Among all fractions that have a positive integer numerator and denominator and satisfy 9/11 <= x <= 5/6 which fraction has the smallest denominator?

Here's my best effort :

Note that, getting common denominators, we have that

9/11 = 54/66 = 108 / 132

5/6 = 55/66 = 110 / 132

The fraction between these two with integer numerator / denominator = 109 / 132

Interested to see if someone else has a better answer !!!!!

I won't mess with your expertise :)

but I understood the problem a little differently than how I think you did...?