$$13\frac{1}{2}:1\frac{1}{3}+16\frac{1}{2}\cdot 1\frac{5}{11}+19\frac{1}{4}:\frac{4}{25} = \frac{27}{2}:\frac{4}{3} + \frac{33}{2} \cdot \frac{16}{11} + \frac{77}{4}:\frac{4}{25} =$$
$$= \frac{27 \cdot 3}{2 \cdot 4} + \frac{33 \cdot 16}{2 \cdot 11} + \frac{77 \cdot 25}{4 \cdot 4} = \frac{81}{8} + \frac{3 \cdot 8}{1} + \frac{1925}{16} = $$
$$= \frac{81}{8} + 24 + \frac{1925}{16} = \frac{81 \cdot 2 + 24 \cdot 16 + 1925}{16} = \frac{162 + 384 + 1925}{16} =$$
$$= \frac{2471}{16} = 154 \frac{7}{16}$$
Ответ: $$154 \frac{7}{16}$$