Results 1 to 4 of 4

Math Help - Proof of neighbor fractions

  1. #1
    Newbie
    Joined
    Aug 2013
    From
    Canada
    Posts
    9

    Proof of neighbor fractions

    *If I turn out to have a wrong answer, please no hints or showing an valid proof. I want to do it on my own !


    ad/bd-bc/bd=+-1/bd is neighbor fraction


    Now, reduce the common numbers :

    a/b-c/d=+-1/bd

    We must now prove that the left hand side has irreductible fractions. Lets see what would happen if these fraction were reductible.

    let a=z*y , b=z*l , c=p*m d=p*n

    z*y/z*l-p*m/p*n equality to be determined +-1/(z*l)*(p*n)

    Reduce:

    *ln (y/l-m/n) equality to be determined (+-1/(z*l)*(p*n))*ln

    yn-lm equality to be determined +-1/z*p

    yn-lm not= +-1/z*p

    We have considered the initial fractions to be reductible and have arrived at a false result. An integer cannot be equal to (+-1/z*p)

    So, the initial fractions must be irreductible.

    *Of course, I'm considering the variables to represents integers.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856

    Re: Proof of neighbor fractions

    What, exactly, are you trying to prove? You say you want to show that the fractions on the left side, \frac{a}{b} and \frac{c}{d}, are reduced to lowest terms. But that is given, isn't it? The definition says that two fractions are "neighbor fractions" if and only if \frac{a}{b}- \frac{c}{d}= \frac{z}{bd} where z= \pm 1 which assumes that the fractions are in lowest terms.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2013
    From
    Canada
    Posts
    9

    Re: Proof of neighbor fractions

    What I'm trying to prove is that these neighbor fraction are irreductible. This is exactly what the first question asks. We don't know that these fractions are irreductible or not. We just know that they're neighbor.(Which doesn't imply that they're irreductible.That's how I understood it atleast.)

    Hope I was clear!
    Last edited by philomath; January 4th 2014 at 02:23 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856

    Re: Proof of neighbor fractions

    So "neighbor fractions" is NOT a property of the numbers, just how they happen to be written? That is, 1/2 and 1/3 are "neighbor fractions" but 2/4 and 1/3 are not? Prove that if a and b, in the fraction a/b, have common factor, n, then ad- bc is a multiple of n?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: October 20th 2012, 04:39 AM
  2. Proof of the partial fractions theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 31st 2011, 03:32 PM
  3. Nearest neighbor!
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: May 17th 2011, 07:00 AM
  4. Proof concerning "neighbor fractions"
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 1st 2010, 12:04 PM
  5. Proof (product of fractions)
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: August 30th 2010, 07:24 PM

Search Tags


/mathhelpforum @mathhelpforum