Question

what does this question mean?
"insert a one fraction in between"
q 1-1/2 and 4/5

Answer 1

I don't know what you mean by "A one fraction", nor what the q is doing there, nor whether your 1-1/2 is supposed to be 1/2 or 1 1/2.

There are an infinite number of fractions that are in between any two fractions.

Answer 2

If you are trying to divide the interval from 1/2 and 4/5 into equal quartiles, the dividing fractions would be:
end point 10/20 (1/2); q1 = 23/40; q2 = 13/20; q3 = 29/40, and end point 16/20(4/5)