48÷2(9+3) = ?

[The Anti-Targ]

They're not called smart phones for nothing you know. My phone's got a PhD so it knows it's shit...what?...oh you have a PhD in Pacific ethnomusicology. OK well I'm sure it's calculator still follows the int'l std for working out mathematical equationy stuff.

[Quoth]

You are missing the point. Rather than dogmatically asserting that there is some true answer to be gleaned from this, the correct response is to tell the writer to bugger off and come back with a clear clarification of meaning. I mean, do you regard 1/2x as clear and unambiguous?

Ummm... Sorry, It is dogmatic. It's basic math. It doesn't change. I'm a firm believer in the sentiment that "words have meaning". That maxim is true for numbers and operands as well. In fact, for numbers, the maxim should be considered as squared if not cubed. :D Is 1/2x clear and unambiguous? Yes! (Well, other than their being a variable involved...) Follow the mathematical rules of construction and you get one, and only one, answer.

We're talkin bout PEMDAS? PEMDAS?

I'm sitting here and looking at franchise boarders and we in here talking bout PEMDAS.

Not a Game. Not politics. Not the hilliness of the Ottoman Empire. We talkin bout PEMDAS.

Sly, PEMDAS is the new hilly Ottoman Empire. Do try to keep up.

If your violin student cannot come up with an answer to sqrt(-9), does that mean the answer isn't "3i"?

Sounds like you're arguing the other side of the discussion, but that is exactly my point. Of course the answer is 3i. There is only the one correct answer. Granted, there are some equations that yield two or multiple results (x = -5 or +5) but we're discussing an expression not an equation. It says precisely what it says. And only what it says.

The fact that it is only a first step does not mean that it is not definitive. Yes, they will have to wait to learn about complex numbers, number systems with bases other than 10, etc. etc., but all of these things build on and complement what they've already learned -- none of them invalidate it. Math is not like the sciences where we teach a sequence of progressively better approximations; the math learned in first grade is still exactly correct in grad school.

Furthermore, in the case of arithmetic, you don't even have to trust grade school to get it right. There are international standards for this: look at the ISO of any widely used programming language (Java, C++, Fortran, Python -- it doesn't matter, they'll all give you the same answer) and you'll see that the precedence for evaluating expressions with multiplication and division is determined by the order from left to right.

Thank you.

[The Marquis de Leech]

Ummm... Sorry, It is dogmatic. It's basic math. It doesn't change.

Intent, however, does. And maths is rather more messy than people think (not that maths' messiness is an issue here: this is simply a case of someone inaccurately expressing their intent).

I'm a firm believer in the sentiment that "words have meaning".

Words don't have meaning outside what people ascribe to them. The purpose of language is to express oneself: if you don't express yourself clearly, people will ascribe different meanings to what you say. So it is with this example.

That maxim is true for numbers and operands as well. In fact, for numbers, the maxim should be considered as squared if not cubed. :D Is 1/2x clear and unambiguous? Yes! (Well, other than their being a variable involved...) Follow the mathematical rules of construction and you get one, and only one, answer.

1/2x can mean either 1/(2x) or (1/2)x depending on the intent of the writer. Hence the importance of expressing oneself in a clear manner.

Sounds like you're arguing the other side of the discussion, but that is exactly my point. Of course the answer is 3i. There is only the one correct answer.

No there isn't. There are two correct answers. 3i and -3i.

[Vestrit]

My phone's got a PhD so it knows it's shit...what?...oh you have a PhD in Pacific ethnomusicology.

In which case, could it please confirm for me whether the term 'dropping' is the relevant term for that effect you often hear in karakia and waiata, where the tone drops suddenly at the end of a line?

[Quoth]

Intent, however, does. And maths is rather more messy than people think (not that maths' messiness is an issue here: this is simply a case of someone inaccurately expressing their intent).

Agreed. But once written, a mathematical expression has a particular value (OK, or a particular set of values... see below, Mr. smarty pants) :P

Words don't have meaning outside what people ascribe to them. The purpose of language is to express oneself: if you don't express yourself clearly, people will ascribe different meanings to what you say. So it is with this example.

Yes. Exactly my point. It's not that the expression in the OP has multiple meanings. It's that the author failed to write what was intended.

1/2x can mean either 1/(2x) or (1/2)x depending on the intent of the writer. Hence the importance of expressing oneself in a clear manner.

I know that it can be interpreted as either in the absence of the rules of construction. That's why the rules exist. If the author meant to say 1/(2x) or (1/2)x, it should have been written precisely that way. Having failed to do so, the author wrote, and conveyed, the value returned by 1/2x. No "interpretation" allowed. If the author says 56, he does mean 56, does he not? If he meant to say 97, he damn well should have said so. If he says 2+2, he is giving the value of 4, not 5. If he meant to discuss values of various infinities, he should have said so.

No there isn't. There are two correct answers. 3i and -3i.

OK. Ya got me. In my defense, it's early and I'm on my first cup of coffee. :lol:

[Arlingzen Bill]

skipped a few pages, but excel says that there is an error in the formula when entered exactly as written. Which I agree with.

[Altherion]

skipped a few pages, but excel says that there is an error in the formula when entered exactly as written. Which I agree with.

Excel just doesn't like the idea of multiplying using parenthesis. If you enter the completely uncontroversial (I hope...) "2(3)" it will complain and tell you to change it to "2*(3)".

[wolverine]

I was taught never to use the division sign but instead use fractions because of bullshit like this.

Frankly, I haven't seen a problem written like this since I was like 9. High school or University wouldn't use notation this sloppy.

I believe I said something very similar to this like 5 pages ago. You don't use cooking recipe fractions when doing math because it causes ambiguous situations like 1/2x. With a cooking fraction who knows if it is one divided by 2x or one-half times x?

Also, when I teach PEMDAS the MD are one step from left to right and the AS are one step from left to right. I often say/write Divide and Multiply to emphasize that they are one step.

[Balefont]

You're talking about "authorative resources" and then name a young pre-algebra student and her textbook? And thus discarding the posts from several people here who actually work in the field?

ErikConrad, meet Cantible.

[IheartTesla]

Doing a problem like this the other way, she says, would be considered incorrect and marked wrong.

Someone already pointed this out ages ago, but since we are all just repeating ourselves, why not.

Unless you are a pure mathematician, an expression like 48/2(9+3) doesn't just exist in a vacuum. Most mathematical expressions arise because we are framing a problem (real life or otherwise) in mathematical terms. The problem could be something like "There are 48 bananas that need to be divided among 9 girls and 3 boys, with 2 bananas being donated to charity for each child. How many bananas does each child get to eat?" And you could write it any way you want, but 288 would not be the answer.

As I said before, if you decide on a convention for mathematical expressions, then there is only one answer. However, discussing those conventions themselves rather than actual mathematical problems is an exercise in banality and tedium. Most of the hard work is done when you go from the statement of the problem into framing it in mathematical terms.

[Balefont]

Someone already pointed this out ages ago, but since we are all just repeating ourselves, why not.

Unless you are a pure mathematician, an expression like 48/2(9+3) doesn't just exist in a vacuum. Most mathematical expressions arise because we are framing a problem (real life or otherwise) in mathematical terms. The problem could be something like "There are 48 bananas that need to be divided among 9 girls and 3 boys, with 2 bananas being donated to charity for each child. How many bananas does each child get to eat?" And you could write it any way you want, but 288 would not be the answer.

As I said before, if you decide on a convention for mathematical expressions, then there is only one answer. However, discussing those conventions themselves rather than actual mathematical problems is an exercise in banality and tedium. Most of the hard work is done when you go from the statement of the problem into framing it in mathematical terms.

:love:

[Quoth]

Unless you are a pure mathematician, an expression like 48/2(9+3) doesn't just exist in a vacuum.

Sure there are. There's a bajillion of them in math text books (to say nothing of standardized tests). Are these meaningless? Of course not. In such a context as text books they are exercises for the mind. Mental push ups, as it were. But, the cold (however elegantly or "poorly" written) expression still has a single value or value set for its solution.

Most mathematical expressions arise because we are framing a problem (real life or otherwise) in mathematical terms. The problem could be something like "There are 48 bananas that need to be divided among 9 girls and 3 boys, with 2 bananas being donated to charity for each child. How many bananas does each child get to eat?" And you could write it any way you want, but 288 would not be the answer.

Oh, absolutely. Thus the need to understand how to and to write the expression correctly. Hence the training exercises mentioned.

As I said before, if you decide on a convention for mathematical expressions, then there is only one answer. However, discussing those conventions themselves rather than actual mathematical problems is an exercise in banality and tedium. Most of the hard work is done when you go from the statement of the problem into framing it in mathematical terms.

Well, God forbid we have a banal or tedious discussion on this board. :lol:

[IheartTesla]

Come on, let's be serious. "Evaluate 48/(2*12) and (48/2)*12" is hardly a mental exercise. Or maybe it is when you are 8. For adults here to waste electrons on this piffle....

But, the cold (however elegantly or "poorly" written) expression still has a single value or value set.

Sure, for one given convention (although the poorly written expression didnt have a * sign). If you really want to be mathematically rigorous then you can't assume implicitly the existance of an operator like '*'. There are probably reams written in group theory about this, and Galois would spin in his grave if he saw this discussion so many hundreds of years after his tragic death.

So if I want to be anal about it, the expression doesnt have a solution. And that's my final word .... for now :smoking:

[Quoth]

Come on, let's be serious. "Evaluate 48/(2*12) and (48/2)*12" is hardly a mental exercise. Or maybe it is when you are 8. For adults here to waste electrons on this piffle....

This suggests that some should have spent more time going over those exercises, then. :lol:

Sure, for one given convention (although the poorly written expression didnt have a * sign). If you really want to be mathematically rigorous then you can't assume implicitly the existance of an operator like '*'. There are probably reams written in group theory about this, and Galois would spin in his grave if he saw this discussion so many hundreds of years after his tragic death.

So if I want to be anal about it, the expression doesnt have a solution. And that's my final word .... for now :smoking:

I was taught that a value or variable just outside parenthesis definitely indicated multiplication... with no need to insert a *. Was that incorrect?

[Altherion]

I was taught that a value or variable just outside parenthesis definitely indicated multiplication... with no need to insert a *. Was that incorrect?

It's correct (or at least both the US and the Soviet Union used this convention so it's probably used by everyone else too).

[IheartTesla]

This suggests that some should have spent more time going over those exercises, then. :lol:

I was taught that a value or variable just outside parenthesis definitely indicated multiplication... with no need to insert a *. Was that incorrect?

Only if you want to use mathematical expressions without the use of mathematical rigour, which is what this thread is purpotedly all about. I would approximate 48/2(9+3) in the absence of any clearly defined set of rules as 48/212 ~ 0.226(an approximate answer)

Edited: for calculation error :smoking:

[Quoth]

Only if you want to use mathematical expressions without the use of mathematical rigour, which is what this thread is purpotedly all about. I would approximate 48/2(9+3) in the absence of any clearly defined set of rules as 48/212 ~ 0.226(an approximate answer)

Edited: for calculation error :smoking:

Actually, I'm with ya there. I'd prefer the insertion of a * as it would be more precise. But I'm comfortable with the practice of skipping it, I guess. *shrug*

But you did lose me there... 212...?

ETA - Oh, I see what you were doing...

[felice]

Not if you say that "x(y+z) is a short way of saying (x * (y+z)) rather than the bare x * (y+z)". You can't have it both ways: if x(y+z) is the same thing as (x * (y+z)) then x(y+z)² is (x * (y+z))²

Nope, it's (x * ((y+z)²)) - exponents take precedence over multiplication unambiguously, so they get implied brackets first.

I'm willing to accept 288 is the correct answer, but it's counterintuitive to me, and writing an equation that ambiguously is a really bad idea.

[Ixodes]

Did anyone

After that, the only number I am thinking about is 187.

You hear me, Coco?? 1 8 7