what is 5/9 divided by 10/11

When you divide by a fraction, you multiply by the reciprocoal, which is 1/(10/11) = 11/10 (flip numerator with denominator).

Thus, 5/9 divided by 10/11 is 5/9 times 11/10 = 55/90. Divide top and bottom by 5 and you get 11/18.