$$2\frac{4}{13} \cdot (5\frac{4}{12} - 7) - 7 : 3\frac{1}{2} = \frac{30}{13} \cdot (5\frac{1}{3} - 7) - 7 : \frac{7}{2} = \frac{30}{13} \cdot (\frac{16}{3} - 7) - 7 \cdot \frac{2}{7} = \frac{30}{13} \cdot (\frac{16 - 21}{3}) - 2 = \frac{30}{13} \cdot (\frac{-5}{3}) - 2 = \frac{-150}{39} - 2 = \frac{-50}{13} - 2 = \frac{-50 - 26}{13} = \frac{-76}{13} = -5\frac{11}{13}$$
Ответ: $$-5\frac{11}{13}$$