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Math Help - Simple Fractions Question

  1. #1
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    Simple Fractions Question

    How do you show which of these is the smallest (the question in mind is related to variance but its not relevant here, I just dont know how to compute the fractions, but in case it makes it any easier, m & n are samples).

    1. o*/n


    2. [(o*/n)/2] + [(o*/m)/2]


    3. o*/m+n


    3 is obviously smaller than 1 but I dont know which is smaller out of 2 & 3, and I need to prove it.


    Any help would be much appreciated. Thanks
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  2. #2
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    Quote Originally Posted by jay85 View Post
    How do you show which of these is the smallest (the question in mind is related to variance but its not relevant here, I just dont know how to compute the fractions, but in case it makes it any easier, m & n are samples).

    1. o*/n


    2. [(o*/n)/2] + [(o*/m)/2]


    3. o*/m+n


    3 is obviously smaller than 1 but I dont know which is smaller out of 2 & 3, and I need to prove it.


    Any help would be much appreciated. Thanks
    I assume that by:

    (a) [(o*/n)/2] + [(o*/m)/2] you mean \frac{\frac{o*}{n}}{2} + \frac{\frac{o*}{m}}{2} = \frac{o*}{2n} + \frac{o*}{2m} ...... = \frac{o*(m + n)}{2mn}.

    (b). o*/m+n you mean \frac{o*}{m + n}


    So the real question is which is larger, \frac{1}{m + n} or \frac{(m + n)}{2mn} \, ?

    \frac{1}{m + n} = \frac{2mn}{2mn(m + n)}.

    \frac{(m + n)}{2mn} = \frac{(m + n)^2}{2mn(m + n)}.

    So I wonder which is larger ...... 2mn or (m + n)^2 .....?
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  3. #3
    GAMMA Mathematics
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    Quote Originally Posted by jay85 View Post
    How do you show which of these is the smallest (the question in mind is related to variance but its not relevant here, I just dont know how to compute the fractions, but in case it makes it any easier, m & n are samples).

    1. o*/n


    2. [(o*/n)/2] + [(o*/m)/2]


    3. o*/m+n


    3 is obviously smaller than 1 but I dont know which is smaller out of 2 & 3, and I need to prove it.


    Any help would be much appreciated. Thanks
    What is o*? If that is zero, then all of these are equal to zero.
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  4. #4
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    o* = Variance
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