Diablo® III

48÷2(9+3) = ?

Posts: 118
My 7th graders would be ashamed.

Oh and if we say:

x = (9+3)


is still different from


My students would say you forgot the implied parenthesis:

48/2(9+3) should be (48/2)(9+3).
That's it, I am putting my kids into a private school. 48/2x is not worked that same way as 48/2(x) or (x)48/2. They are used the same way as brackets { }. You should never assume there are implied parenthesis when it changes the outcome of an answer.
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Posts: 118
Whoever wrote Wolframalpha should be fired, and you shouldn't use it.


It shows 1/2(d) puts (d) in the numerator like it is supposed to be.
In the expample above Sinew gave above it doesn't. Only difference is using numbers or variables, they should always be treated the same since they represent numbers.
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06/14/2012 01:02 PMPosted by Sinew
You know that != means not equal right? Doesn't seem like you do from your napkin math.

How is that even relevant? I know what != means. I just used a simple transitive property to prove that your justification was way out of whack.

06/14/2012 01:02 PMPosted by Sinew
2(9+3) is one term. it cannot be broken without changing the value.

Correct, that term alone cannot be detached. However, the two itself is not attached, but the 48/2 is.

06/14/2012 01:02 PMPosted by Sinew
Retake grades 3-11 please. ty.

Yeah, no I'm cool with my engineering internships dude.

You seriously need to take a class on logic.

I'd like to keep tearing apart your posts, but you'll keep replying with the most illogical things when put in context with what I have said. Basically, you're ignoring any logic I have made in my post, and posting the same thing you have been doing. That, and I already said I was done arguing, so I'm not really going to put more forth.

But this discussion is meaningless anyways. If you want to tell me to retake grades 3-11, that's fine. I'll just get another straight 4.0 (well...with AP credit more like 4.3, but all A's nonetheless) like I did last time. No biggie.

Btw, division and fractions are one of the same.

EDIT: Screw it, this is too much fun.

Sinew, your points would be valid IF you had a logical justification of why 48÷2(9+3) != 48÷2*(9+3). If you can prove that (and I mean prove, not bull!@#$) then I will concede.

However, your attempts at justifying that so far have been wolfram alpha (seeing as WA gets 288 for the problem, you can't use that to justify 2, especially considering it's meant for ease of input and you're exploiting that fact in attempt to prove your point), and illegal moves (ie. saying moving the denominator to the numerator is the same as multiplying by 1).

Try valid reasons. If you can prove that, then your points will make sense. However, I've yet to see anyone besides Speusippus make any logical comments on that.

6 pages and still no progress on that.
Edited by SweetWilly#1217 on 6/14/2012 3:13 PM PDT
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Oooh boy, I guess I’m going to have to do this the old fashioned way. :)

06/14/2012 03:28 PMPosted by Sinew

“Other uses for fractions are to represent ratios and to represent division.”
Pulled straight from the Wikipedia article. You might want to read them before you cite them.
06/14/2012 03:28 PMPosted by Sinew
fractions, implied multiplication or parenthesis multiplication supersede division/multiplication.

Still no justification on this statement.


No sign is assumed to have the same properties. Division, by definition doesn't have these properties. Look at the damn theorems. You are arguing about something demonstrated a million and one ways.

And yet still no evidence that implied multiplication supercedes multiplication.

06/14/2012 03:28 PMPosted by Sinew
Don't do things properly kid, I don't care. You are either lying through your teeth or you went to the worst school in the universe. Seriously, Clownshoes U is really turning out some good ones.

Haha, yes, because insulting me is relevant and changes the truth doesn't it? :)

I have stated many valid mathematical constructs which require implicit multiplication.

=a^2 + b^2 +2ab

=(a^2 + b^2)
=a^2 + b^2

Both valid, yes. But the second one assumes that * is a dot product symbol and not a regular multiplication symbol. Considering the * is used in many places on computers (ie programming languages, calculators, etc.) the two are ambiguous and unless you know the keystroke for the actual dot, it’s impossible to differentiate the two. And yes, they require implicit multiplication. Do they justify it superceding normal multiplication or division? I see no evidence of that.

Also, still no justification on why 48÷2(9+3) != 48÷2*(9+3) (with the * being regular multiplication, just for clarification).

And in response to all the insults you’ve been throwing at me, umad?
Edited by SweetWilly#1217 on 6/14/2012 4:01 PM PDT
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moron. fractions can represent division, division cannot represent fractions.

The justification follows that statement.

Still changes nothing. Eg. (Sqrt(2)*3*8)/(3*4*12) is not a rational number, yet it can still be represented by a fraction, and is a division problem at the same time.

06/14/2012 04:06 PMPosted by Sinew
Completely false on the last point. The absence of the symbol is assumed as dot product. the * symbol itself is not.

Not always. For basic computational purposes, it is assumed as regular multiplication. It can be assumed for basic computational purposes. Example: The problem represented by this thread.

06/14/2012 04:06 PMPosted by Sinew
You clearly cannot read. => You are not worth talking to.

06/14/2012 04:06 PMPosted by Sinew

Haha, and once again you’d rather throw insults than offer valid proof.
Edited by SweetWilly#1217 on 6/14/2012 4:40 PM PDT
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It's funny that the exact things you are saying about my arguments are what I'm saying about yours. You still haven't proved the one bit of evidence that would tie all your logic together.

06/14/2012 04:42 PMPosted by Sinew
Remove the parenthesis. That's what making it equivalent to a fraction.

There's a fraction there either way you look at it.

06/14/2012 04:42 PMPosted by Sinew
Yes. Always. There is not evidence to contradict this here.

Except the existence of calculators.

Your argument has been nothing but, "show me... no thats wrong. 'Cause I just said it is."

You have not invalidated anything. Be quiet.

And so do yours.

Here's some photo proof that some very high credential people think you're wrong.


What? That calculator might have errored out on a specific bit like some calculators do? Then let's check it with a different calculator.


Oh, look at that. They both think you're wrong. Like I said, you want to argue with the math majors? Here ya go:


Enjoy. :)
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Hahaha, once again you can't come up with a valid point so you result to personal attacks? Classy, good sir, very classy.

And yes, if statements and for loops are strings of logic that determine answers. Math like that is not subjective. This isn't English class. There is only one right answer.

And the TI-89 represents years upon years of research and programming in order to obtain that answer. You want to argue that a generation of mathematicians are wrong?


The future is yours buddy. Go show them the error of their ways.
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06/14/2012 07:03 PMPosted by Sinew
Coding anything of any complexity

06/14/2012 07:03 PMPosted by Sinew

Lol you really think this is complex? Double integrals are a lot more complex and my 89 does those just fine.

06/14/2012 07:03 PMPosted by Sinew
More code => more errors.

Agreed. But you want to argue that the 89's code is not concise?


Here ya go dude.

06/14/2012 07:03 PMPosted by Sinew
You must be an engineer of the thomas and friends variety. You obviously don't deal with CAD.

Haha, are you really that mad dude? These attacks are not at all necessary to prove a point and yet you're throwing them at me like a pitching machine throws baseballs. You're calling me irrational?
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ti89 was the best thing I ever bought in college.. I even had Dr. Mario on it.

So much debate over this and it just boils down to which interpration is correct:




I get where the "2" camp is coming from because, 1/2x is 1/(2x), not x/2. But that is because x is a variable. That same concept never applies to integers. At least from all my experience and understanding. 1/2(3) is not 1/6, but 3/2.

Thats why the answer is 288.

Sure writing a problem as 1/2(3) is dumb is the first place and it should be 1/2*3 at a minimum.
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let me rewrite the problem

X = 48÷2(9+3)

9+3 = 12

X = 48÷2(12)

And from what my math teachers told me multiplying with parenthesis like so 2(12) is a greater priority then 1÷2 or 1*2 so

2(12) = 24

X = 48÷24

48÷24 = 2

X = 2

so that means that the answer to 48÷2(9+3) is 2 even tho Google calculator said 288 it rewrote and changed the problem pass my level of understanding.
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48÷2(9+3) = ?

Here is the mechanical, completely correct way of solving it.

Also, the intended way.

First of all, check out wolframalpha.com before posting this, it is a hugely unneccesary thread if you just learn the correct way.

Second of all, there is no such thing as "division", its a simplified way of multiplicating the inverse of a number. So a good approach would be to express it in such a way.

48÷2(9+3) = x
Becomes then
48 * 1/2 * (9+3) = x
Which is the same as
48 * 2^(-1) * (9+3) = x
which can be simplified to:
24 * 12
Which is
10 * 12 + 10 * 12 + 4 * 12 = x
Resulting in
120 + 120 + 48 = x
x = 288.

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whats the problem here

if you read the equation mathematically correct

its simple 48\24 = 2
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lol this thread again
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Posts: 29
well... lets take it through the steps using only the symbols that are given to us: ÷()
and we will assume x as multiplication in order to complement the basic elementary symbols.
So lets get started.

step 1: We have 48÷2(9+3) . Lets start by pulling the 48 out of the equation.


step 2: Lets go ahead and pull that 2 out as well.

48x2(1÷1(9+3)÷4). keep in mind 2÷4 = 1÷2 and that n÷n = 1÷1 = 1 for n>0 , n<0 but not n = 0.

step 3: Clean up.


step 4: 1÷12÷4 or 1÷4÷12 which is the same as 1÷12÷1÷4 or 1÷4÷12. but not 4÷12÷1 or 12÷4÷1 . Because 1÷1 does not equal 2 nor does it equal n. and that 0÷0 does not equal 1. (if you don't understand this then your highest level of math is less than pre algebra or your just clumsy.) If you need help, wolfram alpha will clean it up for you.

96(1÷48) because (1÷12)(1÷4) = (1÷(12x4))

96÷48 = 2.

For those that want further proof... Look into the 1=2 paradox, and read up on l'Hôpital's rule. I would say look at l'Hôpital's rule first... because if it looks confusing to you, then you should not be here responding regardless if you originally believed the answer was 2 or not.

For those that believed the answer was 288. Hurry up and get through high school because its obviously been a cancer on you. Rule of thumb for college if you pick a degree outside of the medical field and it doesn't involve calculus 1, its not worthwhile and you'll likely never find the right job or happiness.
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