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Dumb Question on ratio

  1. May 15, 2009 #1

    uart

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    Dumb Question on "ratio"

    I have some text that implies the following (which makes abolutely no sense to me).

    The ratio of 1/12, 5/12, 7/12, 11/12 is 4/11

    Can anyone think of any context or meaing of "ratio" here for which this statement would make any sense?
     
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  3. May 15, 2009 #2

    berkeman

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    Re: Dumb Question on "ratio"

    Weird. The increment for that sequence is almost 4/12, but not in one case.

    Can you tell us what the context of the statement is? Where did it come from?
     
  4. May 15, 2009 #3

    uart

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    Re: Dumb Question on "ratio"

    Hi berkeman.

    The text of the problem starts out as follows :

    When I read this my understanding is that the proper fractions of denominator 12 which are "resilient" would be 1/12, 5/12, 7/12 and 11/12. But then how could one define the ratio of those to be 4/11.

    In other words this is my problem:
    - I think I understand how the author is defining "resilient" fractions.
    - I think I understand what the author calls "the proper fractions of a denominator that are resilient".
    - But I still don't understand how R(d) is defined or how that example works.

    Perhaps it's just badly worded and I am totally misunderstanding the whole thing.:confused:
     
    Last edited: May 15, 2009
  5. May 15, 2009 #4

    tiny-tim

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    Hi uart! :smile:
    Right … 12 has 11 proper fractions: 1/12, 2/12, … 11/12.

    And 4 of them are resilient … 1/12, 5/12, 7/12, 11/12.

    So the ratio is 4/11. :wink:
     
  6. May 15, 2009 #5

    berkeman

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    Re: Dumb Question on "ratio"

    Oh, I think I see. There are 4 numerators out of the possible 11 numerators of x/12 that are resiliant. Weird way of defining things. I wonder if it's useful somehow later...?

    Edit -- TT beats me to the punch again!!
     
  7. May 15, 2009 #6

    uart

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    Re: Dumb Question on "ratio"

    Thanks to both :).

    So I guess the text could have been better worded as:

    "Furthermore we shall define the resilience of a denominator, R(d), to be the ratio of the number of its proper fractions that are resilient to the total number of it's proper fractions; for example, R(12) = 4⁄11."
     
  8. May 28, 2009 #7
    Re: Dumb Question on "ratio"

    I think this question arose from problem 243 of Project Euler (projecteuler.net)
     
  9. May 29, 2009 #8

    HallsofIvy

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    Re: Dumb Question on "ratio"

    Or "R(d) is the number of integers less than d that are relatively prime to d".

    The whole statement, as given, sounds like something made up by a school boy.

    Added: Ah, yes, I checked "project Euler" and that is precisely what it is.
     
  10. May 29, 2009 #9

    uart

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    Re: Dumb Question on "ratio"

    Yes someone asked me about that particular Project Euler problem and I had trouble making sense of their wording. Tiny-Tim's answer above made it clear though.
     
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