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

[Eclectic Dreck]

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.

Honestly, confusion regarding PEMDAS is quite common it would seem as most people believe that it asserts one MULTIPLIES everything and then DIVIDES everything regardless of their order (because it works that way with parentheses and exponents presumably). The only valid point of ambiguity lies in the fact that the operator between 2 and ( is only implied (by the normal mathematical convention) to be * rather than outright asserted. Even if this were true it is likely that people would still complain about ambiguity where there is none.

If I have a statement like this:

a / b (x + y + z) the order of operations is simply (a / b) * (x + y + z). The ONLY way to link all those other operands and operators to that divisor operator is by the use of parenthesis like this: a/(b(x + y + z)). Given the original equation, if you wanted the result to be 2 one would necessarily have to write it as 48/(2(9+3)).

At no point is this equation ambiguous. It is clearly stated using common mathematical notation. People seem to assume that if they cannot interpret it correctly it must be ambiguous when the actual problem is they have a less than adequate understanding of precedence and notation.

 

[ENKC]

Based on my own education, I would lean towards 288 but it's fair to say that both interpretations have merit.

 

[BabySinclair]

Now if dealing with exponent X and written 48/2X where X = 9+3; then yes the answer is 2 since when an exponent is attached directly to a mathematical value (number or exponent) then it is to be directly multiplied with that value. 48/2X (X=4) = 6; if X=12 f(x)=2. However, since the parenthetical is not a exponent then the actual formula should be written/viewed as 48/2*(9+3) and then resolving the function left to right gives you 24*12=288. To get 2 the formula is 48/2/(9+3) or 48 * 0.5 * (1/(9+3))

 

[Stammer]

Well, whether you use the BEDMAS/PEDMAS formula (which is universal) OR you do it in order, the answer should be 288.

I can't for the life of me see how you would ever Multiply -before- you Divide unless the multiplication was in parentheses itself.

 

[Eclectic Dreck]

but if the eqution is supposed to be writen the way I think it is you would have (48)/(2(12)) so you would either have to dive 48 by 2 and then 12 or multiply the two together and divide that way.

The fundamental problem here is that the only way one could possibly interpret the statement the way you describe is to follow something other than the common rules of precedence and notation. Once you discard those things, math quickly ceases to be generally a useful means for conveying information (it is imply a language after all). Suffice it to say that people who somehow insist my interpretation is incorrect are (in spite of training that implies otherwise) laboring under some notion regarding notation and precedence that both I and the internet at large are ignorant of.

 

[Wintermoot]

48/2(9+3)?
24X12=288

 

[Signa]

I'm completely certain that it's 2.

The reason being that though no one ever really said to do so, I learned to treat division and fractions the same. You literally can not divide

48
----
2x12

that's why you simplify it to forty-eight twenty-fourths before finishing.

All of that is treating the original problem as

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

As some one pointed out though, 288 is a perfectly reasonable answer for how it is written.

 

[rees263]

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 '*'.

It surprises me how differently we have all been taught maths. If I saw x/yz I would assume that it was a fraction with x as the numerator and (yz) as the denominator. Nothing about it implies to me that (xz)/y would be the answer.

It may have something to do with the lack of a proper division symbol on a keyboard and the reliance on the "/" symbol for division. This is why I would always use brackets to remove any doubt, because with a split of opinion like this there is obviously doubt where there should be none.

EDITED for some late night maths fail.

 

[timeadept]

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.

Each time i try to say that it is written in a confusing way or ambiguous my brain slaps me in the face and tells me that there is no arguing with mathematics. If you follow the rules to the letter (and my brain is slapping me again to ask why you would consider doing otherwise) then you will always end up at the same answer. It may be sloppy but that is the writers responsibility, your responsibility is to solve the problem you have in front of you and there really should be no arguing.

 

[tirone231]

its 288
just use BEDMAS(brackets,exponents,division,multiplication,addition,subtraction) left to right
you divide and multiply at the same time so you go left to right

You are totally correct. It's 288. 'Divide' and 'Multiply' are treated by the same weight in the BEDMAS formula (as are 'addition' and 'subtraction'). When you have operators that have equal weight, always start from the left.

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

And if you don't trust me (I'm in university with a math minor), trust Wolfram Alpha =D 48/2(9+3) [http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29]

I, also being in college, (though not with a Math minor or major) am curious as to when the PEMDAS was replaced with BEDMAS. According to the first, the answer is 2, but according to the second, it's 288...why am I sooooo confused?

 

[Mayki5]

Now: Question for you. When entering the problem into my calculator, with the multiplication added in, so 48/2*(9+3), it returns the answer 288.

However: When entering the equation 48/2(9+3) into the SAME CALCULATOR, it returns the answer 2.
By removing the multiplication sign from the equation, the calculater worked it out totally differently.

To tease the brains of those so invested already and perhaps for some amusement, why?

 

[Imat]

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.

Honestly, confusion regarding PEMDAS is quite common it would seem as most people believe that it asserts one MULTIPLIES everything and then DIVIDES everything regardless of their order (because it works that way with parentheses and exponents presumably). The only valid point of ambiguity lies in the fact that the operator between 2 and ( is only implied (by the normal mathematical convention) to be * rather than outright asserted. Even if this were true it is likely that people would still complain about ambiguity where there is none.

If I have a statement like this:

a / b (x + y + z) the order of operations is simply (a / b) * (x + y + z). The ONLY way to link all those other operands and operators to that divisor operator is by the use of parenthesis like this: a/(b(x + y + z)). Given the original equation, if you wanted the result to be 2 one would necessarily have to write it as 48/(2(9+3)).

At no point is this equation ambiguous. It is clearly stated using common mathematical notation. People seem to assume that if they cannot interpret it correctly it must be ambiguous when the actual problem is they have a less than adequate understanding of precedence and notation.

I was just saying that the way it is written will cause just about everybody to, at the very least, go back over the equation to see what was meant. If you just instantly understood the equation from a single scan, left-to-right, then congrats, you have beaten computers at a numbers game. Not that the average man would puzzle over it for half an hour before googling the answer in defeat.

 

[Dragonshredder]

... 42

 

[Eclectic Dreck]

I was just saying that the way it is written will cause just about everybody to, at the very least, go back over the equation to see what was meant. If you just instantly understood the equation from a single scan, left-to-right, then congrats, you have beaten computers at a numbers game. Not that the average man would puzzle over it for half an hour before googling the answer in defeat.

My argument is not that there is no confusion; instead, I am simply guessing as to where the confusion is arising from. The statement is not in any way ambiguous and more to the point is short enough to dramatically reduce the probability of simple mistakes in arithmetic. My only guess is that people are mistaking the rules of PEMDAS. If one assumes that each element is done in exactly that order (i.e. that multiplication and division do not have equal precedence) THEN the answer would be 2. Given that misconceptions of this sort of fairly common, I have to assume this is where the problem lies.

 

[Syntax Error]

Given more thought, I think the answer depends on how you interpret the /. If you see it as the bar in a fraction, the answer is 2. If you see it as a division sign, the answer is 288.

 

[Conza]

I think this can be put to bed, its simple, read left to right and whether or not M or D comes first, once reading from left to right, you get your answer.

in this instance [48/2(9+3)], 288.

If it were written as [48/(18+6)], then, you would have your result of 2. P/B then O/E then there's only a D left.

 

[SageSays]

Now: Question for you. When entering the problem into my calculator, with the multiplication added in, so 48/2*(9+3), it returns the answer 288.

However: When entering the equation 48/2(9+3) into the SAME CALCULATOR, it returns the answer 2.
By removing the multiplication sign from the equation, the calculator worked it out totally differently.

To tease the brains of those so invested already and perhaps for some amusement, why?

In the same way that "we" imply that fractional mathematics assumes that everything after the division symbol is a denominator, the multiplication operator allows the programmed mathematics to imply that the equation now reads 48 divided by 2 and multiplied by 9 plus 3.
Your calculator is programmed to assume human input, so it first reads the equation in fractional maths as 48 divided by; the sum of 9 and 3 which is multiplied by 2.

 

[spacecowboy86]

The fundamental problem here is that the only way one could possibly interpret the statement the way you describe is to follow something other than the common rules of precedence and notation. Once you discard those things, math quickly ceases to be generally a useful means for conveying information (it is imply a language after all). Suffice it to say that people who somehow insist my interpretation is incorrect are (in spite of training that implies otherwise) laboring under some notion regarding notation and precedence that both I and the internet at large are ignorant of.

I never "insisted that your interpretation was incorrect" and never meant to offend your knowledge of mathmatics. I simply was phrasing that the equation's current form can lead some, such as myself, to misinterprate the interaction and relationship between the numbers. can you at least consider that the slash after the 48 could possibly mean that this entire equation is really just one complex fraction, and that it was typed in a confusing manner, and that it could possibly be represented accurately in the follwing manner?

_48__
2(3+9)

_48_
2(12)

48
24

2

 

[timeadept]

its 288
just use BEDMAS(brackets,exponents,division,multiplication,addition,subtraction) left to right
you divide and multiply at the same time so you go left to right

You are totally correct. It's 288. 'Divide' and 'Multiply' are treated by the same weight in the BEDMAS formula (as are 'addition' and 'subtraction'). When you have operators that have equal weight, always start from the left.

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

And if you don't trust me (I'm in university with a math minor), trust Wolfram Alpha =D 48/2(9+3) [http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29]

I, also being in college, (though not with a Math minor or major) am curious as to when the PEMDAS was replaced with BEDMAS. According to the first, the answer is 2, but according to the second, it's 288...why am I sooooo confused?

According to both the answer is the same, 288. You've simply missed the detail that it is not simply PEMDAS, that is just an acronym for Please Excuse My Dear Aunt Sally ( a useful tool for remembering the steps in order). In reality you cannot literally write it in the correct order because multiplication and division take place at the same time, as do addition and subtraction. (Well that's not true, we could merge the M and D and A and S into single letters, then it would literally reflect what is going on.) The way you determine which happens first, (M or D / A or S) is you go back to the start and read the problem from left to right and do the operations in the order that they appear from left to right. In this case, division before multiplication.

sorry if i seemed to be belittling you, i only wanted to be as clear as possible as misunderstanding seems to be the basis for this thread.

 

[Imat]

I was just saying that the way it is written will cause just about everybody to, at the very least, go back over the equation to see what was meant. If you just instantly understood the equation from a single scan, left-to-right, then congrats, you have beaten computers at a numbers game. Not that the average man would puzzle over it for half an hour before googling the answer in defeat.

My argument is not that there is no confusion; instead, I am simply guessing as to where the confusion is arising from. The statement is not in any way ambiguous and more to the point is short enough to dramatically reduce the probability of simple mistakes in arithmetic. My only guess is that people are mistaking the rules of PEMDAS. If one assumes that each element is done in exactly that order (i.e. that multiplication and division do not have equal precedence) THEN the answer would be 2. Given that misconceptions of this sort of fairly common, I have to assume this is where the problem lies.

Oh...I thought you were saying that there is no possible way for it to be confusing at all. That would be my bad.

I think the problem is generated, not from PEMDAS or any other order of operations acronym, but from a fundamental brain problem which is telling the mathematical center that everything after the '/' is in the denominator. I think this mostly comes about as a result of the poor communication skills of simple ascii characters. On paper this could be written much more clearly, leading to complete understanding by any human who understands multiplication and division. On a computer, however, things may not seem so black and white to some folks.

That is just my understanding of the problem at hand, however, based on responses to this thread. I may be completely wrong on that one, but that seems to be a general source of confusion.