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  #1  
Old 06 January 2013, 08:12 PM
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ParaDiddle ParaDiddle is offline
 
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Default The Answer is 9. Really, it's 9

I usually don't get sucked in but this took way too much of my time yesterday. I solved it at a glance, before which I though I sucked at algebra. Reading incorrect answers and the justifications thereto, makes me realize that the public school system what learnt me wasn't too bad after all.

For those without FaceBook it's a graphic of an algebra formula underneath which are the words "Solve It." The formula uses the division symbol, but in simple text it is;

6/2 (1 + 2)

No more, no less. I've offered several proofs to one FB friend incluiding an invitation to plug the formula into Google's search bar. He's still holding to his solution of 1.

::facepalm::
::headdesk::

- P

Last edited by ParaDiddle; 06 January 2013 at 08:20 PM. Reason: typos
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  #2  
Old 06 January 2013, 08:17 PM
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You're right. It's 9. I don't know what it will take to convince him, because I'm sure you've gone through the Order of Operations with him already.
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  #3  
Old 06 January 2013, 08:20 PM
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Tell him you'll give him $100 if he's right, and he only has to give you $10 if you're right. Suddenly, he won't be so sure about his answer. Either that or he'll say "I never bet."
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  #4  
Old 06 January 2013, 08:26 PM
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I can see where "1" would seem to be the logical answer, especially because the common "PEMDAS" mnemonic can trick one into believing that multiplication supersedes division, when in fact they are of equal priority and should simply be solved left-to-right.

Of course, in cases like this, I'd argue for putting parentheses around the 6/2 - although technically unnecessary, it eliminates the ambiguity.

(This is more or less the mathematical version of the Oxford comma debate.)
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  #5  
Old 06 January 2013, 08:34 PM
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If you're arguing over that sort of ambiguity, then it's a badly-written question and there isn't a "right answer". As written, I read it as though everything on the right-hand side of your division sign was on the bottom of the fraction, and so it's 6/6 = 1. That's not "wrong" any more than your answer is wrong. Personally I think it's more correct, but the problem is that the question is deliberately (or perhaps accidentally) poorly formed, not that one side is right and the other wrong.

If you want to write a sum in a single string so that it can be solved unambiguously by reading left to right, then it should be in reverse Polish notation...
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  #6  
Old 06 January 2013, 08:35 PM
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Yes, you're right, however, this is not a very clear way to write it. I hate having to parse things that come down to order of operations technicalities. I generally use more parentheses than strictly required when combining different operations that will get different results depending on the order. Whenever I get the opportunity to refactor some programming code that I've inherited I usually end up inserting some parentheses in complex expressions to avoid ugly order of operations nonsense.

Part of the issue is that personally I think of implicit multiply as being higher priority than explicit multiply. That isn't part of any official rule that they teach, and thus isn't a winning argument, but nevertheless I do think of implicit multiply as the first thing to evaluate. Thus I can see associating the implicit multiply in 2() more strongly than the divide. I would never write the equation in such an ambiguous way, so that would never come up in practice.

Last edited by Errata; 06 January 2013 at 08:40 PM.
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  #7  
Old 06 January 2013, 08:44 PM
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I happened to watch this video immediately afterwards. It's not really anything to do with it, but it's sort of vaguely the same sort of trick question, and it's funny:

"What's heavier, a kilogramme of steel, or a kilogramme of feathers?"

Limmy's Show - Kilogramme
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  #8  
Old 06 January 2013, 08:52 PM
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Technically they're the same weight and mass, but your observations about their weight may vary depending on your methods. It's hard to directly measure weight (and even harder to directly measure mass), because we displace air causing buoyancy. Even though two things with the same real mass should have the same weight (in the same location/velocity/inertial frame of reference), if you're measuring it in atmosphere, you may get more error in your measurement for the less dense thing.
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  #9  
Old 06 January 2013, 08:53 PM
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Er, did you watch the video? It's not really a trick question.
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  #10  
Old 06 January 2013, 08:55 PM
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Yes, I did watch it. It's funny. But it's a slightly more complicated problem than they make it out to be. They don't actually run into those problems because the way they are measuring their "mass" the result is tautological.
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  #11  
Old 06 January 2013, 09:27 PM
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If the denominator is just the 2, and the (1 + 2) appears outside the fraction, then 9 is correct. If the denominator is 2(1 + 2), then 1 is correct.
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  #12  
Old 06 January 2013, 09:33 PM
Saint James Saint James is offline
 
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Musicgeek pretty much nailed it. The main problem (as I see it) is that too many people see math as some sort of magic ritual where rules are followed blindly to get a result, rather than considering what the problem is trying to solve (as much as many people hate word problems, they are at least a little more realistic).

In short, the way this problem is written is vague. When writing out division longhand, it is not uncommon to assume that the denominator is assumed to be in parenthesis, even if not shown explicitly.

For example (warning: algebra ahead):

x / 6x

If we use strict order of operations here, we get x^2/6, while most people evaluating this would assume that you multiply the x by 6 first, which means that x/x simplifies to 1, leaving you with 1/6.

Or consider this example:

4/4(x + 1)

Is the answer x + 1, or 1/(x+1)? (It's not 1/x + 1 however. That would just be silly).

Technically the order of precedence is equal for operations at the same level (addition and subtraction, multiplication and division). Other than the parenthesis, it is in declining order of power. After all, multiplication is just fast addition (5 x 3 means add 5 to itself 3 times), and exponents are fast multiplication (5^3 is multiply 5 to itself 3 times), with subtraction, division (sort of - there's a little fine tuning there), and roots being the inverse operations to those.

Let me come up with a couple of 'word problems' to illustrate the two different ways that to OP problem could be interpreted.

Example 1:
Bill and Betty are having a couple of friends (couples) over for dinner. They're having the Smiths (Bob and Rhonda), and the Joneses (Henry and Maude). They have 6 burgers - how many does each person get?

Well each couple is 2 people, there are two couples invited (plus the one doing the inviting) so we get:

6 Burgers / number in a couple (number of couples invited + original couple)

To which the answer is clearly that each guest is going to feast on 9 burgers (and probably have lots of leftovers. Or maybe they're sliders - but now I'm just overthinking it... ). Then again, 1 would probably make more sense here.

Example 2: Larry is having a BBQ. Because I am using the original numbers he wants to make 6 half pound burgers for each person. He has 2 friends plus himself. How much meat does he need?

(number of burgers per person)(meat for each burger)(number of people)
(6)(1/2) (2 guests+ 1 himself)
(3) (3) = 9.

Wandering slightly off topic, the question of punctuation reminded me of one of the papers a teacher had posted on their wall regarding proper punctuation. It was a simple worksheet - add the correct punctuation the make the sentence make sense. This student had some fun commenting on the meaning of incorrect usage - most notably:

Let's eat grandma

fixed to:

Let's eat, grandma.

And the comment: good punctuation saves lives.
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  #13  
Old 06 January 2013, 10:17 PM
DaGuyWitBluGlasses DaGuyWitBluGlasses is offline
 
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When a number is adjacent to a parenthesis it is also consider a bracketed calculation
ie. 3(4-5) in an equation is the same as (3[4-5])

therefore
6/2(1+2) = 6/(2[1+2]) = 1.

'1,' and only 1 is correct. Type it into any recently bought calculator. (It's something the manufacturers have had to correct from older ones.)
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  #14  
Old 06 January 2013, 11:25 PM
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Quote:
Originally Posted by DaGuyWitBluGlasses View Post
Or in algerbra 6/2x we recognize '2x' as one term.
Who is we? I certainly don't recognize it as a single term.
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  #15  
Old 06 January 2013, 11:30 PM
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http://www.mathsisfun.com/definitions/term.html
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  #16  
Old 06 January 2013, 11:33 PM
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Please excuse my dear aunt Sally for not having a Snopes account, but she wanted me to post that the answer is 9.
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  #17  
Old 06 January 2013, 11:38 PM
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But in that instance, ‘4x’ is a “single term” in the same sense that ‘1/4x’ would be a “single term”. Still doesn't imply a parentheses or modify the order of operations, does it?
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  #18  
Old 06 January 2013, 11:40 PM
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Ah...I see what you're saying. I think you're right.
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  #19  
Old 06 January 2013, 11:42 PM
DaGuyWitBluGlasses DaGuyWitBluGlasses is offline
 
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Quote:
Originally Posted by ASL View Post
But in that instance, ‘4x’ is a “single term” in the same sense that ‘1/4x’ would be a “single term”. Still doesn't imply a parentheses or modify the order of operations, does it?
If it appeared in a quadratic equation then yes it's a term, since that requires adding terms. Other equations that rely on multiplying terms it wouldn't be. By itself like you posted it, i'd say it's not a term, it's an equation. 1/a is likely to be a term when you see it as representing a reciprocal (i.e the 1 is not a variable)

E.g 3x^2 + 1/4x - 3 =0, 1/4x is a term
3x^2 + 1/4*x -3 = 0, 1/4*x is also a term
1/4m * x = 8m^2 has 2 terms to the left of the equal sign, and then 8~ is a term too. 1/4*x is two terms. '1/4', and 'x'

Last edited by DaGuyWitBluGlasses; 06 January 2013 at 11:52 PM.
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  #20  
Old 06 January 2013, 11:49 PM
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Quote:
Originally Posted by DaGuyWitBluGlasses View Post
By itself like you posted it, i'd say it's not a term, it's an equation.
I think you must mean an expression, not an equation. (I would also call it a single term, BTW.)

Last edited by ganzfeld; 07 January 2013 at 12:03 AM.
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