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

[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"

 

[Vrach]

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.

Right with ya on the previous part, but here's where the problem lies. "Writing mathematically". Nothing has stated that this equation has been written mathematically, rather than say, in a way a computer would understand it

 

[Foxbat Flyer]

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). Which gives the answer as 2. To put it in a better way, imagine that in each of these next lines, there's a fraction line seperating the numbers on the top and bottom. So 48/2(12) becomes:

48
2(12)

This then gives:

48
24

Giving an answer of 2. Otherwise, write that second fraction as:

48
2(12)

Becomes:

24
(12)

Which again gives the answer as 2. I hope that makes a bit more sense now

Not really, That makes me more confused...

I was taught that if a number next to a bracket, so with this example we have 24(12), the 24 gets multiplied with whats in the bracket so in this case we get 24*12, but i see where your coming from

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

Its all confusing, it all depends on if you multiply the 2 and the 12 before or after dividing the 48...

Im more confused than i was when i was in school now...

 

[spacecowboy86]

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)).

that's the problem is that some of us are unsure wether it is properly written as (48/2)(9+3) or if it should be written as 48/(2(9+3)) meaning that the the 2 and 9+3 are denominators under the numerator 48. at least, that's why I think it is 2, because I am visualizing this as a fraction with all but 48 in the denominator, meaning that whatever the result of the equation 2*(3+9) is, is what you divide 48 by.

 

[Weedmilk]

This really isn't that ambiguous. Studying for a masters degree in Maths here and my mind is being blown by the people doing degree-level mathematics who insist the answer is 2.

It's definitely 288.

 

[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

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.

Fair point, and to be honest I think that's why so many people are saying that they get the answer 288 when typing it into Google Calculator and other online places. Thing is, they're apparently typing it as is, and so the programs used for those tools are interpreting it in the programming sense. Whereas if you gave the question to any mathematician, they would immediately come up with the answer as being 2. I suppose I should have noticed that myself really, I did a programming module in second year and still have an interest in it now, but Dr Houston's constant plugs in our lectures keep coming back to mind...

 

[Jumplion]

Oh god, can't you all see what he's doing? This is the new .99... = 1 thread, and you're all getting sucked into it.

The truth is that the equation is written ambiguously, so that two answers are both reasonably correct, and everyone argues about it for pages and pages and gets nowhere. Just stop this thing before it goes on for a hundred pages.

Too late.

It has begun!

Besides, it's so clearly 48,293. Duh.

 

[liquidangry]

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.

Damn your reason! >_<

 

[TetrisLing]

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.

Actually, as I mentioned above, the equation is written ambiguously. In real mathematics, you would never write an equation like that. In the end, the answer is not 2 or 288. The answer is write the god-damned thing properly.

 

[Trivun]

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.

Right with ya on the previous part, but here's where the problem lies. "Writing mathematically". Nothing has stated that this equation has been written mathematically, rather than say, in a way a computer would understand it

I think we can safely assume it's a maths problem, as it deals with numbers, mathematical relations and operations, and a mathematical solution. If it was stated as being a programming problem then I'd understand that, but as that's not being said, it is automatically assumed to be a maths problem, and thus remains so unless the OP says otherwise.