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

[The Apothecarry]

Calculator says 288, pen & paper says 2...
http://images1.memegenerator.net/ImageMacro/4746444/THERES-MAGIC-EVERYWHERE-UP-IN-THIS-*****.jpg?imageSize=Medium&generatorName=Magic-Clown

 

[SeaCalMaster]

For the record: When you allow division as an operation, you have to go in order from left to right because division doesn't associate.

 

[Levitas1234]

ahg, i can't go through another one of these, it makes me lose faith in humanity.

 

[Okysho]

Generally speaking, when you write an equation like that, what is written in the parentheses is being multiplied by the whole fraction not just the denominator. Therefore the answer would be 288. Also, Wolfram Alpha agrees [http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29].

Hail wolfram alpha!!

wow, we do things a bit different in Canada.


BEDMAS

Brackets
Exponents
div
mul
add
sub

not that big a difference, just never heard pedmas before.

oh right...

288 left to right after brackets

 

[mrdude2010]

What do you guys get for an answer, 2 or 288?

P
E
M/D
A/S

parentheses, exponents, multiplication/division, addition/subtraction

you get 288 because you do (9+3) first, then since everything else is either multiplication or division you do it from left to right, so you get 48/2 * 12

 

[Lord Beautiful]

The number of people who voted "288" is baffling. What is wrong with you people?

 

[Taerdin]

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

I can agree that it's not written in an obvious manner, but I would never even think to evaluate that statement in such a way as to get 2. I don't think it could go either way, it goes one way and that way is 288; and multiple math applications/devices say the same thing.

The only error here is with the people's work that brings them to the answer 2.

 

[timeadept]

Strictly following the rules will lead you to an answer of 288.

The rules being: Parenthesis, Exponents, Multiplication, Division, Addiction, Subtraction. Solve your problem left to right.

Although, technically the steps of multiplication and division, addiction and subtraction, are interchangeable. Multiplication does not 'need' to be done prior to division in a problem(assuming there are no unique situations). Therefore it is possible to end up with the answer being 2 as well.

As such, I'd say it's a bit of a toss up between the two. Though as I stated in the first place: I think that the answer of 288 is more correct, than the answer of 2.

except that you're forgetting that once you get to the multiply and/or divide step you tackle the problem from left to right, in this case the division is done first.

I'm a little embarrassed to admit that i also put this into my TI-83, exactly as shown. The calculator will always pick to do the steps in the same order and it will always answer 288 in this case. there is no "toss up" there is nothing ambiguous about mathematics if you know the rules.

 

[GraveeKing]

hmm, terribly written but it's definitely 288

 

[spacecowboy86]

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.

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.

Also, if you're anything like the people in my class, I want you to know I'm having a friendly debate and defending my opinion, I think that your reasoning is also very likely and mean no offense by arguing.

 

[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.