Arrange in ascending order:

$\dfrac{5}{6}, \dfrac{7}{9}, \dfrac{11}{12} \text{ and } \dfrac{13}{18}$

All the denominators are already positive, so write each rational number with the LCM of the denominators as the common denominator and arrange the numerators in an increasing order.

LCM of 6, 9, 12 and 18 = 36

$\Rightarrow \dfrac{5}{6} = \dfrac{5 \times 6}{6 \times 6} = \dfrac{30}{36} \\[1em] \Rightarrow \dfrac{7}{9} = \dfrac{7 \times 4}{9 \times 4} = \dfrac{28}{36} \\[1em] \Rightarrow \dfrac{11}{12} = \dfrac{11 \times 3}{12 \times 3} = \dfrac{33}{36} \\[1em] \Rightarrow \dfrac{13}{18} = \dfrac{13 \times 2}{18 \times 2} = \dfrac{26}{36}$

As 26 < 28 < 30 < 33

So, $\dfrac{26}{36} \lt \dfrac{28}{36} \lt \dfrac{30}{36} \lt \dfrac{33}{36}$

$\Rightarrow \dfrac{13}{18} \lt \dfrac{7}{9} \lt \dfrac{5}{6} \lt \dfrac{11}{12}$

Hence, the given rational numbers in ascending order are $\mathbf{\dfrac{13}{18}, \dfrac{7}{9}, \dfrac{5}{6} \text{ and } \dfrac{11}{12}}$.