Realiza las siguientes operaciones. \( \begin{array}{l}\text { a. }\left(-\frac{12}{13}\right) \times\left(-\frac{7}{15}\right) \quad \text { \& }\left(-\frac{32}{11}\right) \times \frac{6}{25} \\ \begin{array}{l}\text { b. } \frac{35}{8} \times\left(-\frac{9}{31}\right) \\ \text { c. }\left(-\frac{15}{26}\right) \div\left(-\frac{24}{7}\right) \\ \text { d. }\left(\frac{1}{9}\right) \div \frac{8}{9} \\ \left.\text { d. }\left(-\frac{1}{2}\right) \times \frac{9}{7}\right) \div\left(\left(-\frac{11}{3}\right)+\frac{5}{12}\right) \\ \text { c. }\left(\frac{15}{18}-\frac{3}{6}\right) \times\left(\left(-\frac{13}{25}\right)+\frac{5}{10}\right)\end{array}\end{array} \$ l \)

Vamos a resolver las operaciones paso a paso. a. 1. \(\left(-\frac{12}{13}\right) \times \left(-\frac{7}{15}\right) = \frac{12 \times 7}{13 \times 15} = \frac{84}{195}\). Simplificando, \(\frac{84}{195} = \frac{28}{65}\). 2. \(\left(-\frac{32}{11}\right) \times \frac{6}{25} = \frac{-32 \times 6}{11 \times 25} = \frac{-192}{275}\). b. \(\frac{35}{8} \times \left(-\frac{9}{31}\right) = \frac{35 \times -9}{8 \times 31} = \frac{-315}{248}\). c. \(\left(-\frac{15}{26}\right) \div \left(-\frac{24}{7}\right) = \left(-\frac{15}{26}\right) \times \left(-\frac{7}{24}\right) = \frac{15 \times 7}{26 \times 24} = \frac{105}{624}\). Simplificando, \(\frac{105}{624} = \frac{35}{208}\). d. 1. \(\left(\frac{1}{9}\right) \div \frac{8}{9} = \frac{1}{9} \times \frac{9}{8} = \frac{1}{8}\). 2. \(\left(-\frac{1}{2}\right) \times \frac{9}{7} = -\frac{9}{14}\), y \(\left(-\frac{11}{3}\right) + \frac{5}{12} = -\frac{44}{12} + \frac{5}{12} = -\frac{39}{12} = -\frac{13}{4}\). Así que, \(-\frac{9}{14} \div -\frac{13}{4} = -\frac{9}{14} \times -\frac{4}{13} = \frac{36}{182} = \frac{18}{91}\). e. \(\left(\frac{15}{18} - \frac{3}{6}\right) \times \left(\left(-\frac{13}{25}\right) + \frac{5}{10}\right)\): 1. \(\frac{3}{6} = \frac{1}{2}\), así que \(\frac{15}{18} - \frac{9}{18} = \frac{6}{18} = \frac{1}{3}\). 2. \(\left(-\frac{13}{25}\right) + \frac{5}{10} = -\frac{13}{25} + \frac{5}{10} = -\frac{13}{25} + \frac{12.5}{25} = -\frac{0.5}{25} = -\frac{1}{50}\). Entonces, \(\frac{1}{3} \times \left(-\frac{1}{50}\right) = -\frac{1}{150}\). Por lo tanto, las respuestas son: a. \(\frac{28}{65}\) y \(\frac{-192}{275}\) b. \(\frac{-315}{248}\) c. \(\frac{35}{208}\) d. \(\frac{1}{8}\) y \(\frac{18}{91}\) e. \(-\frac{1}{150}\)