Вычислите: 2 4/15 - (2 - 1 1/15) : 4/9 + 2/3. Запишите полностью решение и ответ.

1. $2\frac{4}{15} - (2 - 1\frac{1}{15}) : \frac{4}{9} + \frac{2}{3}$ 1) $2 - 1\frac{1}{15} = 1\frac{15}{15} - 1\frac{1}{15} = \frac{14}{15}$ 2) $\frac{14}{15} : \frac{4}{9} = \frac{14}{15} \cdot \frac{9}{4} = \frac{7 \cdot 3}{5 \cdot 2} = \frac{21}{10} = 2\frac{1}{10}$ 3) $2\frac{4}{15} - 2\frac{1}{10} = 2\frac{8}{30} - 2\frac{3}{30} = \frac{5}{30} = \frac{1}{6}$ 4) $\frac{1}{6} + \frac{2}{3} = \frac{1}{6} + \frac{4}{6} = \frac{5}{6}$ **Ответ: 5/6** 2. $1\frac{13}{14} - (2 - 1\frac{11}{35}) : \frac{9}{25} + \frac{4}{21}$ 1) $2 - 1\frac{11}{35} = 1\frac{35}{35} - 1\frac{11}{35} = \frac{24}{35}$ 2) $\frac{24}{35} : \frac{9}{25} = \frac{24}{35} \cdot \frac{25}{9} = \frac{8 \cdot 5}{7 \cdot 3} = \frac{40}{21} = 1\frac{19}{21}$ 3) $1\frac{13}{14} - 1\frac{19}{21} = 1\frac{39}{42} - 1\frac{38}{42} = \frac{1}{42}$ 4) $\frac{1}{42} + \frac{4}{21} = \frac{1}{42} + \frac{8}{42} = \frac{9}{42} = \frac{3}{14}$ **Ответ: 3/14** 3. $3\frac{9}{10} - (2 - 1\frac{11}{35}) : \frac{9}{49} + \frac{1}{2}$ 1) $2 - 1\frac{11}{35} = \frac{24}{35}$ 2) $\frac{24}{35} : \frac{9}{49} = \frac{24}{35} \cdot \frac{49}{9} = \frac{8 \cdot 7}{5 \cdot 3} = \frac{56}{15} = 3\frac{11}{15}$ 3) $3\frac{9}{10} - 3\frac{11}{15} = 3\frac{27}{30} - 3\frac{22}{30} = \frac{5}{30} = \frac{1}{6}$ 4) $\frac{1}{6} + \frac{1}{2} = \frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}$ **Ответ: 2/3** 4. $\frac{9}{10} + \frac{4}{9} : (2 - 1\frac{11}{21}) - 1\frac{2}{3}$ 1) $2 - 1\frac{11}{21} = \frac{10}{21}$ 2) $\frac{4}{9} : \frac{10}{21} = \frac{4}{9} \cdot \frac{21}{10} = \frac{2 \cdot 7}{3 \cdot 5} = \frac{14}{15}$ 3) $\frac{9}{10} + \frac{14}{15} = \frac{27}{30} + \frac{28}{30} = \frac{55}{30} = \frac{11}{6} = 1\frac{5}{6}$ 4) $1\frac{5}{6} - 1\frac{2}{3} = 1\frac{5}{6} - 1\frac{4}{6} = \frac{1}{6}$ **Ответ: 1/6** 5. $\frac{9}{22} - \frac{4}{9} : (3 - 1\frac{8}{15}) + \frac{8}{11}$ 1) $3 - 1\frac{8}{15} = 2\frac{15}{15} - 1\frac{8}{15} = 1\frac{7}{15} = \frac{22}{15}$ 2) $\frac{4}{9} : \frac{22}{15} = \frac{4}{9} \cdot \frac{15}{22} = \frac{2 \cdot 5}{3 \cdot 11} = \frac{10}{33}$ 3) $\frac{9}{22} - \frac{10}{33} = \frac{27}{66} - \frac{20}{66} = \frac{7}{66}$ 4) $\frac{7}{66} + \frac{8}{11} = \frac{7}{66} + \frac{48}{66} = \frac{55}{66} = \frac{5}{6}$ **Ответ: 5/6** 6. $\frac{7}{10} - \frac{9}{49} : (3 - 1\frac{13}{14}) + \frac{2}{5}$ 1) $3 - 1\frac{13}{14} = 2\frac{14}{14} - 1\frac{13}{14} = 1\frac{1}{14} = \frac{15}{14}$ 2) $\frac{9}{49} : \frac{15}{14} = \frac{9}{49} \cdot \frac{14}{15} = \frac{3 \cdot 2}{7 \cdot 5} = \frac{6}{35}$ 3) $\frac{7}{10} - \frac{6}{35} = \frac{49}{70} - \frac{12}{70} = \frac{37}{70}$ 4) $\frac{37}{70} + \frac{2}{5} = \frac{37}{70} + \frac{28}{70} = \frac{65}{70} = \frac{13}{14}$ **Ответ: 13/14**