In order to arrange the fractions in ascending order, all of them should have the same denominator.
For this, we have to first calculate the LCM of the denominators.
The LCM of 5,11,9,6 and 13 is 2574

Representing all the fractions with denominator 12870, the fractions look as below.

$\frac{4}{5} = \frac{10296}{12870}$

$\frac{9}{11} = \frac{10530}{12870}$

$\frac{7}{9} = \frac{10010}{12870}$

$\frac{5}{6} = \frac{10725}{12870}$

$\frac{11}{13} = \frac{10890}{12870}$

Arranging them in ascending order, we get the following order
$\frac{10010}{12870}$, $\frac{10296}{12870}$, $\frac{10530}{12870}$, $\frac{10725}{12870}$, $\frac{10890}{12870}$

So, the fourth number in order is $\frac{10725}{12870}$ which is $\frac{5}{6}$

In order to arrange the fractions in ascending order, all of them should have the same denominator.
For this, we have to first calculate the LCM of the denominators.
The LCM of 5,11,9,6 and 13 is 2574

Representing all the fractions with denominator 12870, the fractions look as below.

$\frac{4}{5} = \frac{10296}{12870}$

$\frac{9}{11} = \frac{10530}{12870}$

$\frac{7}{9} = \frac{10010}{12870}$

$\frac{5}{6} = \frac{10725}{12870}$

$\frac{11}{13} = \frac{10890}{12870}$

Arranging them in ascending order, we get the following order
$\frac{10010}{12870}$, $\frac{10296}{12870}$, $\frac{10530}{12870}$, $\frac{10725}{12870}$, $\frac{10890}{12870}$

So, the fourth number in order is $\frac{10725}{12870}$ which is $\frac{5}{6}$