3. Вычислите: \(\frac{11}{12} : \frac{19}{2} - 9 \frac{2}{3} + 1 \frac{15}{8} \cdot \frac{2}{5}\). Запишите полностью решение и ответ.

3. Вычислим: \(\frac{11}{12} : \frac{19}{2} - 9 \frac{2}{3} + 1 \frac{15}{8} \cdot \frac{2}{5}\).

1) \(\frac{11}{12} : \frac{19}{2} = \frac{11}{12} \cdot \frac{2}{19} = \frac{11 \cdot 2}{12 \cdot 19} = \frac{11 \cdot 1}{6 \cdot 19} = \frac{11}{114}\)

2) \(9 \frac{2}{3} = \frac{9 \cdot 3 + 2}{3} = \frac{29}{3}\)

3) \(1 \frac{15}{8} = \frac{1 \cdot 8 + 15}{8} = \frac{23}{8}\)

4) \(\frac{23}{8} \cdot \frac{2}{5} = \frac{23 \cdot 2}{8 \cdot 5} = \frac{23 \cdot 1}{4 \cdot 5} = \frac{23}{20}\)

5) \(\frac{11}{114} - \frac{29}{3} = \frac{11}{114} - \frac{29 \cdot 38}{3 \cdot 38} = \frac{11}{114} - \frac{1102}{114} = \frac{11 - 1102}{114} = \frac{-1091}{114}\)

6) \(\frac{-1091}{114} + \frac{23}{20} = \frac{-1091 \cdot 10}{114 \cdot 10} + \frac{23 \cdot 57}{20 \cdot 57} = \frac{-10910}{1140} + \frac{1311}{1140} = \frac{-10910 + 1311}{1140} = \frac{-9599}{1140} = -8 \frac{479}{1140}\)

Ответ: \(-8 \frac{479}{1140}\)