The number of distinct rational number x such that $0<x<1andx=\frac{p}{q},$  where $p,q\in \{1,2,3,4,5,6\}$ , is

As $0<x<1,$  we have $p<q.\text{}Ifp=1,q$  may be 2,3,4,5,6 etc.

When $p,q$  have a common factor, we get some rational numbers which are not different from those already counted. There are 4 such numbers:$\frac{2}{4},\frac{2}{6},\frac{3}{6},\frac{4}{6}.$

$\therefore$  The required number of rational numbers =${ }^6{C}_2-4=$15-4=11.