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

[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.

 

[Senaro]

Yes you do brackets first, but after you do the addition inside the brackets you're supposed to go to the division on the far left.

 

[SeaCalMaster]

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.

So do I. In fact, in May I will be graduating from the best undergraduate-level mathematics program in the United States. Stop saying this like it's important or impressive.

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.

You still haven't answered my question. Why do you take this to be a single fraction? What I see (and so does almost every other serious mathematician) is not a fraction but a series of operators. The '/' operator applies only to the next element in the expression; by convention, that element is 2 and not 2(9+3). The latter case would require a set of parentheses to indicate that the entire thing was to be taken as a single element.

If you've ever written a parser, you'll understand what I mean when I say that '/' and '*' bind at the same level, again by convention. You seem to have given '*' priority, violating both the convention and the acronym that you held up earlier, which seems to imply that '/' binds more closely than '*'.

 

[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

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.

As a programmer, I take issue with your assumption

 

[jp201]

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).

This is the most properly explained counter to those who believe the answer is 2 and not 288.

well done.

as posted just before it should be written as http://twitpic.com/4i5yam the first problem is what he is asking and the second one is what some others may be seeing.

 

[Eclectic Dreck]

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.

I understand the confusion, certainly, but it simply has no basis for existing even if you explicitly follow PEMDAS correctly. Here is the step by step process as I go through the list:

P: 48/2(12)
E: 48/2(12)
MD: 24(12) = 288
AS: 288

You sort out the part in parenthesis first (yielding a sum of 12). There is no exponent so you move on to multiplication and division. These two operands have the same precedence and thus are calculated from left to right. No addition and subtraction are necessary.

 

[Taerdin]

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.

Why do you assume that the programming doesn't recognise that there's a multiplication there? Have you looked at the source code? Did you program the calculator? Did you even do a reasonable amount of testing on it?

 

[Avatar Roku]

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.

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.

No, nobody here is stupid, the question is just worded horrendously. Basically, people are unsure which of the following it is:
48 48
------ -------- *(9+3)
2(9+3) 2

Neither side is wrong, as the question could honestly go either way as worded. It's awful.

EDIT: Format fail. I'm not doing it again, just look at this [http://twitpic.com/4i5yam] link someone else in the thread put up.

 

[Imat]

If the (9+3) was intended to also be in the denominator, it should have been written as:

48/(2(9+3))

As it is written, 48/2(9+3) , the answer should be 288 as the bracketed expression is a multiplier.

The disagreements stemming from this wouldn't be because the math is challenging, but because the way it is written is not ideal.

That's just silly.

If you wanted it to be 48/2 times (9+3), then why would you not put a clear symbol between the 2 and the parenthesis? You only omit that if you count that as a single entity. It's much more reasonable to assume that since the multiplication symbol is omitted between the two, they count as a single entity, as the denominator in the division. Any reasonable person I know would assume so, and would write it as "(48/2)*(9+3)" if they wanted to separate them. That's pretty much how you do these things.

I apologize for my double post, should no one have posted between then and now.

Computers will always generate 288 using the equation given (Unless your computer has been hacked to do otherwise, or it can't add in an implied * for x meaning x*y). The parenthetical statement is evaluated first, then it scans left to right for multiplication and division operations, evaluating them in left/right order. Then it scans left to right for addition/subtraction and evaluates them in said order. This order of operations is set in stone for the vast majority of personal computers, no doubt including your own. Therefore the equation will be evaluated as (9+3) = 12, 48/2 = 24, 24*12 = 288.

The equation is written in such a way as to elicit some initial confusion from us mere mortals, but the confusion is obliterated by computers, which follow simple and accepted mathematical rules.

 

[suicide samurai]

I'm a published writer who hates math, yet scores (several times) higher on math vs. English on tests.

I hate math due to its language and rules. This is a prime example.

 

[floobie]

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.

Bingo. I can absolutely see how people could arrive at either answer. I'm pretty sure most of us know the rules for dealing with (what should be) a simple problem like this.

So, as someone about 3 weeks away from getting my BSc in geology with a minor in geophysics, I can say that none of my classmates would ever write a problem that sloppily and ambiguously when an extra set of brackets would completely clarify everything.