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

Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{1}{9}}{\frac{8}{9}}\) - step1: Multiply by the reciprocal: \(\frac{1}{9}\times \frac{9}{8}\) - step2: Reduce the numbers: \(1\times \frac{1}{8}\) - step3: Multiply: \(\frac{1}{8}\) Calculate or simplify the expression \( (35/8)*(-9/31) \). Calculate the value by following steps: - step0: Calculate: \(\frac{35}{8}\left(\frac{-9}{31}\right)\) - step1: Rewrite the fraction: \(\frac{35}{8}\left(-\frac{9}{31}\right)\) - step2: Multiply the numbers: \(-\frac{35}{8}\times \frac{9}{31}\) - step3: Multiply the fractions: \(-\frac{35\times 9}{8\times 31}\) - step4: Multiply: \(-\frac{315}{248}\) Calculate or simplify the expression \( ((15/18)-(3/6))*((-13/25)+(5/10)) \). Calculate the value by following steps: - step0: Calculate: \(\left(\left(\frac{15}{18}\right)-\left(\frac{3}{6}\right)\right)\left(\left(\frac{-13}{25}\right)+\left(\frac{5}{10}\right)\right)\) - step1: Reduce the fraction: \(\left(\frac{5}{6}-\left(\frac{3}{6}\right)\right)\left(\left(\frac{-13}{25}\right)+\left(\frac{5}{10}\right)\right)\) - step2: Reduce the fraction: \(\left(\frac{5}{6}-\frac{1}{2}\right)\left(\left(\frac{-13}{25}\right)+\left(\frac{5}{10}\right)\right)\) - step3: Subtract the numbers: \(\frac{1}{3}\left(\left(\frac{-13}{25}\right)+\left(\frac{5}{10}\right)\right)\) - step4: Rewrite the fraction: \(\frac{1}{3}\left(\left(-\frac{13}{25}\right)+\left(\frac{5}{10}\right)\right)\) - step5: Remove the parentheses: \(\frac{1}{3}\left(-\frac{13}{25}+\left(\frac{5}{10}\right)\right)\) - step6: Reduce the fraction: \(\frac{1}{3}\left(-\frac{13}{25}+\frac{1}{2}\right)\) - step7: Add the numbers: \(\frac{1}{3}\left(-\frac{1}{50}\right)\) - step8: Multiply the numbers: \(-\frac{1}{3}\times \frac{1}{50}\) - step9: Multiply the fractions: \(-\frac{1}{3\times 50}\) - step10: Multiply: \(-\frac{1}{150}\) Calculate or simplify the expression \( (-15/26)/(-24/7) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\frac{-15}{26}\right)}{\left(\frac{-24}{7}\right)}\) - step1: Remove the parentheses: \(\frac{\frac{-15}{26}}{\frac{-24}{7}}\) - step2: Rewrite the fraction: \(\frac{-\frac{15}{26}}{\frac{-24}{7}}\) - step3: Rewrite the fraction: \(\frac{-\frac{15}{26}}{-\frac{24}{7}}\) - step4: Multiply by the reciprocal: \(-\frac{15}{26}\left(-\frac{7}{24}\right)\) - step5: Use the rules for multiplication and division: \(\frac{15}{26}\times \frac{7}{24}\) - step6: Reduce the numbers: \(\frac{5}{26}\times \frac{7}{8}\) - step7: Multiply the fractions: \(\frac{5\times 7}{26\times 8}\) - step8: Multiply: \(\frac{35}{208}\) Calculate or simplify the expression \( (-12/13)*(-7/15) \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{-12}{13}\right)\left(\frac{-7}{15}\right)\) - step1: Rewrite the fraction: \(\left(-\frac{12}{13}\right)\left(\frac{-7}{15}\right)\) - step2: Remove the parentheses: \(-\frac{12}{13}\left(\frac{-7}{15}\right)\) - step3: Rewrite the fraction: \(-\frac{12}{13}\left(-\frac{7}{15}\right)\) - step4: Use the rules for multiplication and division: \(\frac{12}{13}\times \frac{7}{15}\) - step5: Reduce the numbers: \(\frac{4}{13}\times \frac{7}{5}\) - step6: Multiply the fractions: \(\frac{4\times 7}{13\times 5}\) - step7: Multiply: \(\frac{28}{65}\) Calculate or simplify the expression \( (-32/11)*(6/25) \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{-32}{11}\right)\times \frac{6}{25}\) - step1: Rewrite the fraction: \(\left(-\frac{32}{11}\right)\times \frac{6}{25}\) - step2: Remove the parentheses: \(-\frac{32}{11}\times \frac{6}{25}\) - step3: Multiply the fractions: \(-\frac{32\times 6}{11\times 25}\) - step4: Multiply: \(-\frac{192}{275}\) Calculate or simplify the expression \( ((-1/2)*(9/7))/((-11/3)+(5/12)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\left(\frac{-1}{2}\right)\times \frac{9}{7}\right)}{\left(\left(\frac{-11}{3}\right)+\frac{5}{12}\right)}\) - step1: Remove the parentheses: \(\frac{\left(\frac{-1}{2}\right)\times \frac{9}{7}}{\left(\frac{-11}{3}\right)+\frac{5}{12}}\) - step2: Rewrite the fraction: \(\frac{\left(-\frac{1}{2}\right)\times \frac{9}{7}}{\left(\frac{-11}{3}\right)+\frac{5}{12}}\) - step3: Remove the parentheses: \(\frac{-\frac{1}{2}\times \frac{9}{7}}{\left(\frac{-11}{3}\right)+\frac{5}{12}}\) - step4: Rewrite the fraction: \(\frac{-\frac{1}{2}\times \frac{9}{7}}{\left(-\frac{11}{3}\right)+\frac{5}{12}}\) - step5: Remove the parentheses: \(\frac{-\frac{1}{2}\times \frac{9}{7}}{-\frac{11}{3}+\frac{5}{12}}\) - step6: Multiply the numbers: \(\frac{-\frac{9}{14}}{-\frac{11}{3}+\frac{5}{12}}\) - step7: Add the numbers: \(\frac{-\frac{9}{14}}{-\frac{13}{4}}\) - step8: Multiply by the reciprocal: \(-\frac{9}{14}\left(-\frac{4}{13}\right)\) - step9: Use the rules for multiplication and division: \(\frac{9}{14}\times \frac{4}{13}\) - step10: Reduce the numbers: \(\frac{9}{7}\times \frac{2}{13}\) - step11: Multiply the fractions: \(\frac{9\times 2}{7\times 13}\) - step12: Multiply: \(\frac{18}{91}\) Aquí están los resultados de las operaciones solicitadas: ### a. Multiplicaciones 1. \( \left(-\frac{12}{13}\right) \times \left(-\frac{7}{15}\right) = \frac{28}{65} \) 2. \( \left(-\frac{32}{11}\right) \times \frac{6}{25} = -\frac{192}{275} \) ### b. Multiplicación \( \frac{35}{8} \times \left(-\frac{9}{31}\right) = -\frac{315}{248} \) ### c. División \( \left(-\frac{15}{26}\right) \div \left(-\frac{24}{7}\right) = \frac{35}{208} \) ### d. División 1. \( \left(\frac{1}{9}\right) \div \frac{8}{9} = \frac{1}{8} \) 2. \( \left(-\frac{1}{2}\right) \times \frac{9}{7} \div \left(\left(-\frac{11}{3}\right) + \frac{5}{12}\right) = \frac{18}{91} \) ### e. Multiplicación \( \left(\frac{15}{18} - \frac{3}{6}\right) \times \left(\left(-\frac{13}{25}\right) + \frac{5}{10}\right) = -\frac{1}{150} \) Si necesitas más detalles sobre algún cálculo específico, no dudes en preguntar.