1. ## 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

2. Originally Posted by jay85
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 .....?

3. Originally Posted by jay85
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.

4. o* = Variance