Simplify \(\left\{\left(\dfrac{20}{36}\right)\div\left(\dfrac{20}{5}\right)\right\}\div\left(\dfrac{5}{11}\times\dfrac{22}{15}+\dfrac{3}{12}\right)+\dfrac{5}{5}\div\dfrac{33}{21}\text{ of }\dfrac{21}{5}\)
\(\tfrac{10}{33}\)
\(\left(\tfrac{20}{36}\right)\div\left(\tfrac{20}{5}\right) = \tfrac{20}{36}\times\tfrac{5}{20} = \tfrac{5}{36}\).
Inside the bracket: \(\tfrac{5}{11}\times\tfrac{22}{15} = \tfrac23\), plus \(\tfrac{3}{12}=\tfrac14\) gives \(\tfrac23+\tfrac14 = \tfrac{11}{12}\).
First part: \(\tfrac{5}{36}\div\tfrac{11}{12} = \tfrac{5}{36}\times\tfrac{12}{11} = \tfrac{5}{33}\).
For the second part, \(\tfrac55=1\), and \(\tfrac{33}{21}\text{ of }\tfrac{21}{5} = \tfrac{33}{5}\), so \(1\div\tfrac{33}{5} = \tfrac{5}{33}\).
Adding both parts: \(\tfrac{5}{33}+\tfrac{5}{33} = \tfrac{10}{33}\).
Hence, the simplified value of the expression is \(\tfrac{10}{33}\).
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