Results 1 to 9 of 9
Like Tree2Thanks
  • 1 Post By richard1234
  • 1 Post By a tutor

Math Help - fraction problem

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    201

    fraction problem

    One day tom was playing with numbers.he wrote 11 fractions using all natural numbers from 1 to 22 exactly once, either as numerator or as denominator.how many of these fractions,at most,are integers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    65

    Re: fraction problem

    Quote Originally Posted by mastermin346 View Post
    One day tom was playing with numbers.he wrote 11 fractions using all natural numbers from 1 to 22 exactly once, either as numerator or as denominator.how many of these fractions,at most,are integers?
    10.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: fraction problem

    How could it be 10? If you look at the prime numbers 13, 17, 19, at most one of these can be paired with 1, so right off the bat, we know the answer is at most 9.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    65

    Re: fraction problem

    Quote Originally Posted by richard1234 View Post
    How could it be 10? If you look at the prime numbers 13, 17, 19, at most one of these can be paired with 1, so right off the bat, we know the answer is at most 9.
    The answer is 10.

    How will I feel if I'm wrong now?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: fraction problem

    Hmm, you might be correct. 17 could be paired with 19, didn't realize that.
    Last edited by richard1234; August 7th 2012 at 08:57 AM.
    Thanks from mastermin346
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    65

    Re: fraction problem

    Sorry, I'm only joking around. I've had them all written down since before my first post on this thread.

    and







    there








    are







    only














    10.
    Thanks from mastermin346
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: fraction problem

    The only way to get 10 is if one of 13,17, or 19 is paired with 1. WLOG suppose 13 is paired with 1.

    13/1
    17/19

    We have 18 numbers left and want to find the max. number of integers we can obtain. Here is a possible solution.

    22/11
    21/7
    20/10
    18/9
    16/8
    15/5
    14/2
    12/4
    6/3

    It is indeed 10.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: fraction problem

    Lol...but if you're "a tutor," you should at least explain why it's 10, or find a method to get 10 and show why 11 is impossible, right?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Jul 2012
    From
    Jaipur,Rajasthan
    Posts
    36
    Thanks
    1

    Re: fraction problem

    According to me its 10 also.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fraction problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 1st 2009, 10:33 AM
  2. fraction problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 4th 2008, 08:00 AM
  3. Fraction Problem
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 3rd 2008, 05:30 PM
  4. fraction problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 3rd 2008, 09:09 AM
  5. Fraction Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 9th 2008, 11:07 AM

Search Tags


/mathhelpforum @mathhelpforum