Solve 48÷2(9+3)

[a500lbgorilla]

The point is that the collective brainpower of google, bing, texas instruments and all current scientific calculators that I'm aware of all come to a consensus.. so your position then is that they are all wrong or that they all came to the same conclusion by coincidence.

... if you think my point is that the people saying that the answer is 288 are wrong, than you clearly don't know anything.

I answered that it was 288.

... if you think I believe they all came to the same conclusion by coincidence than I am left to only believe that I am not talking to an actual human being.

I wish I wouldn't read any further through your post and I now feel like I owe spoon something because he's right about how awesome it is that argument spreads on the internet because of this question.

[a500lbgorilla]

Yet every single one of us agree that the order of operations is BEMDAS, or brackets (inside), exponents, multiplication and division left-to-right, addition and subtraction left to right.

It doesn't matter what we agree, you fool! If we insert only one person who doesn't agree, then where are we? There is no truth between which order of operations is correct. That is the point. I am filling with frustration.

What you are saying then is that 24(12) is not the same as 24*(12), and that somehow multiplication via the juxtaposition against brackets takes precedence over regular multiplication and division. But if you are going to take the position that there is no authority to decide this, how is it justifiable to add such an arbitrary wrinkle such that a simple problem can be interpreted in more than one way? That doesn't make any sense.

Again, I am not saying this. I am saying that others are saying this. Wow, please read the freaking thread.

The rules of english and maths are quite different I presume.. in this example I believe they actually *are* both correct.. but don't quote me on that; I'm not particularly sure.

Duh, it's an analogy. I'm glad that you think they're both correct because it's a good analogy to what we're talking about right now. Both 2 and 288 are correct. More correct is that the original problem is ambiguous.

*This begs another interesting question. Where specifically are you arguing that multiplication via juxtaposition should be in the order of operations?

From the guy in this thread who said he was taught multiplication by juxta was the proper order of operations. I went through the internet and discovered that yes some people had learned that way and I further found that there was no way to say either way was more correct.

[a500lbgorilla]

I should apologize, I'm getting frustrated for no good reason, but I can not believe that you would resist the idea that this problem is clearly mathematically ambiguous.

I just can't understand how you think that your version of order of operations is the order of operations when someone has already posted in this thread that they were a math major who was taught rigorously a different order of operations and there exists no authority to say which is better than which.

It's all just a language. If some people choose to read that math statement one way and others choose to read it another, unless the head of all math says "let's go with this one" there is no more right answer.

The person forming the statement should have made it more clear which answer they intended. Because they failed, the problem is ambiguous. If you've ever read a peer reviewed engineering or physics paper, you see that they take great lengths to make sure there is only one interpretation of their work because of this.

I don't see how you can't see that.

[Lukie]

... if you think my point is that the people saying that the answer is 288 are wrong, than you clearly don't know anything.

I answered that it was 288.

... if you think I believe they all came to the same conclusion by coincidence than I am left to only believe that I am not talking to an actual human being.

I wish I wouldn't read any further through your post and I now feel like I owe spoon something because he's right about how awesome it is that argument spreads on the internet because of this question.

If you are saying that it is mathematically ambiguous, given that there is basically always 1 way to interpret basic mathematical equations, then by default 288 is not correct, or less correct, or however else you want to put it that there can be varying degrees of correctness in basic algebra.

[Lukie]

It doesn't matter what we agree, you fool! If we insert only one person who doesn't agree, then where are we? There is no truth between which order of operations is correct. That is the point. I am filling with frustration.

If there is only one person who doesn't agree, we call them a fool and nothing ever comes of it. When something like this is split roughly 50/50, we get threads like this all over the internet

Duh, it's an analogy. I'm glad that you think they're both correct because it's a good analogy to what we're talking about right now. Both 2 and 288 are correct. More correct is that the original problem is ambiguous.

Why are you making an analogy between english and math? You are very well smart enough to know that they are governed by very different sets of rules. The comparison is that there is disagreement on both sides and many people think both are correct. Beyond that there is no proper comparison.

[a500lbgorilla]

If you are saying that it is mathematically ambiguous, given that there is basically always 1 way to interpret basic mathematical equations, then by default 288 is not correct, or less correct, or however else you want to put it that there can be varying degrees of correctness in basic algebra.

There is no basically always 1 way to interpret basic mathematical equations as evidenced by the following basic mathematical equation:

48÷2(9+3)

[a500lbgorilla]

Why are you making an analogy between english and math? You are very well smart enough to know that they are governed by very different sets of rules. The comparison is that there is disagreement on both sides and many people think both are correct. Beyond that there is no proper comparison.

Light (colors) and sound are governed by different rules but I can draw a strong analogy between the two.

[a500lbgorilla]

Light (colors) and sound are governed by different rules but I can draw a strong analogy between the two.

Which is to say, order of operations is well analogous to rules of comma placement. There's no way to prove the proper order of operations, it just comes down to what is the standard. And in this problem, there is no standard.

[Lukie]

There is no basically always 1 way to interpret basic mathematical equations as evidenced by the following basic mathematical equation:

48÷2(9+3)

Ok then, logic problem:

Situation A: we follow the order of operations strictly, meaning terms inside brackets, then orders, then division and multiplication left to right, and subtraction and addition left to right. We do not give special preference of varying degrees to mutliplication via juxtaposition against brackets.

Situation B: we (by we, I mean generally a large following of people) give arbitrary special emphasis of varying degrees to such multiplication via juxtaposition, such that seemingly simple problems can be interpreted in multiple ways, and nobody can seemingly agree on anything.

Which makes more sense?

Quoting myself from an earlier post which should even more clearly demonstrate why option B is much murkier:

Example that I am coming up with right here:

3(2*2.5)^2

Do you do the 3* as in left to right (same as parenthesis), before the exponent, after the exponent but before other multiplication, or simply left to right?

[Lukie]

Which is to say, order of operations is well analogous to rules of comma placement. There's no way to prove the proper order of operations, it just comes down to what is the standard. And in this problem, there is no standard.

I'll defer to you on the comma placement thing.. I really don't know.. I've always used thing 1, thing 2, and thing 3 but was under the impression that ommitting that last comma is fine as well.

The point is that it's very well possible that exactly one math method is correct and both english methods are correct, or vise versa.. there's no real correlation.

[a500lbgorilla]

Ok then, logic problem:

Situation A: we follow the order of operations strictly, meaning terms inside brackets, then orders, then division and multiplication left to right, and subtraction and addition left to right. We do not give special preference of varying degrees to mutliplication via juxtaposition against brackets.

Situation B: we (by we, I mean generally a large following of people) give arbitrary special emphasis of varying degrees to such multiplication via juxtaposition, such that seemingly simple problems can be interpreted in multiple ways, and nobody can seemingly agree on anything.

Which makes more sense?

Quoting myself from an earlier post which should even more clearly demonstrate why option B is much murkier:

It should be situation A: Order of operations say multiplcation by juxtaposition will be treated as any other multiplication.

Situation B: Multiplcation by juxta takes precedence over multiplcation or division by other means.

Both make perfect sense.

[rong]

The point of an equation isn't it's answer, it's explaining the journey one takes to reach the answer. So it is nothing more than an explanation or a story, which is meaningless without context, which we lack in the example.

[Lukie]

The person forming the statement should have made it more clear which answer they intended. Because they failed, the problem is ambiguous. If you've ever read a peer reviewed engineering or physics paper, you see that they take great lengths to make sure there is only one interpretation of their work because of this.

I find this very interesting.. although I'm not really sure how relevant it is. There's certainly nothing wrong with adding more brackets, and given that we'll say half the people think each way is correct, it seems very prudent to remove all confusion whatsoever even if it isn't necessary (and I'm arguing that is exactly the case).

48/2(9+3) can easily be re-written as (48/2)(9+3) but writing it as 48/(2(9+3)) completely changes the equation. And I can hear your blood boiling right now so for that I apologize

[a500lbgorilla]

I'll defer to you on the comma placement thing.. I really don't know.. I've always used thing 1, thing 2, and thing 3 but was under the impression that ommitting that last comma is fine as well.

The point is that it's very well possible that exactly one math method is correct and both english methods are correct, or vise versa.. there's no real correlation.

If you are saying that exactly one math method is correct, you are incorrect.

Search for the mathematical proof or Mathematical ruling on which order of operations is most correct and you'll discover why.

[a500lbgorilla]

The point of an equation isn't it's answer, it's explaining the journey one takes to reach the answer. So it is nothing more than an explanation or a story, which is meaningless without context, which we lack in the example.

This is good. Because this is unaffiliated to anything real to measure our results against it makes it more clear why this is like judging the exact proper way to write an English sentence.

The author of this math problem may have been writing under one set of rules, but if interpreted under another set of rules, you'll reach a different answer.

As there is no officially correct set of rules, this problem is ambiguous.

[Lukie]

It should be situation A: Order of operations say multiplcation by juxtaposition will be treated as any other multiplication.

Situation B: Multiplcation by juxta takes precedence over multiplcation or division by other means.

Both make perfect sense.

Ok... this is good. I feel like we are getting somewhere here.

My initial interpretation for the '2' crowd was that because the factor was juxtapositioned against the bracket, that it would get the bracket level in order of operations.. which is why I posed the following question:

3(2*2.5)^2

Why multiplication against a bracket goes after exponents but violates the otherwise-in-effect left to right for multiplication and division doesn't make any sense to me and seems completely arbitrary. The real tipping point is that it adds confusion and ambiguity in mathematics where usually there is none.

So with that, I'm most likely exiting this thread for good, unless I see something I find particularly disagreeable.

[a500lbgorilla]

I find this very interesting.. although I'm not really sure how relevant it is. There's certainly nothing wrong with adding more brackets, and given that we'll say half the people think each way is correct, it seems very prudent to remove all confusion whatsoever even if it isn't necessary (and I'm arguing that is exactly the case).

48/2(9+3) can easily be re-written as (48/2)(9+3) but writing it as 48/(2(9+3)) completely changes the equation. And I can hear your blood boiling right now so for that I apologize

My blood calms.

[Galapogos]

I love it when rilla reminds us how smart he is.

[a500lbgorilla]

I love it when rilla reminds us how smart he is.

My blood delights.

Why multiplication against a bracket goes after exponents but violates the otherwise-in-effect left to right for multiplication and division doesn't make any sense to me and seems completely arbitrary. The real tipping point is that it adds confusion and ambiguity in mathematics where usually there is none.

My blood dances.

It is completely arbitrary and it doesn't make sense to me either. But that is beside the point. Because there exist mathematicians in this world who don't agree with the order of operations we have learned, and because there exists no authority to step in and say which of us is most correct, we are left to take the steps of including extra brackets or parens to make our mathematical statements clear.

By the way, under both sets of rules, I'm pretty sure it solves your problem the same way. 3(2*2.5)^2=3(5)^2=3(25)=75

But someone could just as easily define multiplication by juxtaposition as dominant over even exponents and be allowed to write 3(2*2.5)^2=3(5)^2=15^2=225.

That's the power of math. It's capable of describing great things and flexible enough to be delivered in many ways.

[daviddem]

I messed this one up, it's 288. Think the old division sign got me, plus the fact that I started by the parenthesis and proceeded right to left. Correct way to see it is obviously:
(48/2) * (9+3) because we proceed left to right and multiplication does not have precedence on division.

[kiwiMark]

I lol'd

[Halv]

"obviously" probably not a good word to use itt

[BennyLaRue]

The correct answer is 288 because 288 is bigger than 2 and therefore more correct plus it has synchronicity to it and you can't beat two rights with one wrong.

ldo

[d0zer]

"obviously" probably not a good word to use itt

ldo

[kevster]

Lukie: It's 288
Rilla: Yes, but....
Lukie: IT'S 288!
Rilla: Yes, but....
Lukie: IT'S 288!!!

etc. etc.

fun thread.

[Lukie]

Lukie: It's 288
Rilla: Yes, but....
Lukie: IT'S 288!
Rilla: Yes, but....
Lukie: IT'S 288!!!

etc. etc.

fun thread.

?

Please pull a quotation where I use all caps or am anything other than polite and well-descriptive of the subject matter. Yet I can pull many that were used against me, including several personal attacks from both penney and rilla.

Just because strongly adamant about the the answer (and currently am so more than ever) doesn't imply that I'm yelling, being rude, etc.

[Lukie]

A) Wow thanks for the math lesson, cuz like, totally, no one mentioned how this maffs is sposed' to be done in this thread already!

B) Cool trick, are you part asian or something?!

C) Wao thanks

D) There are any number of reasons why your meathead internet buddies score higher on a "math test" than the ppl in this forum. Maybe they're less confident in their math and decide to read the thread for the correct answer before voting? but nah I guess just carry your shame for FTR and make sure we all know about it etc

... if you think my point is that the people saying that the answer is 288 are wrong, than you clearly don't know anything.

I answered that it was 288.

... if you think I believe they all came to the same conclusion by coincidence than I am left to only believe that I am not talking to an actual human being.

I wish I wouldn't read any further through your post and I now feel like I owe spoon something because he's right about how awesome it is that argument spreads on the internet because of this question.

It doesn't matter what we agree, you fool! If we insert only one person who doesn't agree, then where are we? There is no truth between which order of operations is correct. That is the point. I am filling with frustration.


Again, I am not saying this. I am saying that others are saying this. Wow, please read the freaking thread.


Duh, it's an analogy. I'm glad that you think they're both correct because it's a good analogy to what we're talking about right now. Both 2 and 288 are correct. More correct is that the original problem is ambiguous.


From the guy in this thread who said he was taught multiplication by juxta was the proper order of operations. I went through the internet and discovered that yes some people had learned that way and I further found that there was no way to say either way was more correct.

Just for humor's sake

[Penneywize]

meh, I can be a dick sometimes, it's been known to happen. don't take anything I say too seriously, I fail at being funny etc

[Lukie]

It's cool.. I honestly laughed about it.. I just think Kevster's analysis is about as far off the mark as possible

[Lukie]

so anyway, here is the math proof from the 2p2 thread...

Proposition 48÷2(9+3)=288
Proof
We know in the rational numbers, the following hold:
For any two rationals a,b
(i) Assuming b is nonzero, a÷b = a*(1/b)
(ii) And, ab = a*b
Then,

48÷2(9+3) = 48÷2*(9+3)       by (ii)
          = 48*(1/2)*(9+3)  by (i)
          = 288              by simple computation

QED

another programmer guy ran the equation through a half dozen or so programming languages (c++ etc.) and they all gave the answer of 288, as does google, bing, wolfram alpha, and modern scientific calculators. the only exception seems to be some of the much older calculators. so at least in the online/computational/programing world, there seems to be a pretty strong consensus.

[a500lbgorilla]

(ii) And, ab = a*b.

Yup. And if instead you assume that ab = ab, and that ab takes precedence over a*b and a/b, then you'll find that the answer is 2. QED.

Consensus doesn't matter. I agree that it's 288, but it could be 2. It all depends on what you assume. Which is why this problem is ambiguous.

[a500lbgorilla]

It should be noted that in nullspace's proof, because he states his assumptions, he removes ambiguity. But because these assumptions are not stated in the initial problem, it is ambiguous.

[Lukie]

Mathmematics, almost by definition has exacting set rules that are supposed to be followed one way. It doesn't make any sense that one would be able to interject their own rules into the otherwise clear order of operations, then point to the resulting confusion as proof of the ambiguity, then say that there is no official math authority to decide. In that sense, I almost prefer the answer '2' to the 'it's ambiguous' route which to me just seems like it's the politically correct out as to offend the least amount of people as possible.

As stated before.. modern scientific calculators, programming languages, google, bing, wolfram alpha etc. all give the answer 288. If the question were ambiguous, wouldn't some of these sources (or comparable sources) give '2', or return an error of some sorts? Either that or the '2' crowd is running extremely bad in high level maths.

And we're right back to where we started.

[a500lbgorilla]

Mathmematics, almost by definition has exacting set rules that are supposed to be followed one way.

A fully incorrect statement. As in this instance, order of operations is not an exacting set of rules because we have seen that you can assume a different set of order of operations.

edit which is to say, you can find the whole world over that the answer is 288. But I can say, "alright, but let's assume a different order of operations." You can not say, "No, that isn't proper. There is only one order of operations and it is these."

I'd love to stay and chat but I really should be doing other things right now.

[Lukie]

I'd love to stay and chat but I really should be doing other things right now.

finally something we can agree on

[Lukie]

A fully incorrect statement. As in this instance, order of operations is not an exacting set of rules because we have seen that you can assume a different set of order of operations.

edit which is to say, you can find the whole world over that the answer is 288. But I can say, "alright, but let's assume a different order of operations." You can not say, "No, that isn't proper. There is only one order of operations and it is these."

I'd love to stay and chat but I really should be doing other things right now.

ok you keep ninja editing this so I'm just going to quote it.. I disagree with how you quoted one relatively meaningless sentence out of context from multiple paragraphs, but whatever... here is the rest of the paragraph.

.... It doesn't make any sense that one would be able to interject their own rules into the otherwise clear order of operations, then point to the resulting confusion as proof of the ambiguity, then say that there is no official math authority to decide. In that sense, I almost prefer the answer '2' to the 'it's ambiguous' route which to me just seems like it's the politically correct out as to offend the least amount of people as possible.

as you say...

edit which is to say, you can find the whole world over that the answer is 288. But I can say, "alright, but let's assume a different order of operations." You can not say, "No, that isn't proper. There is only one order of operations and it is these."

and I had pre-emptively said...

"As stated before.. modern scientific calculators, programming languages, google, bing, wolfram alpha etc. all give the answer 288. If the question were ambiguous, wouldn't some of these sources (or comparable sources) give '2', or return an error of some sorts? Either that or the '2' crowd is running extremely bad in high level maths."

[Lukie]

Anyway, I think we've both said what we wanted to say ad nauseum. Let's just agree to disagree so we can both move onto bigger and badder things.

[a500lbgorilla]

I just can't resist.

The main problem is that you really don't understand math. Because you say things like math is not a language and it by definition has an exacting set of rules.

So I will give you a hint for how you can win this argument.

Find the proof which states the proper order of operations.

You will not find it because it doesn't exist.

Order of operations is an assumption. It's such a prevalent assumption that people forget it's an assumption. nullspace went out of his way to specify precisely how he was going to compute the answer and because of it, his is a wholly proper expression of this problem. But as I can write this:

Proposition 48÷2(9+3)=288
Proof
We know in the rational numbers, the following hold:
For any two rationals a,b
(i) Assuming b*c is nonzero, a÷b(c) = a*(1/(b*c))
Then,
Code:
48÷2(9+3) = 48*(1/(2*(9+3)) by (i)
= 48*(1/(2*12)) by simple computation
= 48*(1/24) by simple computation
= 2 by simple computation
QED

There is no deep reason why my assumption is incorrect. It is simply my assumption. And as I am allowed to my assumptions equally as nullspace is allowed to his, the problem is ambiguous.

[Lukie]

Ok. I think we've both said what we wanted to say ad nauseum. Let's just agree to disagree so we can both move onto bigger and badder things.

[a500lbgorilla]

Sure, for practical reasons.

[Lukie]

Your previous post does bring up an interesting implication. Let's move on from the 48/2(9+3) thing and instead focus on something where there would be far greater consensus:

X = 3+4*5

I think we all would agree X = 23.

However, if I were somehow able to convince a great many people (say, half the people who post on forums) to place addition before multiplication, using the exact logic that you posted, this question then becomes ambiguous and 35 would then become an acceptable interpretation and 'it's ambiguous' would perhaps be the best answer'.*

ninja edit*

[boost]

Heres my assumption:

a+b = a+b(-1)

therefore 5+7=-2

Others might assume a+b=a+b and conclue that 5+7=12, but because its possible to assume + really means - (no means yes, and yes means she wants to walk with a limp tomorrow) the the problem 5+7=X is ambiguous.


**clearly I don't think this is right, but I, being a maths newb (man, strategically using "maths" as opposed to "math" is a sick way to give yourself an air of authority when maths are being discussed) cannot see how it is different from what our good friend rilla is positing.

[a500lbgorilla]

An excellent question Lukie. Yes, your problem is ambiguous. No, I don't need half the forum to vote that way to say correctly that it is ambiguous. My position has nothing to do with popularity and everything to do with the math of it.

I welcome you to read about the history of order of operations. Math Forum - Ask Dr. Math

If in the 1600s they had decided on a whim that addition takes precedence over multiplication, your post would read like this:

Your previous post does bring up an interesting implication. Let's move on from the 48/2(9+3) thing and instead focus on something where there would be far greater consensus:

X = 3+4*5

I think we all would agree X = 35.

However, if I were somehow able to convince a great many people (say, half the people who post on forums) to place addition before multiplication, using the exact logic that you posted, this question then becomes ambiguous and 23 would then become an acceptable interpretation and 'it's ambiguous' would perhaps be the best answer'.*

ninja edit*

Obviously it's not a good idea to start tossing out new and unique sets of orders of operations because it would be like learning French before your trip to Spain. Everyone agreed that the best course of action was to get a general consensus on order of ops and stick to them for obvious reasons. But in this instance, some people, for reasons I do not know, differ slightly on how they interpret their order of operations which brings to light the fact that order of operations are an assumption.

Just to demonstrate how many assumptions and the like go into the proof of 1+1=2

Math Forum - Ask Dr. Math

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.

All of the bolded are common sense assumptions but to be unambiguous they need to be stated. That's just how math is. So without stating the assumptions, we're allowed to which ever we please, which makes a lot of grade school math ambiguous.

edit: It all comes down to this: To say 1+1=2 you even need to state that 1 is a number. Of course 1 is a number, everyone knows that! But if you don't state that it is a number, your problem could be ambiguous.

[spoonitnow]

5 * 3 + 4 = 19

omg I'm just assuming that I do 5 * 3 first!

or is it that 5 * 3 is a short-hand for 3 + 3 + 3 + 3 + 3?!

3 + 3 + 3 + 3 + 3 + 4 = 19?!

you can't explain that because we're just assuming that 3 + 3 + 3 + 3 + 3 + 4 = 19

[a500lbgorilla]

Alright, maybe I'm wrong on that one. I really didn't think through any of the reasons for our specific order of operations. Lukie stretched me out a bit by going to a simpler problem and I was just trying to bolster my position that the problem is ambiguous for the above problem. "This is probably because the distributive property implies a natural hierarchy in which multiplication is more powerful than addition."

I was taught the same as everyone else who hit 288. But I don't see any reason why the assumption that multiplication by juxtaposition should take precedence over other multiplication is incorrect. Though I should have taken fewer liberties with how flexible the order of operations are, I now see.

[a500lbgorilla]

Math Forum - Ask Dr. Math

"Well, the concept of "order of operations" is really one that's not inherent
to the structure of mathematics, but rather to mathematical notation.
What I mean by that is that order of operations refers to which operations
should be performed in what order, but it doesn't actually dictate anything
(nor is it dictated by) the operations themselves. So in a sense, it's
just convention.

So if that's true, we should be able to use different "orders of operations"
and come up with a perfectly consistent mathematical system. And in fact,
we can."

Is my central point. Which I myself misinterpreted a bit ago.

[spoonitnow]

It's fun stuff.

In the real number system, we define multiplication as repeated addition as sort of a short-hand, just like we define exponents to be a repeated multiplication (which is then a repeated addition as well), and that's where the order of operations for those things comes from. So when we take a different order of operations, we get screwed up stuff like the following.

3*4+2 = 3*8 = 24
2*1+11 = 2*12 = 24

Set them equal to each other and we have:

3*4+2 = 2*1+11

Subtract 2 from each side and we get:

3*4+2-2 = 2*1+11-2
3*4 = 2*10
12 = 20

On a somewhat related topic, in other mathematical structures, the same symbols for the operations can be used for entirely different operations. Like in group theory, if you have a group that uses + as its operation, then you tend to write repeated use of that operation like we do multiplication by juxtaposition, eg: 5x = x + x + x + x + x However, if you have a group that uses * as its operation, then you tend to write repeated use of that operation with an exponent, eg: x^5 = x * x * x * x * x. What determines whether you use + or * as the symbol for the operation is whether or not the commutative property applies to the group (ie Abelian groups).

Some people prefer to use the additive notation 100% of the time, and some prefer to use the multiplicative notation 100% of the time. Others do each when it's appropriate based on the structure of the group, which is what I was taught is correct.

The topic of multiplication by juxtaposition and the order of operations came up in a couple of my analysis classes, and each of the professors just sort of shrugged it off like people who thought it should alter the order of operations were crazies.

Whoever used the example of something like 10x/5x (though it might have been a different board) is retarded and should die in a grease fire.

[boost]

Rilla, I agree with you that order of operations is not something set in stone, it is just a set of rules that makes mathematical communication possible. I still am having a hard time conceptualizing a system in which parenthesis do not take precedent, but that's besides the point. There are different orders of operations that would allow us to communicate our mathematical ideas.

That being said, when choosing between the two orders of operations that are the subject of this thread, why the fuck would you chose the more complicated and nuanced one that provides 2 as the answer? If there were benefits that came at the cost of complication, then fine... but I see none. So even if both orders of operations are valid, it doesn't mean one doesn't suck donkey balls.

[a500lbgorilla]

Rilla, I agree with you that order of operations is not something set in stone, it is just a set of rules that makes mathematical communication possible. I still am having a hard time conceptualizing a system in which parenthesis do not take precedent, but that's besides the point. There are different orders of operations that would allow us to communicate our mathematical ideas.

That being said, when choosing between the two orders of operations that are the subject of this thread, why the fuck would you chose the more complicated and nuanced one that provides 2 as the answer? If there were benefits that came at the cost of complication, then fine... but I see none. So even if both orders of operations are valid, it doesn't mean one doesn't suck donkey balls.

Well, I didn't. I chose the better one of the two, imo. But because two equally valid order of ops exist, the problem is not unambiguous. Which was what I was getting at with Lukie. I still said it's 288 and if I were ever going to write this problem out, I would include extra parens to remove all doubt.

[a500lbgorilla]

It's fun stuff.

In the real number system, we define multiplication as repeated addition as sort of a short-hand, just like we define exponents to be a repeated multiplication (which is then a repeated addition as well), and that's where the order of operations for those things comes from. So when we take a different order of operations, we get screwed up stuff like the following.

3*4+2 = 3*8 = 24
2*1+11 = 2*12 = 24

Set them equal to each other and we have:

3*4+2 = 2*1+11

Subtract 2 from each side and we get:

3*4+2-2 = 2*1+11-2
3*4 = 2*10
12 = 20

But you wouldn't be able to set them equal to each other because they're essentially statements in different languages. There math expressions in different maths. That's why both 2 and 288 are right. 2 is right in one math world. 288 is right in the other.


That's why we want to have 1 convention, and I agree with you on which one is best, but for some reason a second convention does exist and no one has found reason to state with authority that we should stop using it.

[spoonitnow]

But you wouldn't be able to set them equal to each other because they're essentially statements in different languages. There math expressions in different maths.

You just made no sense so I'm assuming you misread what I typed.

3*4+2 = 3*8 = 24
2*1+11 = 2*12 = 24

Both of these were taken with addition being done before multiplication, so there's no reason you shouldn't be able to set them equal to each other. I was illustrating that an order of operations that puts addition before multiplication in the real number system is incorrect.

[a500lbgorilla]

Okay you just made no sense so I'm assuming you misread what I typed since you don't seem to be that big of a retard.

Because one statement is under 1 order of operations it is incompatible with the other statement under the other order of operations. You yourself showed this when you set them equal to each other and showed it was invalid.

edit oh, I didn't read what you were specifically doing. You were using the same order of operations for both, sorry I thought you were using two different types of order of ops. My bad.

[spoonitnow]

Because one statement is under 1 order of operations it is incompatible with the other statement under the other order of operations. You yourself showed this when you set them equal to each other and showed it was invalid.

Check my edit, I assumed this is what you misread etc.

[a500lbgorilla]

Yeah, I misread it.

[spoonitnow]

My bad on the ninja edit yo.

[spoonitnow]

You were talking about the structures and stuff, and I'm waiting on Michelle to get ready, so I figure I'll ramble off some warble garble.

One of most basic mathematical structures is called a magma, which is just a set with a binary operation on the set with no other rules whatsoever. As you add rules, you get new structures. For example, if you add associativity, an identity element, and inverses, then you get a structure called a group. Going further, if you add commutativity, you get an Abelian group. Up to this point, you still only have one operation, and we tend to call this operation addition.

Now let's add another binary operation. Let's call it multiplication. If this operation is associative and has an identity, and the distributive property holds for this particular combination of multiplication and addition, then now we have a structure called a ring.

You can keep adding rules to the structure if you want, and how the structure is classified changes. If you take a ring and have the multiplication be commutative, then it's called a commutative ring. You can keep adding rules to get structures with complicated-as-fuck names like integral domains, unique factorization domains, vector fields, and so on.

So with all of that being said, what we know as the real number system is a field that's ordered, and the order has a certain property named after some guy I don't feel like looking up.

If you want to take the approach of looking at a list of axioms, you can do so here Construction of the real numbers - Wikipedia, the free encyclopedia

It's fun to point out that 0 < 1 isn't an axiom (because it can be proven by the axioms).

Okay Michelle's ready. Holla back.

[Hawk]

Now that you guys have had your little debate and all I figure it's time to clear this all up.

The answer is obviously 2.

[a500lbgorilla]

[spoonitnow]

I know right. I should have been a fucking history major.

[spoonitnow]

I like what this one guy said about it:

The argument for 288: order of operations.
The argument for 2: some people really mean something other than what they wrote, and you should know what they really meant in that context.

[Imthenewfish]

im still trying to find the old division sign on my keyboard

[Luco]

You just made no sense so I'm assuming you misread what I typed.

3*4+2 = 3*8 = 24
2*1+11 = 2*12 = 24

Both of these were taken with addition being done before multiplication, so there's no reason you shouldn't be able to set them equal to each other. I was illustrating that an order of operations that puts addition before multiplication in the real number system is incorrect.

In rilla's defence, the first one of those is in a crazy maths world where 4+2 = 8

[kevster]

It's cool.. I honestly laughed about it.. I just think Kevster's analysis is about as far off the mark as possible

This is often the case. I was just kidding though. Wouldn't call it analysis.

fun thread.

[a500lbgorilla]

I like what this one guy said about it:

The argument for 288: order of operations.
The argument for 2: some people really mean something other than what they wrote, and you should know what they really meant in that context.

This is a good description.

[spoonitnow]

In rilla's defence, the first one of those is in a crazy maths world where 4+2 = 8

They both are, that was the point :P

[Luco]

So putting addition before multiplication, I read your equations as

3*4+2 = 3*(4+2) = 3*6 = 18
2*1+11 = 2*(11+1) = 2*12 = 24

[spoonitnow]

So putting addition before multiplication, I read your equations as

3*4+2 = 3*(4+2) = 3*6 = 18
2*1+11 = 2*(11+1) = 2*12 = 24

stfu i almost got away with tricking rilla

[spoonitnow]

change it to 4*4+2 and it still shows the point tho, 16 = 20 etc

[Luco]

change it to 4*4+2 and it still shows the point tho, 16 = 20 etc

Yeah I followed it through with

3*4+4
2*1+11

Then subtracted 4 using your method, I got 12=16

[a500lbgorilla]

just cuz this is a mathy thread.

[Ash256]

YouTube - Look Around You - Maths

[PlayToWin]

So, I did learn something after all those years of math classes. I'm so happy.

[JoeHaw]

You old farts can say its 288 all you want but ask high school or college level classroom and they'll say it's 2. That notation (the two being right outside the parenthesis with no multiplication sign) is acknowledged in academia as a grouping of the two factors.

This problem NEVER comes up though because nobody uses slashes OR division signs anymore instead a long bar (like a fraction) is used to separate the two top to bottom.

[StillDeadMoney]

I think everyone can agree that 48÷2(9+3) = 48÷2(12).

The problem is what comes after this. The divison symbol "÷" is almost never used after you leave grade school.

People who do math for a living see the "÷" symbol as "/". Hence, the equation becomes

48/2(12)

Expressing this in a more aesthetically pleasing way gives us

48
-------
2(12)

To which the answer is 2. It is standard in academia for brackets to signify a grouping of this sort. However, it is perfectly reasonable to come up with the answer of 288, because unless you work with math on a daily basis all you're going to remember is BEDMAS.

The people who said 288 remembered "BEDMAS", the people who said 2 said "wtf is that division sign they use in grade school textbooks doing anywhere outside of one?".

ninja edit: as Rilla and others have said, there is no rigorous mathematical proof for either answer. It's kind of like how people suddenly decided a few hundred years ago that the word "their" should not be used to reference a single person when their sex is ambiguous and that "he/she" should be used instead. To use the word "their" is "incorrect" in the same way that the answer of 288 is debatable: a bunch of people who do these sorts of things for a living one day decided arbitrarily what was right and what was wrong.

If I was grading a quiz where the question was "solve 48÷2(9+3)", I would realize my mistake in how ambiguous the question is and give students full marks for either answer (after shooting myself in the head for being so fucking stupid as to use a "÷" symbol).

[celtic123]

I voted 288 , i see the reasoning for 2. so let google decide