$$2\frac{1}{2} \cdot 3\frac{1}{15} = {\frac{5}{2}} \cdot {\frac{46}{15}} = {\frac{5 \cdot 46}{2 \cdot 15}} = {\frac{5 \cdot 23 \cdot 2}{2 \cdot 3 \cdot 5}} = {\frac{23}{3}} = 7\frac{2}{3}$$
Ответ: $$7\frac{2}{3}$$