A recent strange but fascinating poll put up on RAWK regarding the answer to the above equation, had people from both sides of the ... divide... coming up with different answers and justifying it with many methods including mathematical calculators, Google and Wolfram Alpha. Teachers, engineers, average Joe, shopkeepers, professional accountants etc - came up with different answers over both. a) 2 b) 288
A true mathematician would say it's too ambiguous to answer, but in mind mind it's 2 - the 2(9+3) I would take as a single term. Those obeying the BODMAS rules would come up with 288, as they would end up with (48/2)(9+3) by bracketing the division operator first.
I solve the parenthesis first, because that's what I remember from school... And then I end up with 48/2*12. Which one do I do first, the division or the multiplication? Do I just go from left to right? I suck at math.
Mark is right there. Roughly 2/3 of the people out of 300+ chose '2'. Strange enough that mathematics being what it is, there are no 100% consensus on such a simple equation.
BODMAS... This helped me remember something. I went to high school in the US and there we had PEMDAS. So, multiplication before division, that's how I learned it. Therefore, the answer is 2
I always thought that it is common sense to write the division sign last to avoid confusion. So I would have assume that 2(9+3) is a term by itself, thus, the answer is 2. Having said that, my personal opinion is, the guy who wrote such an ambiguous equation should be shot in the head. That won't be any problem if he wrote the equation with care 48÷[2(9+3)] or simply 48(9+3)/2(division comes last) or even 48÷2*(9+3) (this is obvious that you divide 48 by 2 before multiplying the answer) I hope that guys who set this question isn't someone who likes to play with the ambiguity of mathematical expressions.
I'm not so fond of your last example. It's the exact same thing as 48÷2(9+3), only with an added multiplication sign. I would still do the parenthesis first and then not know what to do next, unless I follow PEMDAS or some other such rule. The same holds true for your second example too, actually. The only sound one (if the answer is supposed to be 2) is 48÷[2(9+3)]. If it's supposed to be 288, then it should be (48÷2)(9+3) or something like that.
If you look at the second example in fraction form, 48(9+3) can be interpreted as the numerator and 2 as the denominator. For the third example, you might be right, but for me 2(9+3) and 2*(9+3) are 2 totally different things. 2(9+3) can be interpreted as a whole single term(again this is where the ambiguity comes in) while not so for 2*(9+3) as the latter was separated by an operator. I was taught that multiplication and division share equal precedence, so whatever that comes first(or the left most) will take precedence.
Yes, I was thinking fractions would make everything clearer. The bottom line is, equations shouldn't allow two different answers. There should be one set of rules for the order of operations in the whole world, but apparently that's not the case. If you use BODMAS you do division first, if you use PEMDAS you do multiplication first, and if you use your rule you do whatever is on the left first. This proves the two following points: 1) 2=288 2) math is gay
There is no way multiplication come before division. if you rewrite it as 48 ÷ 2 x (9 + 3), 100% of the people will answer 288.
288 is my answer! Irregardless how daft a mathematician is, there must be unity and coherence in the way a problem is construed and solved. Otherwise, just throw away most every mathematical formula, theorems, what have you...
Why is that? There is the PEMDAS method, which is common in the US, and which places multiplication before division. There is the BODMAS method, common in other English-speaking countries, which places division before multiplication. Then there is the method which Icleing learned, which states that multiplication and division are of equal precedence and you should do the one that comes first (i.e. on the left). I don't see how division somehow takes precedence over multiplication for "100%" of the people. Actually, the correct answer is 2 if you think about it. The division can also be represented through a fraction. If you write is as a fraction, then the answer that comes out is 2.
PEMDAS -> Parenthesis, Exponents, Multiplication or Division from left to right, Addition or Substraction from left to right. MD means Mulitplication or Division from left to right. M comes before D doesn't mean multiplication comes before Divison. Whether PEMDAS or BODMAS, in this case, from left to right, it's division first. If there are 2 ways to solve this formula, the whole world will be in big mess.
Yes, you should always solve the bracket first, that will become 48 ÷ 2 x 12. But still you can't do multiplication first.
Agreed: the lack of explicit symbol between "2" and "(9 + 3)" caused me to treat it as a single term, but BODMAS throws out 288 if the symbol is there. 1/xy is always treated as 1/(xy) and not (1/x)y...
I must have a sunstroke . The sun is shining right in my face and I have no blinds here ... you are correct indeed. Probably used to seeing double brackets ...
Consider this case: Boeing sends a formula to all it's 747 customer like ..... A ÷ B x C ... to calculate some important data. The customers in Finland treat it like A ÷ (B x C). The customers in England treat it like (A ÷ B) x C. It could cause disaster when the 747 is flying from Finland to England.
I would go for 2 as I would read it as 48 / [2(9+3)] I agree with mark that 1/XY would be 1/(XY) because they did not separate 2 with the bracket that means it's one entity
