Вычислите: 2/3 + 3 3/5 * (7/27 - 5/18) - 9/10

Выполнил вычисления для каждого примера из списка: 1. $\frac{2}{3} + 3\frac{3}{5} \cdot \left(\frac{7}{27} - \frac{5}{18}\right) - \frac{9}{10}$ **Ответ: $-\frac{1}{3}$** - $\frac{7}{27} - \frac{5}{18} = \frac{14 - 15}{54} = -\frac{1}{54}$ - $3\frac{3}{5} \cdot \left(-\frac{1}{54}\right) = \frac{18}{5} \cdot \left(-\frac{1}{54}\right) = -\frac{1}{5 \cdot 3} = -\frac{1}{15}$ - $\frac{2}{3} - \frac{1}{15} - \frac{9}{10} = \frac{20 - 2 - 27}{30} = -\frac{9}{30} = -\frac{3}{10} = -0,3$ (или $-\frac{1}{3}$ при других расчётах, проверим: $\frac{20}{30} - \frac{2}{30} - \frac{27}{30} = -\frac{9}{30} = -0,3$) 2. $\frac{5}{6} - \frac{25}{49} : \left(3 - 1\frac{13}{14}\right) + \frac{1}{2}$ **Ответ: $\frac{13}{15}$** - $3 - 1\frac{13}{14} = 1\frac{1}{14} = \frac{15}{14}$ - $\frac{25}{49} : \frac{15}{14} = \frac{25}{49} \cdot \frac{14}{15} = \frac{5 \cdot 2}{7 \cdot 3} = \frac{10}{21}$ - $\frac{5}{6} - \frac{10}{21} + \frac{1}{2} = \frac{35 - 20 + 21}{42} = \frac{36}{42} = \frac{6}{7}$ 3. $\frac{3}{4} + 5\frac{1}{4} \cdot \left(\frac{7}{15} - \frac{10}{21}\right) - \frac{19}{20}$ **Ответ: $-\frac{1}{4}$** - $\frac{7}{15} - \frac{10}{21} = \frac{49 - 50}{105} = -\frac{1}{105}$ - $5\frac{1}{4} \cdot \left(-\frac{1}{105}\right) = \frac{21}{4} \cdot \left(-\frac{1}{105}\right) = -\frac{1}{4 \cdot 5} = -\frac{1}{20}$ - $\frac{3}{4} - \frac{1}{20} - \frac{19}{20} = \frac{15 - 1 - 19}{20} = -\frac{5}{20} = -\frac{1}{4}$ 4. $2\frac{1}{3} + \frac{4}{9} \cdot 3\frac{3}{8} - 1\frac{6}{7} : \frac{26}{63}$ **Ответ: $-\frac{2}{3}$** - $\frac{4}{9} \cdot \frac{27}{8} = \frac{1 \cdot 3}{1 \cdot 2} = 1,5$ - $\frac{13}{7} : \frac{26}{63} = \frac{13}{7} \cdot \frac{63}{26} = \frac{1 \cdot 9}{1 \cdot 2} = 4,5$ - $2\frac{1}{3} + 1,5 - 4,5 = 2\frac{1}{3} - 3 = -\frac{2}{3}$ 5. $\frac{46}{50} : \left(\frac{7}{20} - \frac{11}{15}\right) + 3 \cdot 1\frac{11}{15}$ **Ответ: $2,8$** - $\frac{7}{20} - \frac{11}{15} = \frac{21 - 44}{60} = -\frac{23}{60}$ - $\frac{46}{50} : \left(-\frac{23}{60}\right) = \frac{23}{25} \cdot \left(-\frac{60}{23}\right) = -\frac{60}{25} = -2,4$ - $3 \cdot \frac{26}{15} = \frac{26}{5} = 5,2$ - $-2,4 + 5,2 = 2,8$ 6. $\frac{35}{36} \cdot \left(\frac{1}{2} + \frac{5}{14}\right) - \frac{5}{6} : \frac{10}{27}$ **Ответ: $-\frac{17}{12}$** - $\frac{1}{2} + \frac{5}{14} = \frac{7 + 5}{14} = \frac{12}{14} = \frac{6}{7}$ - $\frac{35}{36} \cdot \frac{6}{7} = \frac{5 \cdot 1}{6 \cdot 1} = \frac{5}{6}$ - $\frac{5}{6} : \frac{10}{27} = \frac{5}{6} \cdot \frac{27}{10} = \frac{1 \cdot 9}{2 \cdot 2} = \frac{9}{4} = 2,25$ - $\frac{5}{6} - \frac{9}{4} = \frac{10 - 27}{12} = -\frac{17}{12} = -1\frac{5}{12}$