Music Banter - 6/2*(1+2)=?

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It doesn't change any of my arguments though. Even the simplest calculator can be programmed to allow for bad syntax.

@chiron: I would assume that they were posting in the language of the rest of the sentence :P

Quote:

Originally Posted by MoonlitSunshine (Post 1046137)

Are you saying that Matlab is programmed to allow for bad syntax?

At any rate, the problem question is underspecified. Therefore, to solve this problem we would have to further specify it. Generally, the simplest solution is always best, as given by Occam's razor. Hence,

For 6/2*(1+2),

It is simpler to say (6/2)*(1+2)

Instead of: 6/(2*(1+2)).

... Which is essentially what I've been saying since the first page. While the most common answer is 9, it is ambiguous without more parentheses. Occam's Razor is an interesting argument in favour of 9, though, but I'm glad you feel the original problem is underspecified!

Quote:

Originally Posted by oojay (Post 1045310)

6/2*(1+2) = 6/2*(3) = 6/6 = 1

Parentheses
Exponents (and Roots)
Multiplication
Division
Addition
Subtraction

This is like sixth grade math guys, seriously.

Mathematical Order Of Operations

oojay has a good wiki link and comes up with the better answer, in my opinion, although his method relies on a mnemonic which shouldn`t be thoughtlessly applied to every case.

Quote:

Originally Posted by MoonlitSunshine (Post 1045317)

The answer is you need more parentheses.

... you cannot define an operator or it's inverse taking "precedence". In fact, you cannot define any operator taking precedence over another, as that is the realm of ambiguous convention. You might as well just say 1+1 = 3 while you're at it. The only true mathematical description of precedence is through the use of parentheses, as that is their explicit function. The fact is that the order in which operators are evaluated is a dangerous form of shortcut which honestly shouldn't be taught.

Conclusion: The statement is ambiguous. In order to have a "true" answer, another pair of parentheses needs to be added.

I think MoonlitSunshine has the clearest analysis so far.
I can`t remember what I was taught (in England) about precedence and order of operations, but we were taught to use parenthesis to avoid ambiguity.
So, if I had wanted the answer to be 9, I would have written : (6/2)(1+2) = 3 x 3 = 9
and if I had wanted the answer to be 1, I would have written : 6/2(1+3) = 6/(2 x 3) = 1

So,it`s an interesting question, EvilChuck, but my answer to the guy would be," Go back and write what you mean properly."

Quote:

Originally Posted by Lisnaholic (Post 1046170)

So, if I had wanted the answer to be 9, I would have written : (6/2)(1+2) = 3 x 3 = 9
and if I had wanted the answer to be 1, I would have written : 6/2(1+3) = 6/(2 x 3) = 1

I think this is the best example of the two possible solutions yet.

I haven't read all of the posts but I think something that people are forgetting with PEMDAS is that

Multiplication and Division get the same priority

So does Addition and Subtraction.

You always do the order of operations from left to right.

Quote:

Originally Posted by Janszoon (Post 1046088)

When you google "order of operations" it doesn't seem like there's much disagreement at all. Every link I click on seems to say that multiplication and division are of equal rank, as are addition and subtraction.

Quote:

Originally Posted by MoonlitSunshine (Post 1046100)

And generally, that's fine, as multiplication and addition are associative operations (it doesn't matter what order you do them in). It's where there's ambiguity over which elements the inverse is being applied to that there's a problem.

Consider a situation where you have a/b/c. Is that (a/b)/c, or a/(b/c)? take an example, 2/3/4. (2/3)/4 = 2/12 = 1/6, but 2/(3/4) = 8/3. The two answers are very, very different, but how do you define which one is the fraction? Which equal priority operation needs to be done first? The same problem holds when you have a/b*c. Is that (a/b)*c, or a/(b*c)? The fact that most people assume it is (a/b)*c does not make the syntax any more correct: If someone writes "I hae that" you could assume they left out a t or a v; depending on which it is they've left out, it makes a big difference to the meaning of the sentence, but you can usually figure out which they mean by the context of the sentence. It doesn't however, make the sentence, if isolated from the context, any less ambiguous. Does that make sense?

Was this a reply to me? Because if so it doesn't really seem to relate to what I was saying.

It was. I was showing why "equal priority/rank" is a minefield.

Quote:

Originally Posted by MoonlitSunshine (Post 1046243)

It was. I was showing why "equal priority/rank" is a minefield.

Why is it a mine field? When they're equal rank you just move from left to right. Seems easy enough.

Because it's all very well to say that, but there's absolutely no guarantee that the person you're communicating with feels the same way... as is evident from this thread.