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Math Help - Pre-Algebra Equation with Negative Mixed Number

  1. #1
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    Pre-Algebra Equation with Negative Mixed Number

    I am very unsure of how to solve this equation, which involves a negative mixed number. Help would be very much appreciated.

    -6/n = -9 5/6
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  2. #2
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     \frac{-6}{n} = -9\frac{5}{6}

     \frac{-6}{-9} = \frac{5}{6}n

     \frac{5}{6}n = \frac{6}{9}

     n = \frac{6\times 6}{9\times 5}

     n = \frac{36}{45}
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  3. #3
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    I'm sorry, but I don't exactly understand your reasoning. May you please explain?
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  4. #4
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    I solved for n by isolating it.
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    Thank you for replying. I'm still not sure how the method you used to isolate "n" with works. May you please explain this as well, if it isn't too much of a problem.
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by pickslides View Post
     \frac{-6}{n} = -9\frac{5}{6}

     \frac{-6}{-9} = \frac{5}{6}n

     \frac{5}{6}n = \frac{6}{9}

     n = \frac{6\times 6}{9\times 5}

     n = \frac{36}{45}
    -9\frac{5}{6}\neq -9\cdot\frac{5}{6}. However, -9\frac{5}{6}=-9-\frac{5}{6}.

    So first rewrite it as an improper fraction:

    \frac{-6}{n}=-\frac{59}{6}\implies \frac{6\cdot 6}{59}=n\implies\frac{36}{59}=n
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  7. #7
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    Quote Originally Posted by Chris L T521 View Post
    -9\frac{5}{6}\neq -9\cdot\frac{5}{6}. However, -9\frac{5}{6}=-9-\frac{5}{6}.

    So first rewrite it as an improper fraction:

    \frac{-6}{n}=-\frac{59}{6}\implies \frac{6\cdot 6}{59}=n\implies\frac{36}{59}=n
    Very silly mistake! My bad...
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  8. #8
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    I'm sorry, but I am still very confounded by how all of this works. Why does

    <br />
-9-\frac{5}{6}<br />
    make sense?

    As well, why do all the digits become positive, and 59 somehow becomes the denominator of the answer? This is all so confusing.
    Last edited by ZushiRoe; August 31st 2009 at 08:59 PM. Reason: Forgot the "n" in confound
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  9. #9
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     -9\frac{5}{6} = -\frac{9\times 6 + 5}{6} = \frac{-59}{6}

     -9-\frac{5}{6} = \frac{-54}{6}-\frac{5}{6}= \frac{-59}{6}

    Therefore  -9\frac{5}{6} = -9-\frac{5}{6}
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  10. #10
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    Quote Originally Posted by ZushiRoe View Post

    As well, why do all the digits become positive,
    If you follow my first post, being mindful of the arithmetic error pointed out by Chris L T521, you will notice a negative number being divided by another negative number, what is the result?
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