О $$15:\frac{5}{18}:3\frac{3}{8} \cdot 2\frac{1}{16}-32\frac{7}{15}$$

Выполним действия с дробями.

1. $$15:\frac{5}{18}=15 \cdot \frac{18}{5}=\frac{15 \cdot 18}{5}=\frac{270}{5}=54$$
2. $$3\frac{3}{8}=\frac{27}{8}$$
3. $$2\frac{1}{16}=\frac{33}{16}$$
4. $$54:\frac{27}{8}=54 \cdot \frac{8}{27}=\frac{54 \cdot 8}{27}=\frac{432}{27}=16$$
5. $$16 \cdot \frac{33}{16}=\frac{16 \cdot 33}{16}=33$$
6. $$32\frac{7}{15}=\frac{487}{15}$$
7. $$33-32\frac{7}{15}=33-\frac{487}{15}=\frac{33 \cdot 15}{15}-\frac{487}{15}=\frac{495}{15}-\frac{487}{15}=\frac{8}{15}$$

Ответ: $$\frac{8}{15}$$