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6/2(1+2)=SOLVED
glithert
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Registered User regular
Some asshole asked this on Facebook and now it's a thing. I don't get how the answer is ambiguous. I thought it was 9. Could someone who knows more about math than I do explain where people are getting a one?
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6/ 2 * 3 = 6 / 6 = 1.
___6__
2(1+2)
Therefore, since parentheses always go first, it is like this
6/2(1+2)
=6/2(3)
Then multiplication/division left to right since there are no exponents.
6/2(3)
=3(3)
=9
But, yeah, if you distribute 2 to (1+2) first you get 6, it is an error in the order though.
The incorrect way would be
6/2(1+2)
=6/(2+4)
=6/6
=1
but they're listening to every word I say
This doesn't seem like a math question so much as a "Gee, lets see who I can fool question." I can not think of any school age instructor that would assign a problem like this, where you are forced to remember some archaic rules that govern ambiguous circumstances like this. That's like the anti-thesis to "learning".
Poke (with a sharp object) your friend on FB who posted this.
a fraction is the same as dividing, just written a different way.
6/2 = 3
6
___ =3
2
but they're listening to every word I say
This. As written, the equation is equal to 9.
It's not even ambiguous, it just is 9. I think whoever posted it is just taking advantage of people who've forgotten/never learned the BODMAS rules.
These are exactly the kinds of problems instructors will put on the board as an example. That way you understand how the rule works. It is important to understand order of operations, one of the basic things in math.
But your friends are just being dicks probably.
but they're listening to every word I say
It ISNT a trick question. It is a question with a definite answer. The people that get six (edit:er.. one) are just doing it wrong because they misunderstood how math works.
but they're listening to every word I say
Yeah but if you're writing it out like that it's implied that the (1+2) term isn't in the denominator as that would be 6/[2(1+2)]. If anyone tells you that 9 is wrong just tell them to put that equation in a calculator as is and if they tell you they get anything other than 9 they're lying.
Again, this. If anyone asks you this again:
6/2(1+2) = 9
6/(2(1+2)) = 1
That extra set of brackets is important as it tells you to divide 6 by (2(1+2)). In the first case, you are multiplying the number in the brackets (1+2) by the fraction (6/2).
In the semesters I student assisted, I never once saw an expression written in such a way. To get a similar effect you would have to write it on the board EXACTLY as is expressed here - no one is going to write it like that. You may write the fraction without parenthesis, but you aren't going to position it so that all numbers, and the division symbol line up as they do. I would say THAT is the "trick" here, not in PEMDAS, but how people read type on a computer.
I can't help but wonder if that's why, in so far, over 1.3 million people have answered incorrectly. People are silly gooses, and you can't rely on them to always write things in the most logical way. But so long as you know the order of operations, you'll know that there's only one way to solve it, regardless of how it's written. The problem with learning mnemonics is that people forget (or were never taught) that some operations take equal precidence and that those should be solved from left to right. If you read through the comments of the question on facebook, the majority (well, I didn't go through all 90,000 or so, but the majority of the ones I read) who berate people for not knowing their mnemonic of choice are the ones who got it wrong.
The reason why, is because the question was written deliberately wrong to imply precedence of bracket/parantheses. Not because of any stupid memonic supremacy
If anyone doesnt believe you as to what the correct answer is, tell them to paste the equation into google. Google tells you 9. Hell, even windows calculator can solve this if theyre running vista/7 and switch to scientific mode.
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This doesn't work quite right... I put in my calculator as it is shown and I get a 1.
Its a Casio fx-300MS for reference.
Most would agree that it would evaluate to (x)/(2y)
Not ((1/2)x)y
This is an illustration of the ambiguities that are introduced when you try to type out this type of math equations.
otherwise, I was taught to get the brackets out first. There really is ambiguity if you have to rely on a left-to-right bias in your reading populace and context-based interpretations of operational symbols. Not all languages work like that, and "left to right" is a hell of an arbitrary rule compared to most math.
The fact that these can be interpreted differently is the reason we have the order of operations. We have agreed before hand that operations will be done in a certain order so as to completely eliminate ambiguity. If you write 2x/4y and do not mean it to be xy/2 when reduced, you've written it wrong. If you want it to be x/(2y) then you need to include some grouping symbols.
Why? Because some mathematicians years ago agreed that there's a certain way to write these things so that we wouldn't have to deal with some jackass on facebook trying to be clever by causing confusion about a perfectly straightforward expression.
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Red for false. Anyone who's done calculus or beyond has seen something like 2x/4y reduced to x/2y and understood it means x/(2y). There's no ambiguity in that statement.
I'm totally throwing in my own (engineering) bias here, but I feel like there's a disconnect between people who learned enough math to navigate simple PEMDAS equations, and those who've gone on to more abstract levels of math.
I think the PEMDAS folks see this as a pure and simple "follow the rules, dummy!" and arrive at the answer 9. But for the more abstract folks, we're used to seeing the "/" not as a division sign, but as the separater in a fraction.
It's still somewhat ambiguous, but if asked us abstract folks are more likely to parse the equation as: Seen this way, the answer is 1.
The logic is that putting the (1+2) in the denominator and omitting the parenthesis implies an assumed grouping. If the author had truly intended the (1+2) to be multiplied, the equation would have been written 6(1+2)/2.
Anyway, on some other website, people but that expression into calculators, google, and programs, and the majority of them gave 9 as the answer. So it would appear that by programming standards, you do not divide by the bracket. Since mathematicians will prefer to express themselves in latex or in non-ambiguous form, I think the programming standard is probably the one to observe here.
I love computers, but there's a reason why computers aren't so great at text translation, speech recognition, and visual navigation ;-)
So there's not actually a / separator or anything like that.
But yeah, I think the general idea is that it is terribly written. If you follow the rules exactly it should be 9, though.
I have done quite a lot of calculus and while people may use 2x/4y* to mean 2x/(4y) the first is still wrong by convention. Period. If you write 2x/4y and mean 2x/(4y) then you're being sloppy. Something like that is perfectly acceptable if you're just farting around with your friends but if you're going to be pedantic as the original question is inviting people to be then you're obliged to be a bit more careful.
The order of operations is not just a curiosity or a suggestion. It is a hard rule precisely to eliminate ambiguity. If you disregard it then _you_ are the source of ambiguity in your work.
This question was answered years and years ago. In cases where the precedence of operations is not clearly indicated by the use of grouping symbols operations are done in the order of 1) any grouping symbols which _are_ present, 2) exponentiation 3) multiplication from left to right (which includes division since division is just a different way of writing multiplication) and 4) addition from left to right (which includes subtraction since subtraction is just a different way of writing addition).
* It is just possible that you might be using 2x/4y when what you mean is This is different. In the above (poorly rendered) example, the fraction bar is itself a grouping symbol equivalent to typing (2x)/(4y) because the fraction bar requires you to divide the entire quantity on top by the entire quantity on the bottom. Since / is only an operator and not a grouping symbol, grouping symbols have to be added to enable you to write 2x/(4y) in ascii.
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Nobody is saying that the order of operations is wrong, or that 1 is actually somehow "right."
They're saying that the writer of the problem purposefully sought out an example of how popular convention is different than what the hard rules dictate should be.
TI calculators fall victim to this exact issue:
http://i.imgur.com/SIQFw.jpg
If you're using '/' to denote division at all, you're being sloppy. There's a reason that it's very rarely used in expressions of any sort of complexity in professional settings, and it's because it causes exactly this type of confusion.
My only beef with this thread is the blunt application of pedantry by those who are 100% positively certain the right answer is and can only be 9.
I hesitate to say that there is a correct answer at all. To make an analogy with your example:
To write it in the former but expect the latter is malice. There are many alternate ways to construct the former so the later is intuitive. Perhaps it is naive to assume the author would want to phrase things in the clearest manner possible, and that any confusion you encounter is due to typos or oversight.
Yes, ultimately pedantry will lead you to the technically correct answer, but I would hardly call any answer "wrong" when given such a maliciously phrased question.
1) Parentheses
2) Exponents
3) Multiplication and division left to right
4) Addition and subtraction done left to right
Correct?
Yes. People who were taught that multiplication comes before division were taught wrong. I suspect that most people who think they were taught that were actually taught it correctly, but are remembering it wrong because they're just blindly following the words that make up PEMDAS. Multiplication and division have equal precedence and are resolved in order left to right.
This problem is intentionally misleading because it is asking you to treat "/" as a divide by sign when we are more accustomed to using it to represent an extended fraction, i.e. everything to the left is a numerator and everything to the right is a denominator until an empty space is reached.
If the intended answer is 9, The problem should have been written as either
6/2 * (1+2)
or
6÷2(1+2)
Edit: regardless, it would still be a bad problem because the onus is always on the presenter to make sure the equation is clearly legible. It isn't clever to intentionally write equations that could be misunderstood.
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6÷2(1+2) is entered as 6/2(1+2) in many mathematics programs such as MatLab. / basically means ÷ when you are doing math on a computer.
I will point out here that when I learned algebra in grade school, it was explicitly taught that if you see /, everything to the left is the numerator and everything to the right is the denominator.
So we were taught that 2x+y/2 = (2x+y)/2, for instance. Or x+y/a+b = (x+y)/(a+b).
By the time I got to high school, we were discouraged from using / at all, and told to only use a horizontal line to show division every time. (I had one teacher who would take a point off for using / even if you had used it correctly.)
I only learned the correct way to use / long after I stopped taking math classes.
the "no true scotch man" fallacy.
When you are asking a computer to solve the function, yes, but not when you are communicating that information to other human beings. Then we use things like Aurora and the "code" tag to make sure the equation is as legible as possible.
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