48÷2(9+3) = ????

[Bill Verburg]

Originally Posted by winders

Bill,

The document was there. There are too many references to it to infer that it never was there.

Your last formula makes is fine if you don't use the convention that says multiplication indicated by juxtaposition is carried out before division. This convention is not uncommon or we would not be having this debate.

I am not arguing that the answer is "2". I am arguing that equation is ambiguous and should not be written the way it is. I am arguing that it is easy to see how many people come up with "2" as the answer.

Your position is far too black and white considering the division this equation inspires in the mathematical community.

Scott

My position is black/white because all you have to do is follow the most basic rules of math w/o making up anything else to get the correct result. No matter which way you do it all you have to do is follow the 6 basic rules as they are supposed to be taught

[sammyg2]

[winders]

Originally Posted by Bill Verburg

My position is black/white because all you have to do is follow the most basic rules of math w/o making up anything else to get the correct result. No matter which way you do it all you have to do is follow the 6 basic rules as they are supposed to be taught

Who is making stuff up? It's not like only one person on the planet says the answer is "2". As I have said several times now, which you seem to ignore, there is even debate as to what the correct answer is in the mathematics community. There is no debate that the equation is poorly written and ambiguous.

If the "rules" were as black and white as you want them to be, the equation would not be poorly written or ambiguous at all.

Scott

[Bill Verburg]

Originally Posted by Geary

Johnny and his wannabe teacher don't know basic algebra.
48÷2(9+3) =
48÷2(12) = 2(12) without a "x" sign means that this multiplication is the next step in the equation. Every time. No exception. You can't just drop the parenthesis at will and replace it with "x". Basic algebra.

Paul, by using that reasoning you are making the claim that division is associative

post #539
division is not associative, you cannot add parentheses as you can w/ multiplication

1*2*x = (1*2)*x = 1*(2*x) =1(2*x) = 1(2x) = 1*(2x) because multiplication is associative

but if any of the multiplications in those expressions are changed to division then they are all mostly different

[Bill Verburg]

Originally Posted by winders

Who is making stuff up? It's not like only one person on the planet says the answer is "2". As I have said several times now, which you seem to ignore, there is even debate as to what the correct answer is in the mathematics community. There is no debate that the equation is poorly written and ambiguous.

If the "rules" were as black and white as you want them to be, the equation would not be poorly written or ambiguous at all.

Scott

I give up, the only reason that there is ambiguity in your or anyone else's mind is that you don't want to adhere to the basics and/or there is a fuzzy understanding of one or more of the basic rules

many of these issues arise solely because of technological limitations, years ago it was the limitations imposed by printing presses and more recently by computer screens, the technology exists but is relatively expensive and not widely distributed, I bought a program called MathType that interfaces with MS Word just to avoid these sorts of issues, nevertheless expressions typed in old fashioned inline type can be consistently evaluated by following the basic rules w/o making up things.

just because something can be made more obvious it does not mean that it was ambiguous to begin w/, It just means that you might have to think a little harder to do the right thing

[DARISC]

Originally Posted by winders

...fine if you don't use the convention that says multiplication indicated by juxtaposition is carried out before division. This convention is not uncommon or we would not be having this debate.

Mr. Verburg addressed "multiplication indicated by juxtaposition is carried out before division"; see post #557:

"'There is a convention that says you do implicit multiplication before division' is a rule only in your world, it is not a convention recognized anywhere else except in the minds of others that don't understand math."

Originally Posted by winders

...I am not arguing that the answer is "2". I am arguing that equation is ambiguous and should not be written the way it is. I am arguing that it is easy to see how many people come up with "2" as the answer.

Mr. Verburg also addressed - and denied - the ambiguity issue, agreeing that the equation might have been written to be more quickly grasped:

"I agree that it should and could be written more clearly, nevertheless w/o implementing any new rules or exceptions you get consistent results by following the basic order of operation rules"

Originally Posted by winders

...Your position is far too black and white considering the division this equation inspires in the mathematical community.

Any "inspired division in the mathematical community" notwithstanding, math IS black and white, understood by using rules that were never, ever, formed by impassioned mathematicians arguing heatedly in committees or in caffeine crazed coffee clatches.

Mr. Verburg addressed this also:

"I agree that there is a lot of controversy but don't see why

people often cite mnemonics like PEMDAS, P - simplify everything inside parenthesis as much as possible, E - exponents, MD - multiply or divide left to right, AS - add or subtract left to right"

Just curious, have you ever had a teacher with the patience of Bill Verburg?

Edit: Oops, Bill finally gave up on you. Oh well, your loss, winders.

[winders]

You two keep missing this fact:

There is even debate as to what the correct answer is in the mathematics community.

Hello? The "mathematics community" means mathematicians both professional and academic.

There is a consensus that the equation is ambiguous. Again, there would be no debate and no ambiguity if the conventions used were in complete agreement.

Scott

[winders]

By the way, I would say the answer is "288" but I understand why half of the people out there in the mathematics community get "2".

Scott

[RWebb]

is it safe to vote yet?

[bell]

42.........

Or......

How many roads must a man travel?

[winders]

Originally Posted by RWebb

is it safe to vote yet?

No, because Bill thinks that at least 64% of the people that voted are mathematical idiots.

My position is that the poll does not give me enough information to determine who, of those that voted, are mathematical idiots.

Scott

[DARISC]

Originally Posted by winders

By the way, I would say the answer is "288" but I understand why half of the people out there in the mathematics community get "2".

Scott

Because they're not sufficiently attentive?

Because they haven't the drive to rise to the challenge of solving an equation not written in the format they are programmed to deal with without exerting their cerebrum?

I mean, c'mon! If one's a math hotshot and sees the equation as awkward, hinkey, ambiguous, why pop out either 2 or 288 without commenting on your perceived problems with the equation?

What, if none of the above applies, is your understanding of why so many got the wrong answer?

Oh, and, You 'would' say the answer is '288'? "Would", if what; you were certain the answer IS 288?

[DARISC]

Originally Posted by winders

...Bill thinks that at least 64% of the people that voted are mathematical idiots.

No, Bill Verburg is a gentleman and a highly respected member of these boards who patiently took a lot of time and spent a lot of effort to try to teach you something about a subject of which he has great knowledge.

The fact that that not only are you not grateful for his efforts to help you understand some basics of a subject about which you know comparatively little, but you then besmirch his character by spouting such an outright lie, speaks volumes of your character and breeding...or lack thereof.

An apology from you is in order.

[winders]

Originally Posted by DARISC

An apology from you is in order.

Yeah, right.....

Bill thinks that anyone who does not agree with him is wrong. Yet half of the mathematics community doesn't agree with him. They are wrong too. UC Berkeley Mathematics Professors that disagree with Bill are wrong too.

I have a race car with a brake setup that Bill thinks should not work. It works great so we have California physics that is wrong.

See the trend? Educator? Dictator more like.....

Scott

[RWebb]

that's not the trend I'm seeing

[winders]

Originally Posted by RWebb

that's not the trend I'm seeing

Then maybe you aren't looking......unless, of course, you think Bill knows more than the mathematics community and the guy that builds a ton of successful race cars with brake bias ratios that Bill says can't work.

But hey, you snuggle your nose up to Bill's butt if that is what makes you happy!

Scott

[winders]

RWebb,

By the way, all I have said that is "answer" is not as clear cut as some would have you believe. I think you can verify that by just looking around the Internet.

I prefer the answer that Bill says is the only correct answer. But, I've been around the academic mathematics community long enough to more pragmatic than that.

Scott

[svandamme]

Originally Posted by winders

There is a convention that says you do implicit multiplication before division. Based on that convention, you get:

48÷2(9+3) = n

48÷2(12) = n

48÷24 = n

n = 2

There is no implcit multiplication, the parenthesis does not include the multiplication

it only influences what is inside the ( ) not what is outside of it.


so

[dad911]

Originally Posted by winders

No, because Bill thinks that at least 64% of the people that voted are mathematical idiots.

My position is that the poll does not give me enough information to determine who, of those that voted, are mathematical idiots.

Scott

I believe I voted for '2' when the poll was first posted. I have since realized my error. No way to change my vote, would if I could, and I doubt Bill thinks me the idiot.

Originally Posted by winders

Look at what Google comes back with: 0.15915494309

Google changes the equation ..... changed 1/2pi to 1/(2*pi)

[Aragorn]

Originally Posted by bell

42.........

That was my answer also but it wasn't one of the choices...

Not too many hitchhiker fans here...