$2\frac{1}{3}\times 5\frac{1}{4}=\frac{7}{3}\times \frac{21}{4}=\frac{147}{12}=\frac{49}{4}$

$3\frac{2}{5}\times 2\frac{1}{7}=\frac{17}{5}\times \frac{15}{7}=\frac{255}{35}=\frac{51}{7}$

$8\frac{1}{6}\div 2\frac{1}{2}=\frac{49}{6}\div \frac{5}{2}=\frac{98}{30}=\frac{49}{15}$