48÷2(9+3) = ??

I discussed this with fellow math majors and some grad students in some of my classes working on a masters in mathematics or actuarial science.

We came up with 3 undecideds, 3 288's, and 2 2's.

Going 100% by PEMDAS, we get 288. But the problem with this is this is that we are doing

48÷2(9+3) = 48÷2(12) = 24(12)=288

BUT by this logic

48÷(9+3) = 48÷(12) = 48(12) = 576...
What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this:
48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576

By contradiction, we have proven that the answer is 2.

However, there is the chance that this is still incorrect. There are a lot of rules that we could be missing here, similar to how 0!=1 and not 0. Is there one here?

Our professor (PhD in Mathematics from Yale) wouldn't give an answer and said that the problem is incorrect. Not the answer, the problem. No person who would be asking/writing the problem would know so little as to use such poor notation. She said that depending on what field of mathematics you are in, either answer could be correct. She unfortunately didn't give examples, and we had to get started with class.

Dr. Hess wrote: MS Excel and SQL Server both answer your question with 288. One or both of these products probably had something to do with your paycheck, and also fits the rule of Inside the brackets first, then multiplication and division left to right then addition and subtraction left to right. There's more to the rule, like logs, exponentials, etc., but you don't have any of that in your equation. Your girlfriend good at math, is she? Pics or it didn't happen. That's a pretty funny pic, Eddie. I bet a HP gets it right, though.

I wouldn't say she was amazing at it, but she wasn't horrible. I found her input potentially more relevant than mine simply because she had done this sort of thing more recently than i had, and that she hadn't progressed as far past it as i had.

Turns out i didn't forget near as much as i thought i had, though.

I may go home and dig out the calculator and do some graphing checks, replacing values with x with the equation equaling 2 vs. 288.

If we're appealing to credentials now, I just messaged this to my sister, who has a PhD in theoretical limits of algorithmic computation, which means she's approx. ten billion times smarter than me, and she said the answer was 2. It took her all of five seconds to figure it out.

Dr. Hess wrote: Your girlfriend good at math, is she? Pics or it didn't happen.

damnit! I was gonna say that

yeah same here, i'm just surprised I remembered what I did

Jay wow! and mtn NICE!!

Uh, guys. Did you see the...

Oh, nevermind. It will be interesting to see who wins.

mtn wrote: Going 100% by PEMDAS, we get 288. But the problem with this is this is that we are doing 48÷2(9+3) = 48÷2(12) = 24(12)=288 BUT by this logic 48÷(9+3) = 48÷(12) = 48(12) = 576... What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this: 48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576 By contradiction, we have proven that the answer is 2.

Holy E36 M3! I've been racking my brain all day trying to come up with a tidy way to demonstrate that the "288" people were doing something wrong. That nails it. Nice one!

But... weren't you on the other side of the argument?

mtn wrote: Our professor (PhD in Mathematics from Yale) wouldn't give an answer and said that the problem is incorrect. Not the answer, the problem. No person who would be asking/writing the problem would know so little as to use such poor notation. She said that depending on what field of mathematics you are in, either answer could be correct. She unfortunately didn't give examples, and we had to get started with class.

Now that I've argued my point out, I agree with your prof. The question is poorly written and (deliberately!) ambiguous. But I can't think of any field of mathematics where you'd legitimately perform the counterintuitive procedure to get 288. (Unless you consider internet trolling to be a field of mathematics!) Doing that looks wrong because the equation doesn't "read" that way. It is wrong.

I suspect we've been trolling ourselves.

my brain's not in a good mood with me after today

Jay wrote: Now that I've argued my point out, I agree with your prof. The question is poorly written and (deliberately!) ambiguous.

Test one two. This mic on?

Can you guys see my posts? I thought I explained that already.

fast_eddie_72 wrote:

Jay wrote: Now that I've argued my point out, I agree with your prof. The question is poorly written and (deliberately!) ambiguous.

Test one two. This mic on? Can you guys see my posts? I thought I explained that already.

Yarp, you did the question is missing a vital piece of information, In other news "I accidentally a starter motor"

Jay wrote: Holy E36 M3! I've been racking my brain all day trying to come up with a tidy way to demonstrate that the "288" people were doing something wrong. That nails it. Nice one! But... weren't you on the other side of the argument?

Yes, and I still am. I just try to see all sides of it and fully understand it.

My proof is flawed. 2(9+3) is the same thing as 2*(9+3). The * operator is implicit.

My head hurts. Can we get pancakes?

mtn wrote:

After a bit of thought, that would not work if you were to convert .9999... into the correct fraction.

mtn wrote:

That's not trolling, that's a well accepted tenet in mathematics. There are a dozen proofs that show exactly that.

Here's another one:

9/9 = 1
1/9 = 0.1111111....
9x(1/9)=9x0.1111111....=0.9999999....
But 9x(1/9)=9/9=1
Therefore 0.9999999....=1

OK, so I work in a community college, and decided to run this by a variety of people yesterday.

lab manager = 2
lab prep = 288
accounting prof = 2
microbiology prof = 2
biology prof = 2
graphic arts/media production = 2
chemist = 2
physicist = 2
student = 288
student = 288
math prof = 288
math prof = 288
math prof = 288
clerical = 36 (<=== Don't ask)

I then forwarded this to one of the math profs who said 288.

Going 100% by PEMDAS, we get 288. But the problem with this is this is that we are doing 48÷2(9+3) = 48÷2(12) = 24(12)=288 BUT by this logic 48÷(9+3) = 48÷(12) = 48(12) = 576... What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this: 48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576 By contradiction, we have proven that the answer is 2.

Her response was:

I e-mailed my middle and high school math teacher, and I did learn it your way first! At least I know that I am not going crazy. :) He says that he teaches it my way nowadays because students were getting too confused. After googling, it appears that the order is not set in stone yet. People over the age of 30 typically do it your way, and people in their 20's and under plus math teachers do it my way. My husband is a math teacher and learned it my way. It seems that different texts will disagree. One site had a letter from an engineer asking about it, because he does it your way and was trying to help his kid with some homework. Several times, people suggested using ( ) to avoid ambiguity in the first place. This has been very interesting. :)

Thus, I contend that the most accurate post in this entire thread has been spitfirebill's

spitfirebill wrote: Stupid new math Old math says 2.

^^^ that all makes sense now

Can we work on world hunger next?

I enjoy how being a math teacher is implied to make someone good at math. There's no real quality control for K-12 teachers that I've seen.

No offense to knowers of teachers on here, I'm sure yours is brilliant.

mtn wrote: I discussed this with fellow math majors and some grad students in some of my classes working on a masters in mathematics or actuarial science. We came up with 3 undecideds, 3 288's, and 2 2's. Going 100% by PEMDAS, we get 288. But the problem with this is this is that we are doing 48÷2(9+3) = 48÷2(12) = 24(12)=288 BUT by this logic 48÷(9+3) = 48÷(12) = 48(12) = 576... What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this: 48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576 By contradiction, we have proven that the answer is 2.

The locals are not liking this. Not one bit.

"YOU CAN'T JUST STICK A 1 IN FRONT OF THE (9+3)!!!!!!!111!!ONE!!"

Uh... sorry. It was there in the beginning.

92CelicaHalfTrac wrote:

mtn wrote: I discussed this with fellow math majors and some grad students in some of my classes working on a masters in mathematics or actuarial science. We came up with 3 undecideds, 3 288's, and 2 2's. Going 100% by PEMDAS, we get 288. But the problem with this is this is that we are doing 48÷2(9+3) = 48÷2(12) = 24(12)=288 BUT by this logic 48÷(9+3) = 48÷(12) = 48(12) = 576... What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this: 48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576 By contradiction, we have proven that the answer is 2.

The locals are not liking this. Not one bit. "YOU CAN'T JUST STICK A 1 IN FRONT OF THE (9+3)!!!!!!!111!!ONE!!" Uh... sorry. It was there in the beginning.

How do you get to the 48÷(12) = 48(12) part? Can anyone help me understand that? Then disprove my proof, because I think that's rock solid...

RossD wrote:

92CelicaHalfTrac wrote:

mtn wrote: I discussed this with fellow math majors and some grad students in some of my classes working on a masters in mathematics or actuarial science. We came up with 3 undecideds, 3 288's, and 2 2's. Going 100% by PEMDAS, we get 288. But the problem with this is this is that we are doing 48÷2(9+3) = 48÷2(12) = 24(12)=288 BUT by this logic 48÷(9+3) = 48÷(12) = 48(12) = 576... What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this: 48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576 By contradiction, we have proven that the answer is 2.

The locals are not liking this. Not one bit. "YOU CAN'T JUST STICK A 1 IN FRONT OF THE (9+3)!!!!!!!111!!ONE!!" Uh... sorry. It was there in the beginning.

How do you get to the 48÷(12) = 48(12) part? Can anyone help me understand that? Then disprove my proof, because I think that's rock solid...

Using strict PEMDAS rules...

48÷(12) = 48÷1(12)

If you get 288, you got there with the original equation by figuring 48÷2*(9+3).

Therefor, if you have 48÷(12), which is exactly the same as 48÷1(12)... You would figure it as 48÷1*(9+3). Which is... 576. And i think we all agree that 48÷12 is 4. Not 576.

48÷1(9+3)
48÷1(12)
48*12 = 576

If there is no number notated in front of a parantheses expression, there is a 1. The only time you put a number in front of the parantheses is if it's a number other than 1. 1 "unit" of (9+3), 2 "units" of (9+3).

Therefor, original equation, you'd be dividing 48 by 2 "units" of (9+3) to get 2. But if you break the "units" away from (9+3), you get a wildly different answer.

In reply to 92CelicaHalfTrac:

48÷(12) = 48÷1(12) This is wrong. Can you explicitly describe the the algebraic property or definition to prove this statement? And in doing so can you disprove my proof.

What you mean to say is: 48÷(12) = 48*(1/12) which is the definition of division.

Anyways PEMDAS is a way of teaching children how to do basic math and is fallible; this equation is a prime example.

http://www.purplemath.com/modules/orderops.htm

"A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first."

and

"(Note: Speakers of British English often instead use "BODMAS", which stands for "Brackets, Orders, Division and Multiplication, and Addition and Subtraction". Since "brackets" are the same as parentheses and "orders" are the same as exponents, the two acronyms mean the same thing.)"

Notice the order of multiplication and division change depending on the origin of the Mnemonics.

RossD wrote: In reply to 92CelicaHalfTrac: 48÷(12) = 48÷1(12) This is wrong. Can you explicitly describe the the algebraic property or definition to prove this statement? And in doing so can you disprove my proof. What you mean to say is: 48÷(12) = 48*(1/12) which is the definition of division. Anyways PEMDAS is a way of teaching children how to do basic math and is fallible; this equation is a prime example. http://www.purplemath.com/modules/orderops.htm "A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first." Notice the order of multiplication and division change depending on the origin of the Mnemonics.

I'll look... but mtn would be better to ask for the actual law. I haven't spoken in "laws" in long enough that it was a stretch for me to remember the Law of Distribution. At the moment, i just remember that in front of any bracketed expression, there is a 1, whether its visible or not, unless notated otherwise. (Ergo: "2" in the original equation) Being that this is algebra, you could bring in quite a few laws/processes... even including Factoring of Polynomials.

But in the meantime, can you tell me what number is in front of (9+3) if it isn't 1?

Multiplying anything by 1 will get you what you started with.

48÷(12) = 48*(1/12) isn't what i mean to say. I'm familiar with that one. What i'm saying is unrelated. Keep in mind this stems with what mtn posted earlier on this page.

My problem with your proof is that it says that if you substitute "a" for 48, "b" for 2, and "c" for (9+3), you get a÷b*c, which i don't like.

It should be a÷bc.