# So, what's the answer to this problem?



## LLiz (Apr 9, 2011)

A friend gave me the following maths problem: (No I ain't saying "math" to keep you Americans happy lol)
48Ã·2(9+3) = ?

What's your answer?

Basically he was observing a thread on another board where there was a war between the answers of "288" and "2".  

Also, here's the image that sparked the war: 






Try to answer the poll before you read any replies. 













Come on be brave, answer before reading any replies... I won't think less of you if you give the wrong answer (ok, maybe I will... a little bit... but the poll answers shouldn't be public anyway ... hopefully)


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## CannonFodder (Apr 9, 2011)

It's 2, what you've never heard of a calculator or something?


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## Ariosto (Apr 9, 2011)

Put patherentheses where they go, don't cheat.

If read straight, the answer is two.


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## CAThulu (Apr 9, 2011)

48Ã·2(9+3) 
= 24(12)
= 24x12
= 288

Calculators aren't perfect, y'all.


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## Folgrimeo (Apr 9, 2011)

I voted for 2. I think () has precedence over multiplication/division, so 48Ã·2(9+3) = 48Ã·2(12). Then multiplication and division are the same precedence, and I'm assuming left to right, so = 48Ã·24 = 2.


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## Alstor (Apr 9, 2011)

Order of Operations.

48/2(9+3)
48/2(12)
48/24
2

OR

48/2(9+3)
48/18+6
48/24
2


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## Ariosto (Apr 9, 2011)

CAThulu said:


> 48Ã·2(9+3)
> = 24(12)
> = 24x12
> = 288
> ...



Depends of how you read it:

(48/2)(9+3)=288
((48)/(2(9+3)))=2


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## CAThulu (Apr 9, 2011)

Ooo...good point Folgrimeo.   I think you're right on that.

I've always used the disclaimer that  as a rule artists suck at math, and I'm using that now for my previous answer *L*



AristÃ³crates Carranza said:


> Depends of how you read it:
> 
> (48/2)(9+3)=288
> ((48 /(2(9+3)))=2



That's the point.  Which one is correct?


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## LLiz (Apr 9, 2011)

The CORRECT answer is 2, but people seem to think its 288 because its how computers will work it out. 

If you hand write a division then you put whats on the left on top and whats on the right on the bottom so its: 

     48
---------------    =  2
  2 x (9 + 3)

but a computer evaluates the expression at each operator, so it'll say: 

 48
----- x (9 + 3)    = 288
  2

So for a computer to work it out you need to write:
48 / (2 x ( 9 + 3 ) )

And it evaluates whats in the parenthesis as a group.  

Anyway, I suck at maths, but I managed to get it right, after the war that supposedly happened on this other forum I was interested to see how people would answer it here.... being sophisticated furries and all... * cough *


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## Lobar (Apr 9, 2011)

The answer is 2.  Parentheses take precedence over everything else.

I think the TI-86 is parsing "48/2" as "forty-eight over two", that is, as a single term, which it is then multiplying the parenthesized terms by.  Meanwhile the TI-85 is parsing it as "forty-eight, divided by two", which is two seperate terms, forty-eight and two, and only multiplying the latter of them, two, into the parentheses.


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## Alstor (Apr 9, 2011)

Lobar said:


> The answer is 2.  Parentheses take precedence over everything else.
> 
> I think the TI-86 is parsing "48/2" as "forty-eight over two", that is, as a single term, which it is then multiplying the parenthesized terms by.  Meanwhile the TI-85 is parsing it as "forty-eight, divided by two", which is two seperate terms, forty-eight and two, and only multiplying the latter of them, two, into the parentheses.


 Would "(48 )/(2(9+3))" fix it for the TI-86? That's what happens on my TI-84.


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## LLiz (Apr 9, 2011)

You know... this is apparently going to be a pretty talked about thing for the next few days... its popping up all over the interwebs. 

I totally get why a computer comes up with the answer 288, because its the way that computers evaluate expressions, but humans aren't computers...


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## Alstor (Apr 9, 2011)

To answer my own problem,

http://i53.tinypic.com/6jogg2.png

Taken from a TI-84 Plus Graphing Calculator. The first expression is the regular question, while the second one is stretching it out according to the Order of Operations.


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## Unsilenced (Apr 9, 2011)

I swear it's 288. 

Equal operations go left to right. You divide the 48 by 2 before you multiply in the 12. 

48/2â€¢12=288

Looks weird because they're using the parenthesis to do the multiplication, but that's how it goes.

Granted when we (humans) read a problem, we usually act as if two numbers put next to each other are being multiplied within parenthesis, but I'm pretty sure that's not how you're *supposed* to do it if you want to be technical. 



Folgrimeo said:


> I voted for 2. I think () has precedence over multiplication/division, so 48Ã·2(9+3) = 48Ã·2(12). Then multiplication and division are the same precedence, and I'm assuming left to right, so = 48Ã·24 = 2.


 
You just went right to left bro...

Unless I'm just trippin'

That's entirely a possibility.


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## Alstor (Apr 9, 2011)

Unsilenced said:


> 288, y'all
> 
> Equal operations go left to right. You divide the 48 by 2 before you multiply in the 12.
> 
> ...


 I stole this from another forum, so this isn't mine.

Replace (9+3) with x

48/2x=2
48=2(2x)
24=2x
12=x
Since (9+3)=12 and x=12, this works.

48/2x=288
48=288(2x)
1/12=2x
1/24=x
Since (9+3)=12 and 1/24=x, this cannot work.


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## Lobar (Apr 9, 2011)

Alstor said:


> I stole this from another forum, so this isn't mine.
> 
> Replace (9+3) with x
> 
> ...


 
I was just about to try to explain it this way.  Putting the 2 outside the parentheses effectively makes it a coefficient of what's inside them, just as if it were 2x.  If the problem were written as 48 / 2 * (9 + 3), I would agree that the answer is 288.


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## Azure (Apr 9, 2011)

the answer is, uhhhhh, $50. Gimmie.


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## Waffles (Apr 9, 2011)

I thought in order of operations (PEMDAS) Multiplication/Division go by whichever comes first. Same with addition/subtraction.
48/2(12)
24(12)
288?


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## cavewolf (Apr 9, 2011)

Alstor said:


> I stole this from another forum, so this isn't mine.
> 
> Replace (9+3) with x
> 
> ...


 
That's a brilliant way to approach and explain it!  Thanks!


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## Unsilenced (Apr 9, 2011)

Would it be different if it were writte 2â€¢(9+3) instead of 2(9+3)? 

I'm pretty sure I was taught that it wouldn't...


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## Xenke (Apr 9, 2011)

Depends on what the intended order of operations is. Some retard didn't add enough parenthesis to their raw equation.

Obviously 2, though.


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## Bloodshot_Eyes (Apr 9, 2011)

I'm getting 288... :/


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## Garfang (Apr 9, 2011)

well you doing the 9+3 inside the Parenthesis then propagate with 2 and later divide that with 48 and the answer is 2


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## Takun (Apr 9, 2011)

It's either or, just not clarified.

In it's given state I'd take it as

48Ã·2(9+3)  parenthesis first

48Ã·2(12)

48Ã·2*12  This isn't 48 over 2(12) but 48 divided by 2and then multiplied by whatever was in the brackets.

24*12

288


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## Garfang (Apr 9, 2011)

Takun said:


> It's either or, just not clarified.
> 
> In it's given state I'd take it as
> 
> ...



ah ok :/ but you wrong because you have to do the 9+3 * 2 because of parenthesis have priority and then you do the divide


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## Unsilenced (Apr 9, 2011)

Garfang said:


> ah ok :/ but is divide has priority over to Propagation?I think propagation is first and then divide.


 
Nope. 

Multiplication and division are equal in the order of operations, so you go left to right. 

Of course, none of this would happen if we were writing this on paper and not a computer. Paper makes it easier to show exactly what you mean.


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## Kihari (Apr 9, 2011)

How is everyone aware of order of operations but still ending up with 2?

48 / 2 * (*9 + 3*)

*48 / 2* * 12

*24 * 12*

288


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## Garfang (Apr 9, 2011)

yeah as i edited my post  because i though it better , In the end the parenthesis go first then the others


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## Lobar (Apr 9, 2011)

Kihari said:


> How is everyone aware of order of operations but still ending up with 2?
> 
> 48 / 2 * (*9 + 3*)
> 
> ...


 
Because I say formatting it as 2(9 + 3), which is how the original problem has it formatted and not the way you wrote it, groups it into a single expression in a way that 2 * (9 + 3) does not, and the parentheses step is not completed until the 2 is propagated into it.  Much like how 2x is simply 2 * x, but you cannot say 48 / 2x = 24x (though 48 / 2 * x = 24x is correct).


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## TreacleFox (Apr 9, 2011)

Kihari said:


> How is everyone aware of order of operations but still ending up with 2?
> 
> 48 / 2 * (*9 + 3*)
> 
> ...



_48_/_2_(_9_+_3_) = _48_/_2_(12) = 48/24 = 2

Also, my $200 from school says its 2.

:C


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## Hateful Bitch (Apr 9, 2011)

This is how I'd write it down anyway

Since 2(9+3) is one value, just like 2y, where y=9+3

or something


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## Kihari (Apr 9, 2011)

Lobar said:


> Because I say formatting it as 2(9 + 3), which is  how the original problem has it formatted and not the way you wrote it,  groups it into a single expression in a way that 2 * (9 + 3) does not,  and the parentheses step is not completed until the 2 is propagated into  it.  Much like how 2x is simply 2 * x, but you cannot say 48 / 2x = 24x  (though 48 / 2 * x = 24x is correct).


 
Oh, I see what's happening here. Not only are you claiming the  juxtaposition of 2 and (9 + 3) implies multiplication, you're also  mentally placing grouping symbols around them, as in 48 / (2 * (9 + 3)).  That would indeed make 2 correct if that's how you  interpret it.

In order to perform the computation using _a single, definitive multiplication operator_, you would need to manually form the grouping, which is not done in the original problem.

In order to perform the computation _as it appears in the original problem_, the grouping is implied by a special notation for multiplication.

That is interesting.



Meadow said:


> Also, my $200 from school says its 2.


 
Google would like to have a few words with you.


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## Hateful Bitch (Apr 9, 2011)

This thread is a brilliant example of why the division symbol is the shittiest thing ever.

Lines kick ass


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## ArgonTheFox (Apr 9, 2011)

why the hell does my calculator think its 21 DX


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## OssumPawesome (Apr 9, 2011)

Fuck PEMDAS.

Seriously.


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## CaptainCool (Apr 9, 2011)

the way it is written here its 2 while 48/2*(9+3) would be 288.
without the multiplication symbol the 2 is part of the parenthesis which has to be done before the devision. if you add the symbol it becomes a regular multiplication and you have to solve it from left to right.
thats how i would explain it. 
plus, alstors explanation is brilliant


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## Kihari (Apr 9, 2011)

CaptainCool said:


> the way it is written here its 2 while 48/2*(9+3) would be 288.
> *without the multiplication symbol the 2 is part of the parenthesis* which has to be done before the devision. if you add the symbol it becomes a regular multiplication and you have to solve it from left to right.


 
Be careful with that.

Evaluate 2(3 + 4)Â².


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## Lobar (Apr 9, 2011)

Kihari said:


> Be careful with that.
> 
> Evaluate 2(3 + 4)Â².


 
I say 98.


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## Jw (Apr 9, 2011)

All I got to say is this: if you answered 288 and are going to go to school to become a pharmacist, you might as well give up now and go home. Or keep going and kill some people. Your choice.

also, couple posts above, answer is 98. 
2(3+4)^2= (Parentheses)
2(7)^2=(Exponent)
2(49)=(Multiplication/Division)
98=


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## Kihari (Apr 9, 2011)

Lobar said:


> I say 98.


 
Right you are. Here we're considering the problem to be 2 * ((3 + 4)Â²), not (2 * (3 + 4))Â², which was the interpretation of how multiplication-by-juxtaposition worked for the previous problem.

Remember, the 2 was "part of the parentheses," and by order of operations, parenthetic statements have a higher priority than division and exponentiation both.

This multiplication business needs to be defined much more carefully.


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## Lobar (Apr 9, 2011)

Kihari said:


> Right you are. Here we're considering the problem to be 2 * ((3 + 4)Â²), not (2 * (3 + 4))Â², which was the interpretation of how multiplication-by-juxtaposition worked for the previous problem.
> 
> Remember, the 2 was "part of the parentheses," and by order of operations, parenthetic statements have a higher priority than division and exponentiation both.
> 
> This multiplication business needs to be defined much more carefully.


 
I'm amending my position.  While writing it as 2(9 + 3) does not make the multiplication happen in the parentheses step, it still nonetheless groups it into a single expression that must be fully evaluated before other operators can act on it.  PEMDAS is applied in full to just this expression, which satisfies the ability for 2(3 + 4)Â² = 98 to be true, and then PEMDAS is applied again to the problem as a whole.

Also, anyone who writes problems like these in the future with division not represented as fractions need to be shot.


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## Tycho (Apr 9, 2011)

OK, even I can see the answer here.  And I'm horrid at math.  That one calc is either broken or they messed with the way it reads problems between one model and the next.  Which would still make it broken.



Lobar said:


> Also, anyone who writes problems like these in the future with division not represented as fractions need to be shot.


 
this

That stupid little division sign belongs in 5th grade math.  Not in this kind of stuff.


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## CaptainCool (Apr 9, 2011)

i should have added that i suck at maths i guess ;D


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## Kihari (Apr 9, 2011)

Lobar said:


> While writing it as 2(9 + 3) does not make the multiplication happen in the parentheses step, it still nonetheless groups it into a single expression that must be fully evaluated before other operators can act on it.  PEMDAS is applied in full to just this expression, which satisfies the ability for 2(3 + 4)Â² = 98 to be true, and then PEMDAS is applied again to the problem as a whole.


 
But-but-but! Be careful how you're implementing this, because it has to work _the same way_ for every problem. In the first you want the grouping to occur as 48 / (2(9 + 3)), which _excludes_ the nearby division operator, but in the second you're doing (2(3 + 4)Â²), which _includes_ the exponentiation.

Really, I think what this whole thing boils down to is that, for example, 1 / 2(3) looks an awful lot like the fraction with 2(3) in the denominator, as in that's what it _visually_ resembles, so that's how most tend to treat it even though there's no rule that says to do so (or if there is such a rule, I'd sure love to know).


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## Thatch (Apr 9, 2011)

Garfang said:


> ah ok :/ but you wrong because you have to do the 9+3 * 2 because of parenthesis have priority and then you do the divide


 
Priority is for what's INSIDE the parenthesis.



Unsilenced said:


> Multiplication and division are equal in the order of operations, so you go left to right.


 
/THREAD

But seriously, if you don't want  computer to crap out, give it unambiguous expressions.


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## Lobar (Apr 9, 2011)

Kihari said:


> But-but-but! Be careful how you're implementing this, because it has to work _the same way_ for every problem. In the first you want the grouping to occur as 48 / (2(9 + 3)), which _excludes_ the nearby division operator, but in the second you're doing (2(3 + 4)Â²), which _includes_ the exponentiation.


 
I should have clarified that this prioritized grouping includes that exponent as well.


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## Kihari (Apr 9, 2011)

Lobar said:


> I should have clarified that this prioritized grouping includes that exponent as well.



Fair enough, but just so long as you know what whoever wrote the problem _meant_ with their notation and can determine the right grouping accordingly.



Thatch said:


> give it unambiguous expressions


 
Of everything in this thread, ^this line right here is surely the best.


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## Hateful Bitch (Apr 9, 2011)

Oh heck, that caught me out
I blame the fact that I never see these kinds of problems written out with division signs


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## H.nightroad (Apr 9, 2011)

Ok so we have two logical choices
(48/2)(9+3) = 288 and
48/(2(9+3)) = 2
so then we go looking and both of them are possible
     288 = (48/2)(9+3)
288/12 = 48/2
        12=12

Then
     2=48/(2(9+3))
48/2=2(12)
   24=24
So they are both equally true, though the classical method for this equation would mean it would look like this

48
--------
2(9+3)

So 2 is the answer, because before anything else the brackets and anything to their immediate left are evaluated


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## Hateful Bitch (Apr 9, 2011)

H.nightroad said:


> 48/(2(9+3)) = 2


 
That isn't the question. That's just a false interpretation you got there.


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## Rakuen Growlithe (Apr 9, 2011)

It's 2. I learned this in junior school. BODMAS. Brackets. Of. Division. Multiplication. Addition. Subtraction.


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## Waffles (Apr 9, 2011)

Rakuen Growlithe said:


> It's 2. I learned this in junior school. BODMAS. Brackets. Of. Division. Multiplication. Addition. Subtraction.


 Are you doing the divion/multiplication correctly? The way the problem is written, if you do multiplication/division left to right (they have equal  value) then it should go 24(12).


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## LizardKing (Apr 9, 2011)

The correct answer is clearly _fuck division signs._

Bam, ambiguity gone, answer is obvious.


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## Kihari (Apr 9, 2011)

Hateful Bitch said:


> That isn't the question. That's just a false interpretation you got there.


 
They skipped a few steps in showing the process. You can arrive at that,  but I think all they've done for both equations is go through the steps  in the order that gives the right answer for each interpretation; if  so, then it still doesn't prove anything.



H.nightroad said:


> the classical method for this equation would mean it would look like this
> 
> 48
> --------
> 2(9+3)


 
I still want to see the hard-and-fast rule where this is defined as the _correct_ way of setting up the fraction. Otherwise, I'm just reading the equation left-to-right, performing multiplication and division as I see 'em.


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## Leafblower29 (Apr 9, 2011)

I'm shitty at math but I voted 2.


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## Candy (Apr 9, 2011)

I was told that when a number is attached to something in parentheses (like the 2(x)), it's pretty much stuck to it. You have to figure that out before doing the rest. It's 2x and you can't leave the (x) off to the side for later.


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## RLR (Apr 9, 2011)

Distributive property:
48/2(9+3)=48/(18+6)=48/24=2


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## Seas (Apr 9, 2011)

So, the question is settled for 2 as soon as anyone provides evidence that putting a number without the multiplication mark before the parentheses makes it part of the parentheses receiving a higher  operation priority than multiplication/division.

Otherwise, it's 288 and you are all bad at math :V


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## Larkstarr (Apr 9, 2011)

according the bedmas I'd get 288

48Ã·2(9+3)=48Ã·2(12)=24(12)=288


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## Ariosto (Apr 9, 2011)

This reached three pages?!
Oh FAF not you!


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## Rakuen Growlithe (Apr 9, 2011)

Larkstarr said:
			
		

> according the bedmas I'd get 288
> 
> 48Ã·2(9+3)=48Ã·2(12)=24(12)=288​



You're doing it wrong. You must remove the brackets before you can do the division. 48/2(12) = 48/24 [brackets first] = 2


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## Kihari (Apr 9, 2011)

Rakuen Growlithe said:


> You're doing it wrong. You must remove the brackets before you can do the division. 48/2(12) = 48/24 [brackets first] = 2


 
Again, reducing any grouping refers to evaluating the expression _inside _the brackets. The multiplication appears on the _outside_, and is being performed on the parenthesized expression as a whole.


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## Larkstarr (Apr 9, 2011)

There's no rule stating, as far as I know, that anything OUTSIDE the brackets must be dealt with / solved first.

48/2(12) = 48/2*12 = 24*12 = 288.


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## Ariosto (Apr 9, 2011)

So I asked to a mathematician friend and he said the answer is 288 for the same reason that Unsileced claimed: multiplication and division being equal in order of operation.


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## Larkstarr (Apr 9, 2011)

DM and AS of bedmas are equal, I was taught, that's when you proceed to solve it left-to-right. But that just seems to be an unwritten or undefined rule (LtR that is).


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## Rakuen Growlithe (Apr 9, 2011)

It's 2. Distributive property of multiplication over addition says you can either add terms and then multiply or multiply terms by a factor and then add them.
http://www.math.unt.edu/mathlab/emathlab/distributive_property_of_multipl.htm

So that means it's equally correct to say 48/2(9+3) = 48/(18+6) = 48/24 = 2


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## Thatch (Apr 9, 2011)

Rakuen Growlithe said:


> You're doing it wrong. You must remove the brackets before you can do the division. 48/2(12) = 48/24 [brackets first] = 2


 
Say this one more time and I'll fly there, and strangle you with that fucking parenthesis.



Rakuen Growlithe said:


> It's 2. Distributive property of multiplication over addition says you can either add terms and then multiply or multiply terms by a factor and then add them.
> http://www.math.unt.edu/mathlab/emathlab/distributive_property_of_multipl.htm
> 
> So that means it's equally correct to say 48/2(9+3) = 48/(18+6) = 48/24 = 2


 
THAT. DIVISION. IS. DONE. FIIIIIIIRST!!!!!!

That theorem has no relevance to the problem. This is about order of operation. Just fucking shut up already, I'll burst a vein because of you.


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## Rakuen Growlithe (Apr 9, 2011)

Thatch said:
			
		

> Say this one more time and I'll fly there, and strangle you with that fucking parenthesis.



Left bracket (
Right bracket )
Square brackets [ ]
Spiky brackets { }
Brackets, brackets, brackets


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## Larkstarr (Apr 9, 2011)

Rakuen Growlithe said:


> It's 2. Distributive property of multiplication over addition says you can either add terms and then multiply or multiply terms by a factor and then add them.
> http://www.math.unt.edu/mathlab/emathlab/distributive_property_of_multipl.htm
> 
> So that means it's equally correct to say 48/2(9+3) = 48/(18+6) = 48/24 = 2



No, it's not. You still can't perform operations out of order. Material in the bracket must be dealt with first.

The only way you can apply the distributive law is 48 / 2(9+3) = 24(9+3) = (216 + 72) = 288


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## Thatch (Apr 9, 2011)

Rakuen Growlithe said:


> Left bracket (
> Right bracket )
> Square brackets [ ]
> Spiky brackets { }
> Brackets, brackets, brackets


 
Wow, even while trying to purposefully piss people off, you still don't quite get what made them rage in the first place.

Bravo.


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## Jashwa (Apr 9, 2011)

It's 288, stupid people. division/multiplication work from left to right

48 divided by 2=24

times (9+3)=288

The left calculator was just bad with syntax. This is how the math should be.


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## Thatch (Apr 9, 2011)

Jashwa said:


> The left calculator was just bad with syntax. This is how the math should be.


 
Again, as I said already, if you don't want computers to crap out, be unambiguous.


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## Jashwa (Apr 9, 2011)

Thatch said:


> Again, as I said already, if you don't want computers to crap out, be unambiguous.


 This is why PARENTHESIS AROUND EVERYTHING on my engineering/physics homework.


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## Larkstarr (Apr 9, 2011)

Garbage in, Garbage out! 

And hopefully, lesson learned?


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## Kihari (Apr 9, 2011)

Rakuen Growlithe said:


> Distributive property of multiplication over addition says you can either add terms and then multiply or multiply terms by a factor and then add them.


 
Mind the rest of the operators in the equation.



Kihari said:


> Be careful with that.
> 
> Evaluate 2(3 + 4)Â².


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## Jashwa (Apr 9, 2011)

I wish this poll was public so I could laugh at everyone that voted 2.


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## Alstor (Apr 9, 2011)

Continuing what my last post did and applying it to every integer in the expression.


```
48/x(9+3)=2
48/(9x+3x)=2
48/12x=2
48=2(12x)
48=24x
2=x
Since the original expression had x=2, and x=2 here, this works.

48/x(9+3)=288
48/(9x+3x)=288
48/12x=288
48=288(12x)
48=3,456x
0.14=x
Since the original expression had x=2, and x=0.14 here, this does not work.


x/2(9+3)=2
x/2(12)=2
x/24=2
x=24(2)
x=48
Since the original expression had x=48, and x=48 here, this works.

x/2(9+3)=288
x/2(12)=288
x/24=288
x=288(24)
x=6,912
Since the original expression had x=48, and x=6,912 here, this does not work.


48/2(x+3)=2
48/(2x+6)=2
48=2(2x+6)
48=4x+12
36=4x
9=x
Since the original expression has x=9, and x=9 here, this works.

48/2(x+3)=288
48/(2x+6)=288
48=288(2x+6)
48=576x+1,728
-1,680=576x
-2.92=x
Since the original expression had x=9, and x=-2.92 here, this does not work.


48/2(9+x)=2
48/(18+2x)=2
48=2(18+2x)
48=36+4x
12=4x
3=x
Since the original expression had x=3, and x=3 here, this works.

48/2(9+x)=288
48/(18+2x)=288
48=288(18+2x)
48=5,184+576x
-5,136=576x
-8.92=x
Since the original expression had x=3, and x=-8.92 here, this does not work.
```


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## Maisuki (Apr 9, 2011)

Sounds like a lot of you need to go back to sixth-grade math and re-learn the order of operations.

Pemdas, my friends. (parenthesis, exponents, multiplication, division, addition, subtraction)

if followed correctly, you get the answer two, the correct answer.


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## Thatch (Apr 9, 2011)

Jashwa said:


> This is why PARENTHESIS AROUND EVERYTHING on my engineering/physics homework.


Exactly.

And actually putting the multiplication symbol in OP's problem. I'm wondering if then they would show the same.


----------



## Rakuen Growlithe (Apr 9, 2011)

Kihari said:
			
		

> Evaluate 2(3 + 4)Â².



You must square them first.



			
				Thatch said:
			
		

> Again, as I said already, if you don't want computers to crap out, be unambiguous.



The change in notation implies that the groupings.


----------



## Jashwa (Apr 9, 2011)

Alstor said:


> [wrong]


 Alstor, multiplication and division are on the same step. They work left to right. Therefore, you do the division before you can multiply and distribute.


----------



## Larkstarr (Apr 9, 2011)

Maisuki said:


> Sounds like a lot of you need to go back to sixth-grade math and re-learn the order of operations.
> 
> Pemdas, my friends. (parenthesis, exponents, multiplication, division, addition, subtraction)
> 
> if followed correctly, you get the answer two, the correct answer.




sounds like you need to read up on order of operations more. - https://secure.wikimedia.org/wikipedia/en/wiki/Order_of_operations - division and multiplication are of equal precedence.


and Alstor, all of your math is fundamentally flawed.


----------



## Alstor (Apr 9, 2011)

Jashwa said:


> Alstor, multiplication and division are on the same step. They work left to right. Therefore, you do the division before you can multiply and distribute.


see


Alstor said:


> To answer my own problem,
> 
> http://i53.tinypic.com/6jogg2.png
> 
> Taken  from a TI-84 Plus Graphing Calculator. The first expression is the  regular question, while the second one is stretching it out according to  the Order of Operations.



You must remove the second set of parentheses before doing the division.


----------



## Larkstarr (Apr 9, 2011)

you modified the original expression with an OoO that makes the multiplication go first, which is WRONG.


----------



## Jashwa (Apr 9, 2011)

Alstor said:


> You must remove the second set of parentheses before doing the division.


 There is no second set of parenthesis. Your "stretching it out according to the order of operations" is completely wrong and changes the problem entirely. 

Trust me, Alstor, I'm a Mechanical Engineering major in one of the top 10 schools for it in the country. I got 770 on both my math 1 and math 2 SAT's and I've taken four pure math courses in college. 

I'm right.


----------



## Thatch (Apr 9, 2011)

Rakuen Growlithe said:


> The change in notation implies that the groupings.


 
...Implies that the groupings what?

Seriously, just don't say anything. You're not able to make sense.


----------



## Kihari (Apr 9, 2011)

Alstor said:


> Continuing what my last post did and applying it to every integer in the expression.
> 
> 
> ```
> ...


Same mistake Rakuen was making on the last page, you're performing the multiplication of the divisor x with the quantity (9 + 3).



> ```
> x/2(9+3)=288
> x/2(12)=288
> x/24=288
> ...


Between lines 2 and 3, performing equal-priority operations from right-to-left, not left-to-right.



> ```
> 48/2(x+3)=288
> 48/(2x+6)=288
> 48=288(2x+6)
> ...


Again, multiplying with the divisor (this time 2).



> ```
> 48/2(9+x)=288
> 48/(18+2x)=288
> 48=288(18+2x)
> ...


...and same issue, again with 2.


----------



## Alstor (Apr 9, 2011)

Ok, for shits and giggles, I'll try it the other way.


```
(x/2)(9+3)=2
(x/2)(12)=2
x/2=1/6
x=0.08
Since the original expression has x=48, and x=0.08 here, this does not work.

(x/2)(9+3)=288
(x/2)(12)=288
x/2=24
x=48
Since the original expression has x=48, and x=48 here, this works.
```

That's how it would go if you see it as two separate problems, which I believe is not so.


----------



## Larkstarr (Apr 9, 2011)

Kihari - THANK YOU. I didn't want to waste the time.

dude, it's left to right on equal priority operations. Believe it to be so. BELIEVE!


----------



## Jashwa (Apr 9, 2011)

This thread makes me seriously sad.


----------



## Alstor (Apr 9, 2011)

Kihari said:


> Same mistake Rakuen was making on the last page, you're performing the multiplication of the divisor x with the quantity (9 + 3).
> 
> Between lines 2 and 3, performing equal-priority operations from right-to-left, not left-to-right.
> 
> ...


 I see all of that. There needed to be parentheses around everything for that to be right.

Your way is better than just saying I'm wrong and using test scores to "prove" it. :V


----------



## Maisuki (Apr 9, 2011)

I fail at math.

Brb trolling trade chat in wow with this math problem.


----------



## Jashwa (Apr 9, 2011)

This problems much easier if you just put it all as multiplication

48*(2)^(-1)*(9+3)

There, just follow order of operations, no more division.


----------



## Kihari (Apr 9, 2011)

Alstor said:


> I see all of that. There needed to be parentheses around everything for that to be right.
> 
> Your way is better than just saying I'm wrong and using test scores to "prove" it. :V


http://oi51.tinypic.com/f2stxd.jpg

Maybe this will illustrate better. This is what you're trying to do in three of those cases, jamming (9 + 3) into the denominator rather than treating (48 / 2) as a fraction as order of operations _and _left-to-right parsing calls for.

EDIT: Hey TinyPic, kindly fuck off.


----------



## Rakuen Growlithe (Apr 9, 2011)

I interpret 48/2(9+3) as (48)/(2(9+3)). If it were 48/2*(9+3) then I would read it as (48)/(2)(9+3).


----------



## Thatch (Apr 9, 2011)

Jashwa said:


> 48*(2)^(-1)*(9+3)


 
96^(-12) :V



Rakuen Growlithe said:


> I interpret 48/2(9+3) as (48)/(2(9+3)). If it were 48/2*(9+3) then I would read it as 48/(2)(9+3).


 
Math isn't subjected to your interpretation. It's objective.


----------



## Rakuen Growlithe (Apr 9, 2011)

Thatch said:
			
		

> Math isn't subjected to your interpretation. It's objective.



And the question is at best ambiguously written.


----------



## Xenke (Apr 9, 2011)

Jashwa said:


> 48*(2)^(-1)*(9+3)


 
Still not enough parenthesis.

The only thing I've learned from this thread is that I learned PEMDAS, and some people learned it as BEDMAS or some shit, and that people have obviously never had to write equations in WebWork.


----------



## Larkstarr (Apr 9, 2011)

are you ****ing serious?

48*(2)^(-1)*(9+3)
48*0.5*12
24 * 12 OR 48 * 6
288


----------



## Thatch (Apr 9, 2011)

Rakuen Growlithe said:


> And the question is at best ambiguously written.


 
That in no way reflects on the fact that math is not subjected to interpretation. You do it one way, or you're doing it wrong.

YOU are doing it wrong.


----------



## Alstor (Apr 9, 2011)

I admitted that I was wrong. Can you guys stop trying to prove me wrong now?


----------



## Plantar (Apr 9, 2011)

I really don't understand some of the wacky answers people are giving. Parentheses are at the very top priority to get out of the way... :|


----------



## Kihari (Apr 9, 2011)

Rakuen Growlithe said:


> And the question is at best ambiguously written.


 
See page 2.



Xenke said:


> Still not enough parenthesis.


 
You best be trollan.

48*(2)^(-1)*(9+3)

P - Evaluate expressions in parentheses.

48*2^-1*12

E - Evaluate exponentiation.

48*0.5*12

MD - Evaluate multiplication and division (with equal priority).

24*12

288



Alstor said:


> I admitted that I was wrong. Can you guys stop trying to prove me wrong now?


 
You know we all love your guts Alstor. ~<3


----------



## Jashwa (Apr 9, 2011)

Rakuen Growlithe said:


> And the question is at best ambiguously written.


 No, it's not. 2(12) is 2*(12) NO MATTER WHAT


Kihari said:


> You best be trollan.


 He's kidding and saying that everything needs more parenthesis. He knows that it's right.


----------



## Xenke (Apr 9, 2011)

Jashwa said:


> He's kidding and saying that everything needs more parenthesis. He knows that it's right.


 
WHAT IF ARABICS ARE DOING THEM MATHS?

THEY READ BACKWARDS.


----------



## Kihari (Apr 9, 2011)

Jashwa said:


> No, it's not. 2(12) is 2*(12) NO MATTER WHAT
> 
> He's kidding and saying that everything needs more parenthesis. He knows that it's right.


 
Oh good.


----------



## Larkstarr (Apr 9, 2011)

Then the question would be (3+9)2/48 . Obviously.


----------



## Thatch (Apr 9, 2011)

Xenke said:


> WHAT IF ARABICS ARE DOING THEM MATHS?
> 
> THEY READ BACKWARDS.


 
WHAT IF WE COUNTED IT IN ROMAN NOTATION!?


----------



## Itakirie (Apr 9, 2011)

...I am never going to trust the calculators in my math class ever again.


----------



## Larkstarr (Apr 9, 2011)

as you shouldn't.


----------



## Thatch (Apr 9, 2011)

Itakirie said:


> ...I am never going to trust the calculators in my math class ever again.





Larkstarr said:


> as you shouldn't.


 
This person speaks the truth.

Not to mention that they don't allow calculators in any math class I have or ever had.


----------



## Randy-Darkshade (Apr 9, 2011)

Folgrimeo said:


> I voted for 2. I think () has precedence over multiplication/division, so 48Ã·2(9+3) = 48Ã·2(12). Then multiplication and division are the same precedence, and I'm assuming left to right, so = 48Ã·24 = 2.



I've never done this type of math before and this is the way I did it to get the answer two.



CannonFodder said:


> It's 2, what you've never heard of a calculator or something?



Calculators are for cheats.


----------



## H.nightroad (Apr 9, 2011)

> Unfortunately, there exist differing conventions concerning the unary operator âˆ’ (usually read "minus"). In written or printed mathematics, the expression âˆ’32 is interpreted to mean âˆ’(32)*=*âˆ’9, but in some applications and programming languages, notably the application Microsoft Office Excel and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus (negation) has higher precedence than exponentiation, so in those languages âˆ’32 will be interpreted as (âˆ’3)2*=*9. [1]. In any case where there is a possibility that the notation might be misinterpreted, it is advisable to use brackets to clarify which interpretation is intended.
> 
> Similarly, care must be exercised when using the slash ('/') symbol. The string of characters*"1/2x" is interpreted by the above conventions as*(1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of brackets will clarify the meaning and should be used if there is any chance of misinterpretation.


so after reading the above article from the great and almighty Wikipedia, I have come to the conclusion that the answer is 288 and I have been wrong, the guy that said that to get 288 out of the equation was impossible algebraically was wrong as well, case closed Wikipedia has spoken! Though the guy who wrote the original calculation on the calculator was a douche for not removing the ambiguity that is inherent in his equation
/THREAD


----------



## Unsilenced (Apr 9, 2011)

Jashwa said:


> I wish this poll was public so I could laugh at everyone that voted 2.


 
I accidentally'd 2 because it was 4am and I hadn't thought about it for more than 5 seconds. 

Don't hurt me. ;.;


----------



## LLiz (Apr 9, 2011)

Wow I expected one page at best, but 5 pages?



Thatch said:


> Say this one more time and I'll fly there, and strangle you with that fucking parenthesis.





Rakuen Growlithe said:


> Left bracket (
> Right bracket )
> Square brackets [ ]
> Spiky brackets { }
> Brackets, brackets, brackets


 
In the queen's English they're called brackets, so you can take your parenthesis and shove them right up your bracket!


----------



## Rakuen Growlithe (Apr 10, 2011)

H.Nightroad said:
			
		

> so after reading the above article from the great and almighty  Wikipedia, I have come to the conclusion that the answer is 288 and I  have been wrong, the guy that said that to get 288 out of the equation  was impossible algebraically was wrong as well, case closed Wikipedia  has spoken! Though the guy who wrote the original calculation on the  calculator was a douche for not removing the ambiguity that is inherent  in his equation
> /THREAD



Way to link to the article. You could have written that out yourself. In any case looking it up just shows that you didn't read the article particularly well or were deliberately quote-mining and attempting to misinform people. I hope you were just sloppy and not dishonest. What it says in the line exactly above your quote is this.



			
				http://en.wikipedia.org/wiki/Order_of_operations said:
			
		

> Some mathematicians hold that multiplication by juxtaposition (omitting  the x sign, ex. 2(4+3) ) is a symbol of grouping. No fixed convention  exists.



Which supports the interpretation of the answer being 2 and is the way that all maths I have seen does it. And the source for that links directly to a page with this example.



			
				http://www.purplemath.com/modules/orderops2.htm said:
			
		

> This next example displays an issue that almost        never arises but, when it does, there seems to be no end to the arguing.
> 
> 
> *Simplify 16 Ã· 2[8 â€“ 3(4 â€“ 2)] + 1.*
> ...


----------



## LizardKing (Apr 10, 2011)

LLiz said:


> Wow I expected one page at best, but 5 pages?



This thread on the same thing has 98 pages (20 posts per page)
Or how about this one with 52 pages? (50 posts per page) (Yes, 2500+ posts)
Edit: I just realised those 2500+ posts have been over the course of _2 days_. Goddamn.


There's hundreds of threads on this. No one can ever reach an agreement on anything other than saying it's terribly formatted and division symbols like that need to DIAF, and instead the problem should be correctly represented as fractions instead.


----------



## EdieFantabulous (Apr 10, 2011)

Hmmm... 48/2(9+3) = 48/2(12)
48/2=24
24(12)=288...

Division and multiplication come as whichever is first, so this is correct to me.


----------



## HillyRoars (Apr 10, 2011)

It's 2 in my book.


----------



## CynicalCirno (Apr 10, 2011)

It's meme in my book.


----------



## Xipoid (Apr 10, 2011)

So does .999... = 1?


If someone could get back to me on that, I'd be entertained.


----------



## Thatch (Apr 10, 2011)

Xipoid said:


> So does .999... = 1?
> 
> 
> If someone could get back to me on that, I'd be entertained.


 
Wikipedia says Yes.


----------



## CynicalCirno (Apr 10, 2011)

Xipoid said:


> So does .999... = 1?
> 
> 
> If someone could get back to me on that, I'd be entertained.


 
It doesn't take much to prove it, you know.


----------



## Xipoid (Apr 10, 2011)

Yes, I know, but I'm waiting for someone to attempt the opposite.


----------



## Volkodav (Apr 10, 2011)

i declare this answer as 288


----------



## Scotty1700 (Apr 10, 2011)

Please Excuse My Dear Aunt Sally :v

48Ã·2(9+3) = ?

Parenthesis first, so it'd be simplified to 48Ã·2(12) = ?
Exponents next, none are present. 48Ã·2(12) = ?
Multiplication 48Ã·24 = ?
Division 48Ã·24 = 2
Addition, none present.
Subtraction, none present.

Final answer: 2


----------



## Jashwa (Apr 10, 2011)

Scotty1700 said:


> Please Excuse My Dear Aunt Sally :v
> 
> 48Ã·2(9+3) = ?
> 
> ...


Wrong.


See the past 5 pages for why.


----------



## Llamapotamus (Apr 11, 2011)

Instead of this insipid problem, I'd like to see an example where PEMDAS gives the wrong answer.


----------



## Scotty1700 (Apr 11, 2011)

Jashwa said:


> Wrong.
> 
> 
> See the past 5 pages for why.


 
Now see I thought at first that multiplication and division along with addition and subtraction went together but I just went off the acronym lol


----------



## EdieFantabulous (Apr 11, 2011)

Llamapotamus said:


> Instead of this insipid problem, I'd like to see an example where PEMDAS gives the wrong answer.


 
I used that. :<


----------



## Llamapotamus (Apr 11, 2011)

EdieFantabulous said:


> I used that. :<


 
Me too, but according to the other mechanical engineering student, it's the wrong method. Meh.


----------



## LLiz (Apr 11, 2011)

Alrighty... what's the answer to this perplexing mystery of an equation: 

1 + 1 = ?


----------



## Rakuen Growlithe (Apr 11, 2011)

Jashwa said:
			
		

> Wrong.
> 
> 
> See the past 5 pages for why.



Wrong. If you look at the last page both are acceptable because there isn't a definite convention on whether omitting the multiplication sign means that they the numbers are grouped. If you follow the convention where that groups them, like me and the majority of the people here, then the correct answer is 2. If you don't follow that then it's 288 but neither is more correct.


----------



## Jashwa (Apr 11, 2011)

Rakuen Growlithe said:


> Wrong. If you look at the last page both are acceptable because there isn't a definite convention on whether omitting the multiplication sign means that they the numbers are grouped. If you follow the convention where that groups them, like me and the majority of the people here, then the correct answer is 2. If you don't follow that then it's 288 but neither is more correct.


 That page is just saying that there are people like you that disagree about it. The standard and acceptable way is to NOT group them weird. Parenthesis, as you find most places and not bumfuck Africa, signify regular multiplication, not this special multiplication shit.


----------



## EdieFantabulous (Apr 11, 2011)

I'm going to say that using PEDMAS it's 288.
You know, the way most schools in Canada teach. ^^;


----------



## fleetfoot (Apr 11, 2011)

Many of you are wrong (I think

Right, so we all agree that you do the parentheses thing first, yah? 3+9=12.

The thing is you're supposed to go left to right. Therefore, we have 48/2*12. We all know PEMDAS, right? Multiplication comes first here. We multiply 2 by 12 first and get 24. We then divide 48 by 24 and get 2.

Did I do it right? I'm pretty sure I did.


----------



## Rakuen Growlithe (Apr 11, 2011)

Jashwa said:
			
		

> That page is just saying that there are people like you that  disagree about it. The standard and acceptable way is to NOT group them  weird. Parenthesis, as you find most places and not bumfuck Africa,  signify regular multiplication, not this special multiplication shit.



Actually the standard way according to Purplemath "is that "multiplication by juxtaposition"  (that is, multiplying        by just putting things next to each other,  rather than using the "Ã—" sign) indicates        that the juxtaposed  values must be multiplied together before processing other operations." So the standard way will give the answer of 2. The site is also run by an American mathematician and gets most of it's traffic from North America.


----------



## Scotty1700 (Apr 11, 2011)

Did anyone see what google had to say :v

Edit: Oh I see. It has it grouped (48Ã·2) * (9+3) = 288


----------



## EdieFantabulous (Apr 11, 2011)

fleetfoot said:


> Many of you are wrong (I think
> 
> Right, so we all agree that you do the parentheses thing first, yah? 3+9=12.
> 
> ...


 No, PEDMAS, the Division comes first because the question is read left to right.
DM and AS are just done as whichever comes first. :3


----------



## Xenke (Apr 11, 2011)

LLiz said:


> 1 + 1 = ?


 
It's 1 using my favorite kind of algebra.


----------



## Conker (Apr 11, 2011)

The internet: a place where you can argue about the correct answer to math problems which are almost always absolute and objective.

ILU INTERNET <3


----------



## Thatch (Apr 11, 2011)

Scotty1700 said:


> Now see I thought at first that multiplication and division along with addition and subtraction went together but I just went off the acronym lol


 
It's an example of something simple that is overcomplicated by putting it in a completely different and unsuitable presentation.

It's not hard to remember that it's ()/^/*Ã·/+-
Simple concept, I have no idea why would someone ever need an acronym. An acronym actually gives more to remember than learning what goes first.



LLiz said:


> 1 + 1 = ?


 
11


----------



## Scotty1700 (Apr 11, 2011)

Thatch said:


> It's an example of something simple that is overcomplicated by putting it in a completely different and unsuitable presentation. It's not hard to remember that it's ()/^/*Ã·/+-
> Simple concept, I have no idea why would someone ever need an acronym. An acronym actually gives more to remember than learning what goes first.


 
Maybe for you. I find it easier to remember "Please Excuse My Dear Aunt Sally" rather than a set of symbols.


----------



## Thatch (Apr 11, 2011)

Scotty1700 said:


> Maybe for you. I find it easier to remember "Please Excuse My Dear Aunt Sally" rather than a set of symbols.


 
And you got it wrong because of it.

Still easier?


----------



## Larry (Apr 13, 2011)

Looks like this is now a meme.
http://knowyourmeme.com/memes/48293


----------



## EdieFantabulous (Apr 13, 2011)

larry669 said:


> Looks like this is now a meme.
> http://knowyourmeme.com/memes/48293


 
Using PEMDAS or BEDMAS you should still get the same answer...
You do whatever comes first in the equation, not how the acronym is written out...
Jeez. >:C


----------



## Gavrill (Apr 13, 2011)

Why has no one said this yet?

42.


----------



## JoahnsDelakore (Apr 14, 2011)

5 days behind the pack, but the answer is 288.
Order of operations say that all problems must be worked from the inside of parenthesis out, then from left to right. The reason a computer would answer the equation as 288 is because it is following the rules as to how the equation is written. In order for it to be two, it would have to be written as : 48/(2(9+3)) . The reason for this is that it has to be shown that 2(9+3) is to be divided into 48. As it is written, it is to be read as forty-eight divided by two multiplied by the sum of nine and three. This is 288.


My shock at the sight of the poll was a bit strong. I've been known to over think some of my Calculus problems, but that was simple Algebra.


----------



## EdieFantabulous (Apr 14, 2011)

JoahnsDelakore said:


> 5 days behind the pack, but the answer is 288.
> Order of operations say that all problems must be worked from the inside of parenthesis out, then from left to right. The reason a computer would answer the equation as 288 is because it is following the rules as to how the equation is written. In order for it to be two, it would have to be written as : 48/(2(9+3)) . The reason for this is that it has to be shown that 2(9+3) is to be divided into 48. As it is written, it is to be read as forty-eight divided by two multiplied by the sum of nine and three. This is 288.
> 
> 
> My shock at the sight of the poll was a bit strong. I've been known to over think some of my Calculus problems, but that was simple Algebra.


I just said this. :3


----------



## Rakuen Growlithe (Apr 14, 2011)

Both 2 and 288 are acceptable answers! The question is badly written and contains an area of maths that is not subject to any standard custom. Here's what I wrote as a journal entry and that summarises the whole thread...

*****

There's been a whole bunch of forum posts over the question of does 48/2(9+3) = 2 or 288

Some people have argued that multiplication and division have the same order of precedence resulting in the equation being resolved as...
48/2(9+3)
=48/2(12)
=24(12)
=288

However others, me included, maintain that multiplication by juxtaposition has a higher order of precedence, giving the result as
48/2(9+3)
=48/2(12)
=48/24
=2

As far as I've been able to tell there is no set convention on whether multiplication by juxtaposition has a higher priority or not, making both answers equally valid. However it does appear that giving multiplication by juxtaposition a higher priority is the most accepted practice.

This is what is stated on the Purplemath site. "The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "Ã—" sign) indicates that the juxtaposed values must be multiplied together before processing other operations." -http://www.purplemath.com/modules/orderops2.htm

This was also stated on the American Mathematical Society guidelines in 2001 where they carried the instructions, "We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division." -http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html

This only applies to multiplication by juxtaposition however. Although at times multiplication has been considered to have a higher priority than division they are now considered equal and done in order from left to right. -http://jeff560.tripod.com/operation.html

The question has become famous now because of the different methods that various calculators and computers use when calculating their answers. This problem was recognised before it's current fame and in 2001 Mark Farris wrote a paper on 'Coping with Multiple Calculator Models in College Algebra'  In it he makes two points that are particularly important in the current situation.
* "avoid using this construction of a division followed by an implied multiplication."
*"emphasis appropriate use of parentheses."
-http://archives.math.utk.edu/ICTCM/VOL13/C026/paper.pdf

Use of brackets can actually remove any need for an order of operations, although then losing simplicity. So what is being promoted now is the standard order of operations but it's your own responsibility to use brackets to indicate the correct grouping to make an unambiguous equation. 48/2(9+3) is ambiguous because depending on your treatment of multiplication by juxtaposition it can be read as either (48/2)(9+3) or 48(2/(9+3)). Of course this is only a problem when the entire equation is written out linearly. The dropping of the AMA guideline on linearising equations probably stems from the ease with which equations can now be written in the correct format, eliminating such misunderstandings.

*****

Your normal order of operations generally does not apply to multiplication by juxtaposition. This isn't even a new problem. I found a mention of it in 2000 where a professor asks the same question because the working out that gives the answer 288 is contrary to most other mathematical rules. Read it here (http://mathforum.org/library/drmath/view/57021.html) and recognise that both answers are acceptable but 2 is more consistent with the rest of mathematics and the generally accepted resolution to the question.


----------



## ArielMT (Apr 14, 2011)

Wow, even simple RPN calculators are smarter than that "advanced" TI-86.  That's just sad.

48Ã·2(9+3) â†’ 48 2 9 3 + * /
= 2

My vote is 2, and this is my logic: One of the rules of division holds that A / B = C only if A = B * C.  In this problem, A is 48 and B is 2(9+3) or 18+6 or 24, so 48 = 24 * C, so C must be 2.

Multiplication is associative but division is not, which seems to need division to have a slightly lower precedence than multiplication.  Therefore, the implied multiplication also implies that the multiplication expression's product (two times a sum), not simply the lone integer, must be regarded as the divisor of the division expression.  The answer under this interpretation, where the expression can be identically read as [sup]48[/sup]/[sub]2(9+3)[/sub] is 2.

If the intended answer is 288, then the expression would be better written as (48Ã·2)(9+3) or the fraction [sup]48[/sup]/[sub]2[/sub] (9+3) to remove the ambiguity of precedence.

The difference in calculator answers comes from the expression being more ambiguous to machine readers than to human readers as well as how calculators resolve that ambiguity: equal precedence with strict right or left associativity, resulting in 2 or 288 respectively.


----------



## DelStimpson (Apr 14, 2011)

The answer it 2 
The order of operations is meant to go
Parenthesis, multiplication, division, addition, subtraction. 

Thus 
48Ã·2(9+3) = ?

Parenthesis: (9+3) = 12

Multiplication: 2x12 = 24

Division: 48Ã·24 = 2


----------



## Thatch (Apr 14, 2011)

DelStimpson said:


> The answer it 2
> The order of operations is meant to go
> Parenthesis, multiplication, division, addition, subtraction.


 
I
will
END
YOU!

READ THE GODDAMN THREAD!

Why is it still going on?



ArielMT said:


> Multiplication is associative but division is not, which seems to need division to have a slightly lower precedence than multiplication.


 
Division is the same as multiplication of something with a negative power. 1/2=1*(2^(-1)). Every division can be presented as a multiplication and every multiplication can be presented as a division.


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## LizardKing (Apr 14, 2011)

Thatch said:


> Why is it still going on?


 
People are stupid.


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## Thatch (Apr 14, 2011)

LizardKing said:


> People are stupid.


 
No shit >.<

What people are doing here is the equivalent of saying that 1-2+3 is -4, because addition is more important and you have to do it first.

Just in case someone does think that (I know some of you fuckers would), it isn't, and the answer is +4.


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