21/3 × 3/4 + (3 1/2 − 1 5/6) ÷ 2/3

Выполним действия по порядку:

\[\frac{21}{3}\cdot\frac{3}{4}=7\cdot\frac{3}{4}=\frac{21}{4}.\]

\[3\frac{1}{2}-1\frac{5}{6}=\frac{7}{2}-\frac{11}{6}=\frac{21}{6}-\frac{11}{6}=\frac{10}{6}=\frac{5}{3}.\]

\[\frac{5}{3}:\frac{2}{3}=\frac{5}{3}\cdot\frac{3}{2}=\frac{5}{2}.\]

\[\frac{21}{4}+\frac{5}{2}=\frac{21}{4}+\frac{10}{4}=\frac{31}{4}=7\frac{3}{4}.\]

Ответ: \(7\frac{3}{4}\).