Results 1 to 6 of 6

Math Help - Rational Number Proof

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    Wisconsin
    Posts
    29
    Thanks
    1

    Rational Number Proof

    Hello all,

    While practicing proofs I came across one that I'm having trouble with. Here it is:

    Let x and y be non-zero rational numbers. Prove that (4x + 7y) / 6y is a rational number.

    Let:
    x = a/b . . . where b cannot equal 0
    y = c/d . . . where d cannot equal 0

    Then:
    (4(a/b) + 7(c/d)) / 6(c/d)

    Wouldn't this last statement be a proof in it self since I have expressed (4x + 7y) / 6y as a ratio of two integers, namely 4(a/b) + 7(c/d) and 6(c/d), where 6(c/d) cannot equal 0? Doesn't this show that (4x + 7y) / 6y is rational?

    Thanks for any suggestions or pointers to similar problems.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Rational Number Proof

    I would take it a step further:

    \frac{4 \cdot \frac{a}{b}+7 \cdot \frac{c}{d}}{6 \cdot \frac{c}{d}} \cdot \frac{bd}{bd}= \frac{4ad+7bc}{6bc}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2012
    From
    Wisconsin
    Posts
    29
    Thanks
    1

    Re: Rational Number Proof

    Nice. I didn't see that. Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2012
    From
    Wisconsin
    Posts
    29
    Thanks
    1

    Re: Rational Number Proof

    Although, wouldn't it be possible for c to equal 0, making 6bc = 0?
    Last edited by nicnicman; October 30th 2012 at 02:08 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Rational Number Proof

    If x and y are non-zero, then none of a,b,c,d can be zero.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Oct 2012
    From
    Wisconsin
    Posts
    29
    Thanks
    1

    Re: Rational Number Proof

    Oh yeah. Thanks again.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof that recurring number must be rational?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 10th 2010, 05:20 AM
  2. Rational Number Proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 23rd 2009, 07:09 AM
  3. Rational number if n is even proof
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: January 15th 2009, 12:19 PM
  4. Rational Number Proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 14th 2006, 06:05 PM
  5. Proof that sum is rational number
    Posted in the Algebra Forum
    Replies: 6
    Last Post: May 28th 2006, 05:31 PM

Search Tags


/mathhelpforum @mathhelpforum