thirds of anything

Discussion in 'Math' started by samjesse, Aug 10, 2014.

  1. samjesse

    Thread Starter Active Member

    Sep 14, 2008
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    Hi

    How many thirds are in 2? 6 or 3?

    Divide 2 by 1/3 you get 6.
    There is always 3 thirds of any quantity so the answer is 3.

    which is the correct answer?

    Thank you
     
  2. MrChips

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    Oct 2, 2009
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    The answer is 3.
     
  3. DerStrom8

    Well-Known Member

    Feb 20, 2011
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    If you define "a third" as "a third of one", or "1/3", then there are 6 0.33333...s in 2. If you define "a third" as "a third of the total", or "1/3 of 2", also written as "2/3", then there are 3 thirds of two in that total.
     
  4. samjesse

    Thread Starter Active Member

    Sep 14, 2008
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    This question was in an exam for primary grade and there was no definition for the word "third".
    why MrChips choose one definition over the other?
     
  5. DerStrom8

    Well-Known Member

    Feb 20, 2011
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    The question is very ambiguous, and an argument can be made for either answer. Three thirds make a whole, so if the whole is 2, then there would be 3 thirds of 2. However, one may define a third as a third of 1, in which case there are 6 thirds in 2.

    Whoever wrote that question should re-write it to make it less ambiguous.
     
  6. MrChips

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    Oct 2, 2009
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    If the question is in an exam for primary grade, then the answer is 6. However the question is badly worded for that level.

    If the question is in a general test of IQ, the answer is 3.

    How many thirds are in a whole?

    How many thirds are there of anything?
     
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  7. THE_RB

    AAC Fanatic!

    Feb 11, 2008
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    However 2 divided by 1/3 is pretty bulletproof.

    And a "third" of 2 is actually 2/3; "two thirds".

    I think if mathematics is the important point then "third" = 1/3 or 0.33 repeating.

    If it's not a math test but a pholosophical discussion then "third" might indicate one third of whatever is being discussed. Like "I spend a third of my wage on booze and hookers". ;)
     
  8. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Whatever level this question was posed at, the author should be fired for incompetence.

    How many thirds are there in zero?
     
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  9. ErnieM

    AAC Fanatic!

    Apr 24, 2011
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    Why would you divide by the reciprocal? Divide 2 by 3 and you get .666(and so on).

    There are always three thirds in anything.

    There are no thirds in zero because zero ain’t something, it’s nothing.

    I once read where Isaac Asimov essay where he got into a disagreement with an English professor back when he was an undergrad. Seems the prof categorized mathematicians under the general category of “mystics” as they believed in something called “imaginary numbers.” Asimov questioned him on this, I forget the smug answer the prof offered. So Asimov engaged him further, asking him if he could hand back one half of a piece of chalk. The prof happily agreed, pulled out a fresh piece, snapped it in two and handed one part over.

    “What is this?” Asimov queried. “I asked for half a piece of chalk, you gave me one piece.”

    “It is one half of a standard piece of chalk.”

    “Well now you are offering arbitrary definitions. And even were that to be accepted, can you be sure it is exactly one half of such an arbitrary length?”

    Asimov was quickly ejected from the class. Sounds like a win to me.

    Question Authority.
     
  10. studiot

    AAC Fanatic!

    Nov 9, 2007
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    So you have proved my point.

    The number of thirds in a number depends upon the number.

    There are a different number of thirds in 0 from the number of thirds in 1, both of which are valid numbers.
     
  11. MrChips

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    Oct 2, 2009
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    A third is not a number.
    A third is a fractional part of something.

    One may ask how many quarters are there in two dollars? The answer is eight.
    In this case, a quarter is an accepted numerical value of a quarter of one dollar.
     
  12. inwo

    Well-Known Member

    Nov 7, 2013
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    So, doing good on an IQ test requires, not knowledge, but the ability to answer trick questions, yet not outsmarting the author.:rolleyes:
     
  13. jpanhalt

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    Jan 18, 2008
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    We know very little about the particular test referenced by the OP. This is more of a general comment about some of the standardized tests mentioned by others.

    There are several metrics used in evaluating questions on (good) standardized tests. A simple one is the percentage getting the question right. One doesn't want questions that only a very small percentage of the test takers get right. One metric that I liked was the "discrimination index." That index measures whether those with the best overall performance did better or worse on a particular question than those with poorer performance. (Often times, such tests include questions being evaluated for a subsequent test that are not included in the final scoring for an individual.)

    The sort of question for which the one who does better on the overall test is more likely to get wrong than a person who does much more poorly overall will get a negative discrimination index. Committees that should review every question is such tests may simply delete the question or try to modify it to remove ambiguity. There is no guarantee such careful review happens. And certainly for non-standardized tests (e.g., those used in classrooms), it is doubtful any such review or analysis ever happens.

    All testing has noise in it. That noise may result in the very best or brightest not getting the highest grade, but it rarely makes that person fail.

    John
     
  14. studiot

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    Of course it's a number.

    It's a member of the set of rational numbers.

    Note this is the mathematics forum, so we expect mathematical definitions.
     
  15. ErnieM

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    Apr 24, 2011
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    I made no generalized statement concerning numbers.

    I specifically discussed things, as in something and nothing.
     
  16. studiot

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    I rephrased your statement but you did indeed offer two solutions to the question, depending upon the number.

    You offered the solution zero for the number of thirds in zero.

    By anything it is reasonable to assume any number other than zero, since the original question was about numbers.

    So you offered the solution 3 for other numbers.

    It would also not be true to say that anything at all I care to imagine could be divided into thirds.

    Following the example of the piece of chalk, I would ask you to look at a hole and offer me a third of a hole.

    Or perhaps a third of a bullseye in a target, or a third of a hole in one in golf.....
     
  17. joeyd999

    AAC Fanatic!

    Jun 6, 2011
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    Studiot:

    You must be a great deal of fun at parties. I mean it!

    Any time you want to hang out, let me know...
     
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  18. THE_RB

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    Feb 11, 2008
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    I'll disagree with that!

    "A third" is another way of saying "one third" which is the english language representation of this rational number; 1/3 or 0.333 repeating.

    So as I said earlier in a math context (like a math question) "third" directly equals 1/3.

    The only time it deviates from 1/3 is when you get outside the math context and are using general language.
     
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  19. atferrari

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    Jan 6, 2004
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    Non-native, as most of you know already, I consider this question a bad way of cheating. While I do not like answering questions with questions, this deserves: "thirds of what?"

    I strongly feel that the use of "in" is wrong here, provided the above is not clear at all. After all, how much is the half of two plus two?

    Teachers asking those questions should be hanged from the balls in the main square.
     
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