Poll: What is the answer to 48/2(9+3)?

[Vrach]

This gives us 48/2(12).

2(12) means exactly the same as '2 x 12', which gives 24. We do this step next because of the 'multiplication' part, which comes next in the BODMAS order.

Quoting where you've gone wrong. You're saying BODMAS, to emphasise, boDMas and saying multiplication comes next before division.

Can check via Google calculator as well if you want. It's 288.

 

[DefunctTheory]

288.
I use BOMDAS
(brackets orders multiplication division addition subtraction)
and it has the word "BOMB" in it!

Missing a 'B' there.

Nah he just had the M and the D the wrong way round.

I was just referring to the fact that there's no Bomb in there, one way or another.

But, yah. How did I miss that too?

 

[jp201]

According to BODMAS (Brackets, Division, Multiplication, Addition, Subtraction) the answer is 288. I don't see how you can get 2...

48/2 x (9+3)| 48/2 x (12) | 24 x (12) | 288

So incorrectly, some might do... umm BOMDAS?

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

The first example is correct (now to read why 100/240 did theirs wrong).

When people see for example PEMDAS which is used in America quite often people eventually believe that multiplication happens before the division which is not that case. It is whichever comes up first from left to right. Doing it wrong would result in 2 since they would multiplied first.

Your correct and that is what I was thinking also as to why this question with an absolute answer is not highly favored on 288.

That or this is a huge troll thread.

 

[XzarTheMad]

If what he just said apparently went right over your head then please just give up at this point.

for god sakes your quote after reading what he was trying to convey to you "The lack of a clear multiplication symbol implies that the 2 and the paranthesis are a single entity." he just proved with logic that your statement there is false. Yes it is completely relevant to this problem by the way.

I already gave up. Not that it changes my mind. And I do realize he's correct - I never faulted his logic. I tried to explain the way I see the problem, which I still stand by as the only reasonable and logical solution, to people who were not professors in math. Was what I was saying not 100% accurate? No. I freely admit that. Can't fault me for trying, though. Or, I guess you can. If it helps you sleep at night, I suppose.

Congratulations. You "win" by default. I'll go sleep. Me and my "superior Denmark math".

 

[Trivun]

Seems everyone has one of theese, I learnt this one in year 6, BOMDAS Brackets or multiplication (If there is brackets) devision then addition and subtraction. so by my method, it becomes
48/2(9+3)
48/2(12)
24(12)
24*12
288

Sorry, but that's wrong. As I pointed out to someone else in my previous post. Your mistake is that you've forgotten that the (12) is still on the bottom of the fraction, and thus your third line should still read 24/12, not 24(12).

What makes you think this is a single fraction? There is nothing in the problem to indicate that. If we translate the problem directly into English, we get "Multiply 48 by the multiplicative inverse of 2 and then multiply by the quantity (9+3)." The division sign only applies to the next term (i.e. 2) and not to everything to the right.

I mentioned in another post I study university-level maths. The fraction continues, because the 2(9+3) is implied to be 2*(9+3) by the conventions of modern mathematical writing. The way that mathematicians nowadays write fractions, formulae and equations of this sort, including the way I was taught, shows that the fraction is correct in the way I interpreted it, as having 48 as the numerator and 2*(3+9) as the denominator.

And for the record, I learnt all this from a guy named Kevin Houston, at the University of Leeds (UK). He just so happens to have written a book called 'How To Write Like A Mathematician', which he seems to take every opportunity to plug during lectures. Here's the link to the Amazon page, as my source...

http://www.amazon.co.uk/How-Think-Like-Mathematician-Undergraduate/dp/052171978X

 

[MagusVulpes]

Seems everyone has one of theese, I learnt this one in year 6, BOMDAS Brackets or multiplication (If there is brackets) devision then addition and subtraction. so by my method, it becomes
48/2(9+3)
48/2(12)
24(12)
24*12
288

Sorry, but that's wrong. As I pointed out to someone else in my previous post. Your mistake is that you've forgotten that the (12) is still on the bottom of the fraction, and thus your third line should still read 24/12, not 24(12).

What makes you think this is a single fraction? There is nothing in the problem to indicate that. If we translate the problem directly into English, we get "Multiply 48 by the multiplicative inverse of 2 and then multiply by the quantity (9+3)." The division sign only applies to the next term (i.e. 2) and not to everything to the right.

Unless it's interpreted as "Multiply 48 by the multiplicative inverse of 2 times the quantity of 9 plus 3." Which would be where the debate lies. The a(x+y) has to be dealt with as though it's a single entity becoming (ax+ay) through the distributive property. If it read 48/2*(9+3) then we could say that the 48/2 and (9+3) are separate entities, but without the '*' it's implied that 2(9+3) is a single entity and exists 'under' the division symbol (if written as a fraction).

 

[TetrisLing]

The equation as written is ambiguous at best and deliberately misleading at worst. The problem here is that internet does not allow proper mathematical typesetting. So I fired up Mathematica.

http://twitpic.com/4i5yam

Glad this is all settled now.

 

[Pyro Paul]

You are all Wrong... the Answer is 'Cake'

 

[thelonewolf266]

288.
I use BOMDAS
(brackets orders multiplication division addition subtraction)
and it has the word "BOMB" in it!

Missing a 'B' there.

Nah he just had the M and the D the wrong way round.

I was just referring to the fact that there's no Bomb in there, one way or another.

But, yah. How did I miss that too?

There are loads of different versions for different countries or even just different schools so its easy to get confused I have always been taught and used BODMAS as in brackets,orders, division and multiplication,Addition and subtraction.

Orders(Powers and square roots just in case anyone didn't know and possibly a few other things I'm not sure)

 

[spacecowboy86]

I used distribution and got 2...
if it was the fraction 48/2 times the function (9+3), wouldn't it be written (48/2)(9+3)?

 

[Trivun]

This gives us 48/2(12).

2(12) means exactly the same as '2 x 12', which gives 24. We do this step next because of the 'multiplication' part, which comes next in the BODMAS order.

Quoting where you've gone wrong. You're saying BODMAS, to emphasise, boDMas and saying multiplication comes next before division.

Can check via Google calculator as well if you want. It's 288.

Ah, but I haven't gone wrong there. Division and multiplication are exactly the same. That's because division is equivalent to multiplying by a fraction (or decimal). They are equivalent relations, according to the theory of groups and symmetry, which I covered in my second year of university.

Which means that division and multiplication can be swapped around in that order and it still works completely accurately. By the same method, addition and subtraction can also be swapped around, because subtraction is simply the same as adding negative numbers. It's another equivalence relation.

And for the record, Google Calculator is wrong here. The reason being because it hasn't been programmed to recognise the multiplication that should be included between the '2' and the '(9+3)' bits. That multiplication step is directly implied by the standards of writing mathematically, as I stated in my previous post (with a subject-approved source, no less). The programming simply doesn't take that into account, but if you put brackets around them then it works fine.

 

[MagusVulpes]

You are all Wrong... the Answer is 'Cake'

I'm sorry, but that answer is a blatant lie.

 

[rees263]

EDIT:

In reality, if someone presented me with that problem I would tell them to stop being a dick and write it legibly. Even after completing a degree in mathematics I've never been expected to solve such a problem (ie a broken one).

With most of a degree in engineering, I agree. If I had to answer it, there'd be a note in the corner from me saying "Ambiguous:- I interpreted equation as ()".

I'm glad I'm not the only one.

Funnily enough, and having thought about the problem some more, I think I end up finalising my answer as 2.

As mentioned by others in the thread, if I saw 2(9+3) in any context I would interpret that as ((2*9)+(2*3)).

I'm sure there is a difference in this logic between mathematicians and engineers (I lived with one). As you said, you used software to test it, where I wouldn't think to do that.

I also agree that a computer program would give the result 288. I would say that is down to a difference between "computer syntax" and what I've been taught. There must be an infinite number of perfectly simple equations that if input incorrectly into a program would come out incorrect, if at all, even though they would make sense on paper.

 

[Taerdin]

It is frightening to me that 42% of people got this question wrong. I mean... you're on the internet, you have access to websites that do math. This shouldn't be that difficult.

The answers 288 btw.

 

[Eclectic Dreck]

I don't know why you want us to do your homework for you, but I got 288... after you do the parentheses, you're supposed to do them from left to right. I think it's a poorly written problem, though.

lol it's not a homework problem man, I'm not in middle school. This question is blowing up other forums and reddit.

48/2(12) = 2 using PEMDAS

Common misconception with PEMDAS is on display here. The reality is the order is (P)(E)(MD)(AS). In other words, parenthesis come first, then exponents. Multiplication and division are done from left to right; Multiplication does NOT always come first as it has equal precedence to division. Addition and subtraction are much the same.

The correct answer is 288 because of this as it could be (correctly) rewritten as (48/2) * (9+3). In a radically different style of notation that would be (* (/ 48 2) (+ 9 3)).

-EDIT- I will also not concede that the problem was written incorrectly. The ambiguity people seem to complain about is unfortunately necessary to demonstrate the problem outlined above with a misinterpretation of precedence rules. It is widely accepted that a statement k(c) is equivalent to saying k*(c). Even the argument that it might mean (2*9 + 3*9) is invalid given that, if one correctly follows rules of precedence, we get 24*9 + 24*3 (48/2), which simplifies to 216 + 72, which is 288. If you want an utterly unambiguous rewrite it would be ((48/2)*9)+((48/2)*3).

Modern mathematical conventions generally assert that 48/2(9+3) would not imply that the denominator of the fraction is 24. For that to be true the statement would be written as 48/(2(9+3). In any other format save standard text there is room for ambiguous interpretation here but the rules with respect to this format are actually quite concise. That said, there is a reason WHY I posted that silly version of the equation above: because that format was designed in the hopes of removing possible uncertainty (which it generally fails at because I am forced to rearrange it in my head before I do a calculation. It does however make solving equations of various sorts via a simple program incredibly easy).

 

[Spadge]

Seems everyone has one of theese, I learnt this one in year 6, BOMDAS Brackets or multiplication (If there is brackets) devision then addition and subtraction. so by my method, it becomes
48/2(9+3)
48/2(12)
24(12)
24*12
288

Sorry, but that's wrong. As I pointed out to someone else in my previous post. Your mistake is that you've forgotten that the (12) is still on the bottom of the fraction, and thus your third line should still read 24/12, not 24(12).

What makes you think this is a single fraction? There is nothing in the problem to indicate that. If we translate the problem directly into English, we get "Multiply 48 by the multiplicative inverse of 2 and then multiply by the quantity (9+3)." The division sign only applies to the next term (i.e. 2) and not to everything to the right.

I mentioned in another post I study university-level maths. The fraction continues, because the 2(9+3) is implied to be 2*(9+3) by the conventions of modern mathematical writing. The way that mathematicians nowadays write fractions, formulae and equations of this sort, including the way I was taught, shows that the fraction is correct in the way I interpreted it, as having 48 as the numerator and 2*(3+9) as the denominator.

And for the record, I learnt all this from a guy named Kevin Houston, at the University of Leeds (UK). He just so happens to have written a book called 'How To Write Like A Mathematician', which he seems to take every opportunity to plug during lectures. Here's the link to the Amazon page, as my source...

http://www.amazon.co.uk/How-Think-Like-Mathematician-Undergraduate/dp/052171978X

I will defer to you here, and suggest the context becomes important as interpretations change between fields. In engineering, we're influenced by programming in this kind of notation, and most programming languages (off the top of my head) would lead to a answer of 288, since they evaluate left-to-right.

 

[liquidangry]

Holy sweet jesus people are stupid.... really!? This is split 60% and 40%?

It's 288 hands down, discussion over. I didn't need one but that huge percentage made me double check my graphing calculator just to make sure. Sure enough, written in the exact same format, this equation equals 288.

PEMDAS
Multiplication and division are interchangeable. When they're next to each other like that you go left to right ALWAYS! No wonder people think math is hard. This is 3rd/4th grade math people. Knowing the basics helps out in your algebra/trig/precalc/calc classes. If you can't get this equation right, then you can't pass any of these classes.

 

[tholomew92]

I get 2.

48 48
-- = -- = 2
2(9+3) 24

However, if it is written

48
-- * (9+3)
2

Then yeah, the answer is 288. It is a just a matter of how you interpret where the 12 is.

 

[flacmcfae]

It depends upon your assumptions as to what [/] is. If you assume it is a fractional, then 2(9+3) is done before dividing into 48 giving the answer of 2. If you assume that it is representative of division, then you get 288. Like many people have said, it is a poorly written equation.

 

[Spadge]

EDIT:

In reality, if someone presented me with that problem I would tell them to stop being a dick and write it legibly. Even after completing a degree in mathematics I've never been expected to solve such a problem (ie a broken one).

With most of a degree in engineering, I agree. If I had to answer it, there'd be a note in the corner from me saying "Ambiguous:- I interpreted equation as ()".

I'm glad I'm not the only one.

Funnily enough, and having thought about the problem some more, I think I end up finalising my answer as 2.

As mentioned by others in the thread, if I saw 2(9+3) in any context I would interpret that as ((2*9)+(2*3)).

I'm sure there is a difference in this logic between mathematicians and engineers (I lived with one). As you said, you used software to test it, where I wouldn't think to do that.

I also agree that a computer program would give the result 288. I would say that is down to a difference between "computer syntax" and what I've been taught. There must be an infinite number of perfectly simple equations that if input incorrectly into a program would come out incorrect, if at all, even though they would make sense on paper.

lol, that's the thing with engineers. We learn all this maths, and then our first reaction if we're at a computer is "Get the computer to do it"