I am not sure about this but here goes. If 1/4 =5/20ths and 2/5ths =8/20ths then 6/20ths would be the answer. but don't take my word for it. :)
What Is An Even Fraction Between One Fourth And Two Fifths?
It depends on what you mean by "even." The average of 1/4 and 2/5 is the average of .25 and .40, which is (.25 + .40)/2 = .65/2 = .325
.325 = 325/1000 = 13/40 This value is halfway between 2/5 and 1/4 (on a linear scale).
You can also compute it as (1/4 + 2/5)/2 = (5/20 + 8/20)/2 = 13/(20*2) = 13/40.
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If you want the geometric mean of these numbers, that is a different story. The geometric mean is a value that differs from each of these by the same factor. In symbols, the geometric mean "a" of 1/4 and 2/5 is
a/(1/4) = (2/5)/a, or
a2 = (1/4)*(2/5)
"a" is computed as sqrt[(1/4)(2/5)] = sqrt[2/20] = sqrt[1/10] = sqrt[10]/10.
So, a = sqrt[10]/10 is halfway between 1/4 and 2/5 on a logarithmic scale.
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There are an infinite number of other non-linear scales for which an "even" division between 1/4 and 2/5 could be calculated.
.325 = 325/1000 = 13/40 This value is halfway between 2/5 and 1/4 (on a linear scale).
You can also compute it as (1/4 + 2/5)/2 = (5/20 + 8/20)/2 = 13/(20*2) = 13/40.
_____
If you want the geometric mean of these numbers, that is a different story. The geometric mean is a value that differs from each of these by the same factor. In symbols, the geometric mean "a" of 1/4 and 2/5 is
a/(1/4) = (2/5)/a, or
a2 = (1/4)*(2/5)
"a" is computed as sqrt[(1/4)(2/5)] = sqrt[2/20] = sqrt[1/10] = sqrt[10]/10.
So, a = sqrt[10]/10 is halfway between 1/4 and 2/5 on a logarithmic scale.
_____
There are an infinite number of other non-linear scales for which an "even" division between 1/4 and 2/5 could be calculated.
I am not sure but I think it is 1 6ths
Two eighths, four tenths, fourteen twentieths
Seven/sixteenths
Only integers have even or odd values. See: en.wikipedia.org