Question 978938
One way to write a fraction between ANY two other fractions is to average the numerators and denominators respectively.

Eg. a fraction between a/b and c/d is (a+c)/(b+d) (assuming that both fractions are the same sign). (this can be proven mathematically, and is a useful exercise for the mathematically literate).

So.. a fraction between 1/2 and 3/4 is: (1+3)/(2+4) = 4/6 = 2/3

A fraction between 1/4 and 1/2 is: (1+1)/(4+2) = 2/6 = 1/3.

Of course, there are MANY fractions which meet these conditions, but this general rule will always guarantee to find one.