There are infinitely many fractions between 1 and 2 and I have no intention of even starting to list them.
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there are an infinite amount of fractions between any two numbers (including the interval [1/2,1]). eg. you can divide the distance between 1/2 and 1 (1-1/2)=1/2 in 2 parts(1/4), and one of those parts into 2 parts(1/8), and so on (approaching 0)
There are many different fractions between one third (1/3) and one half (1/2). The fraction that is exactly halfway between them is five twelfths (5/12).
2 fractions equivalent to 1/8
Halfway between two fractions would be the average of the two fractions, so add the two fractions together and divide by two! Let's take 1/2 and 3/4 as an example. Add 1/2 (or 2/4) and 3/4 and you get 5/4. Now divide by two ( or multiply the bottom part by two) and your answer is 5/8!
If you are asking how many different fractions lie in this range the answer is an infinite amount. If you are asking what fraction lies in the center it is 1/2