Solve 48÷2(9+3)

[a500lbgorilla]

meh.. the TI-85 is almost 20 years old and was replaced by the TI-86.. the 86 returns 288 as does the TI-83+ and TI-89 that I own.

Windows vista calculator, google calculator, and bing calculator all also give the answer 288.

Google

48/2(9+3) - Bing

we'll just have to agree to disagree. It wouldn't make much sense to have an order of operations if it were necessary to add brackets to everything to make it unambiguous... in that case the order of operations might as well read 'B', then do everything else left to right. Another point is that the field of mathematics is such that there is usually exactly one correct answer and it would blow my mind if something as relatively simple as this could be (correctly) interpreted in more than one way.

No you can agree that we just have to agree to disagree, but the original problem is ambiguous and that has been made very clear in this thread.

If you think the authority of your calculators is the final authority on this issue, then you really don't understand this issue.

I'll say this clearly. Because there is no authority to decide, and because both the order of operations you know and are comfortable with and the order of operations you don't agree with have been taught as true, the original problem is mathematically ambiguous.

It's like saying: Which is correct: The colors of the birds are red, white and blue. OR The color of the birds are red, white, and blue.

There is no deep truth to which order of operations is correct, so yours is no better than theirs. You can not like this for the rest of your days but if you say the original problem is unambiguous you need to qualify it with, "to me." Because it is ambiguous.

edit: also, something like this can be correctly interpreted in more than one way. Three ways. And one way is more correct than the other two.

The answer is 2.

The answer is 288.

The question should be ignored because it is ambiguous.

[Lukie]

No you can agree that we just have to agree to disagree, but the original problem is ambiguous and that has been made very clear in this thread.

If you think the authority of your calculators is the final authority on this issue, then you really don't understand this issue.

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.

I'll say this clearly. Because there is no authority to decide, and because both the order of operations you know and are comfortable with and the order of operations you don't agree with have been taught as true, the original problem is mathematically ambiguous.

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.

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. *

It's like saying: Which is correct: The colors of the birds are red, white and blue. OR The color of the birds are red, white, and blue.

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.

There is no deep truth to which order of operations is correct, so yours is no better than theirs. You can not like this for the rest of your days but if you say the original problem is unambiguous you need to qualify it with, "to me." Because it is ambiguous.

I can assure you that I want to spend less time thinking about this in the future, not more


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

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?

[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.

[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.

[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)

[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?

[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.

[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.

[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]

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]

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.