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Math Help - What's wrong in it

  1. #1
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    What's wrong in it

    Please tell me where I am mistaking in the following problem


    1/5 < 3/5 (1)
    therefore 1 x 5 < 3 x 5
    and 5 < 15


    but 1/5 = -1/-5 (2)

    therefore from 1 and 2

    -1/-5 < 3/5
    therefore -1 x 5 < 3 x -5
    and -5 < -15


    but we know that this is not the case.
    So please tell me where have I mistaken.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by uspatange View Post
    Please tell me where I am mistaking in the following problem


    1/5 < 3/5 (1)
    therefore 1 x 5 < 3 x 5
    and 5 < 15


    but 1/5 = -1/-5 (2)

    therefore from 1 and 2

    -1/-5 < 3/5
    therefore -1 x 5 < 3 x -5
    and -5 < -15


    but we know that this is not the case.
    So please tell me where have I mistaken.
    When you multiply (or divide) both sides by a negative you reverse the "sense" of the inequality. So
    \frac{-1}{-5} < \frac{3}{5}

    -5 \cdot \frac{-1}{-5} > -5 \cdot \frac{3}{5}

    -1 > -3

    -Dan
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  3. #3
    MHF Contributor
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    Quote Originally Posted by topsquark View Post
    When you multiply (or divide) both sides by a negative you reverse the "sense" of the inequality.
    You can prove this by addition.

    Is -5 < -3?

    Rather than multiply by -1 and reverse the inequality, add 5 and then add 3 (resist the temtation to simplfy everything.)

    -5 < -3

    Add 5

    0 < -3 + 5

    Add 3

    3 < 5
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