always resolve correctly, but you can just type in the correct expression]
When you write "2(9+3)", it's inferred that you mean "2 x (9+3)" which is an expression, not a single term.
Perhaps 2(x) is considered a single term, but I think it remains an expression when you're dealing with known values.
Of course, I'm a librarian and not a mathematician. If you teach mathematics at the university level (or you can point to a resource that backs up what you're saying) then I'll be more than happy to sit down and shut up. Otherwise, I'll continue to sit comfortably in the 288 camp.
So either the Wolfram calculator is flawed or the 2 crowd needs a little more 'merican schoolin'.
calculators don't usually respect the same order of arithmetic operations that compilers follow (compilers are programs used for producing computer code from code written and readable by humans)
Did you look at the Wolfram site? I referred to it as a calculator in a post but it's designed to solve expressions, not to behave like a simple calculator (i.e. it does follow order of operations). They use the term "Computational knowledge engine" to describe it. That thing is my new Google. I'm going to start typing all of my life's problems into it, though I'm not sure how helpful it's going to be.
Anyway, I do agree with Waxjunky that the expression is ambigious to begin with (obviously if its been fooling the entire frickin' internet). Very poor maths.
This is interesting because there isn't a true consensus about multiplication by juxtaposition. There is no 'right' answer, because the expression is written ambiguously. I always understood that juxtaposition came first, but I guess it depends on who you ask.
Before this became a 3 pager I showed it to a friend who uses algebra at work.
She said 288.
Said she just worked left to right. (Respecting parentheses obviously.)
Had never heard FOIL OR PEMDAS.
But I explained to her she was wrong according to all you all.
But then this happened.
Parentheses=12
exponents none
Multiply Really? What am I multiplying? 2x12 or 24x12? can't be 24 by 12 because division has not happened yet. So lets divide.
Division=24
Now lets multiply=
288
So PEMDAS gives us 288.
But not before I rant how stupid PEMDAS is. FOIL is a mnemonic.
PEMDAS is nothing. So some one came up with Pretty Edith MAkes Dem Aunts SAlly or something like that, like that is easier to remember than what ever it was we were trying to remember.
So not only does PEMDAS not give us 2, but it is a stupid memory device.
Anyway, like so many math puzzles this one is a trick based on a false (ambiguous) assumption (equation).
it is a badly written equation. a good math teacher would take either 2 or 288. however, a good math teacher wouldn't write the equation in this way... a piece of shit math teacher would.
Good lord. It's written poorly as an equation, but it boils down to this:
Draw a line. Put 48 on top. Put 2(9+3) on the bottom. Solve. The answer is 2.
What it boils down to depends on whether you believe "2(12)" is equivalent to "2 x 12".
Everyone agrees that you do what's inside the parentheses first. So we're all looking at:
48??2(12)
This is where we diverge.
If you believe that "2(12)" is equivalent to "2x12" [which is the camp I'm in], then following order of operations you'd solve left to right, first dividing 48 by 2 and then multiplying the result by 12, ending up with 288.
If you believe that "2(12)" is not equivalent to "2x12" and should be treated as a number (and thus exists outside of traditional order of operations), then you'd solve "2(12)" first and divide 48 by the result, ending up with 2.
If you believe that "2(12)" is equivalent to "2x12" [which is the camp I'm in], then following order of operations you'd solve left to right, first dividing 48 by 2 and then multiplying the result by 12, ending up with 288.
This was my understanding and how I originally voted.
Comments
Is this even algebra? LOL
I can see how this might seem correct, except that 2(12) is actually just one term, while 2 x 12 is two terms. Not the same.
No, actually.
Well, I simply don't agree. And neither does the WolframAlpha computation engine. [edit ... that link doesn't always resolve correctly, but you can just type in the correct expression]
When you write "2(9+3)", it's inferred that you mean "2 x (9+3)" which is an expression, not a single term.
Perhaps 2(x) is considered a single term, but I think it remains an expression when you're dealing with known values.
Of course, I'm a librarian and not a mathematician. If you teach mathematics at the university level (or you can point to a resource that backs up what you're saying) then I'll be more than happy to sit down and shut up. Otherwise, I'll continue to sit comfortably in the 288 camp.
Send your kids to Shanghai or Finland.
'mericans will argue about anything. This thread proves that if nothing else.
'merican and proud of it!!!
but when you put in 48??2(9+3), which was the original question, it gives you 288. So does google search, btw. I'm converted.
Yeah ... I mentioned that in one of my earlier longwinded dorktastic remedial math posts. So either the Wolfram calculator is flawed or the 2 crowd needs a little more 'merican schoolin'.
I'm a chef with an English degree.
Did you look at the Wolfram site? I referred to it as a calculator in a post but it's designed to solve expressions, not to behave like a simple calculator (i.e. it does follow order of operations). They use the term "Computational knowledge engine" to describe it. That thing is my new Google. I'm going to start typing all of my life's problems into it, though I'm not sure how helpful it's going to be.
Anyway, I do agree with Waxjunky that the expression is ambigious to begin with (obviously if its been fooling the entire frickin' internet). Very poor maths.
For me, there is only one Lio
Ha ha. A chef and a librarian debating mathematics on Soulstrut.
now everyone sees that right?
48??2(9+3) =
this problem is exactly the same, because the first bracket is not necessary
Euroman to the rescue
Phew! You sure came around in the nick of time!
Ha!
48??2(9+3)
Before this became a 3 pager I showed it to a friend who uses algebra at work.
She said 288.
Said she just worked left to right. (Respecting parentheses obviously.)
Had never heard FOIL OR PEMDAS.
But I explained to her she was wrong according to all you all.
But then this happened.
Parentheses=12
exponents none
Multiply Really? What am I multiplying? 2x12 or 24x12? can't be 24 by 12 because division has not happened yet. So lets divide.
Division=24
Now lets multiply=
288
So PEMDAS gives us 288.
But not before I rant how stupid PEMDAS is. FOIL is a mnemonic.
PEMDAS is nothing. So some one came up with Pretty Edith MAkes Dem Aunts SAlly or something like that, like that is easier to remember than what ever it was we were trying to remember.
So not only does PEMDAS not give us 2, but it is a stupid memory device.
Anyway, like so many math puzzles this one is a trick based on a false (ambiguous) assumption (equation).
Draw a line. Put 48 on top. Put 2(9+3) on the bottom. Solve. The answer is 2.
What it boils down to depends on whether you believe "2(12)" is equivalent to "2 x 12".
Everyone agrees that you do what's inside the parentheses first. So we're all looking at:
48??2(12)
This is where we diverge.
If you believe that "2(12)" is equivalent to "2x12" [which is the camp I'm in], then following order of operations you'd solve left to right, first dividing 48 by 2 and then multiplying the result by 12, ending up with 288.
If you believe that "2(12)" is not equivalent to "2x12" and should be treated as a number (and thus exists outside of traditional order of operations), then you'd solve "2(12)" first and divide 48 by the result, ending up with 2.
This was my understanding and how I originally voted.