 # Finding average of denominator knowing average of numerator and average of fraction Good day to you April Bush 2022-06-25 Answered
Finding average of denominator knowing average of numerator and average of fraction
Good day to you all. I have a little problem I have been banging my head on for a while.
I have come to think that it is impossible, but I hope you can save me.
I have a fraction, $\frac{nu{m}_{i}}{de{n}_{i}}$., which takes different values over time.
The objective is to calculate $\frac{average\left(nu{m}_{i}\right)}{average\left(de{n}_{i}\right)}$
I have at my disposal $average\left(\frac{nu{m}_{i}}{de{n}_{i}}\right)$ and $average\left(nu{m}_{i}\right)$
Is there any way to do this, or do I need to get $average\left(de{n}_{i}\right)$ also?
Thanks a lot for your help.
Edit with an example
Let's take $\frac{1}{2},\frac{1}{3},\frac{1}{4}$
The information at my disposal is:
The average of numerators is 1.
The average of fractions is 0.36
Is it possible with the information I have to retrieve the average of denominators?
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No, consider the example:
$A=\left\{\frac{1}{2},\frac{1}{3},\frac{1}{6}\right\}$
$B=\left\{\frac{1}{2},\frac{1}{4},\frac{1}{4}\right\}$
We have the numerator average $1$ and fraction average $\frac{1}{3}$ for both cases yet average for denomiators are not the same.

We have step-by-step solutions for your answer! kixEffinsoj
This is impossible.
First case, consider the series $\frac{1}{2},\frac{2}{6}$.
Then, $avg\left(num\right)=\frac{3}{2},avg\left(den\right)=4,avg\left(num/den\right)=\frac{5}{12}$ and $avg\left(num\right)/avg\left(den\right)=\frac{3}{8}$
Second case, consider the series $\frac{2}{4},\frac{1}{3}$
Then, $avg\left(num\right)=\frac{3}{2},avg\left(den\right)=\frac{7}{2},avg\left(num/den\right)=\frac{5}{12}$ and $avg\left(num\right)/avg\left(den\right)=\frac{3}{7}$
In both cases your two givens are the same, but the answer is different. Therefore you cannot find the answer from the givens.
Edit: I see you got another answer that was both faster and better. Well done.

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