Answer
$\dfrac{15}{22}$
Work Step by Step
RECALL:
(1) $\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{a}{b} \div \dfrac{c}{d}$
(2) $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b}\cdot \dfrac{d}{c}$
Use the rules above to obtain:
$\dfrac{5}{18} \div \dfrac{11}{27}
\\=\dfrac{5}{18} \cdot \dfrac{27}{11}$
Cancel the common factor, $9$, and then simplify to obtain:
$\require{cancel}
=\dfrac{5}{\cancel{18}2} \cdot \dfrac{\cancel{27}3}{11}
\\=\dfrac{5}{2} \cdot \dfrac{3}{11}
\\=\dfrac{5(3)}{2(11)}
\\=\dfrac{15}{22}$
