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Math Help - Help with simple proving

  1. #1
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    Is this rational and why?

    if a, b, c, d, e, and f are all integers prove that r is rational



    r = [(a/b) - (e/f)] / c/d
    Last edited by Mathwizard4; March 2nd 2010 at 07:14 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Mathwizard4 View Post
    if a, b, c, d, e, and f are all integers prove that r is rational

    r = [[((e)(f))/d] - [((f)(a))/d ]]/(f)(c)/d
    ....isn't the quotient of integers always rational? Simplify that monstrosity.
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    ....isn't the quotient of integers always rational? Simplify that monstrosity.
    sorry not good with using this site yet. basically the numerator is a ratio of integers minus a ratio of integers and the denominator is a ratio of integers. I'm having trouble proving that the result is a rational number.

    I made my original equation more clear.
    Last edited by Mathwizard4; March 2nd 2010 at 06:24 PM.
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  4. #4
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    First, you need to make sure that you never divide by 0.

    Second, all integers are rational, and rational numbers are closed under addition, subtraction, multiplication and division by a non-zero (i.e., the result of the operation is again rational).
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