Вычислите: 4/15 + 6/35 : (2 - 1 41/49) - 1 1/6. Запишите полностью решение и ответ.

Привет! Давай решим примеры с дробями по порядку. 40. $\frac{4}{15} + \frac{6}{35} : (2 - 1\frac{41}{49}) - 1\frac{1}{6}$ 1) $2 - 1\frac{41}{49} = 1 - \frac{41}{49} = \frac{49}{49} - \frac{41}{49} = \frac{8}{49}$ 2) $\frac{6}{35} : \frac{8}{49} = \frac{6}{35} \cdot \frac{49}{8} = \frac{3}{5} \cdot \frac{7}{4} = \frac{21}{20} = 1\frac{1}{20}$ 3) $\frac{4}{15} + 1\frac{1}{20} = \frac{16}{60} + 1\frac{3}{60} = 1\frac{19}{60}$ 4) $1\frac{19}{60} - 1\frac{1}{6} = 1\frac{19}{60} - 1\frac{10}{60} = \frac{9}{60} = \frac{3}{20}$ **Ответ: 3/20** 41. $\frac{11}{14} + \frac{8}{15} : (4 - 2\frac{26}{27}) - 1\frac{1}{10}$ 1) $4 - 2\frac{26}{27} = 1\frac{1}{27} = \frac{28}{27}$ 2) $\frac{8}{15} : \frac{28}{27} = \frac{8}{15} \cdot \frac{27}{28} = \frac{2}{5} \cdot \frac{9}{7} = \frac{18}{35}$ 3) $\frac{11}{14} + \frac{18}{35} = \frac{55}{70} + \frac{36}{70} = \frac{91}{70} = 1\frac{21}{70} = 1\frac{3}{10}$ 4) $1\frac{3}{10} - 1\frac{1}{10} = \frac{2}{10} = \frac{1}{5}$ **Ответ: 1/5** 42. $\frac{17}{12} : 3\frac{2}{5} - \frac{2}{5} \cdot (2 - 1\frac{1}{12})$ 1) $2 - 1\frac{1}{12} = \frac{11}{12}$ 2) $\frac{17}{12} : \frac{17}{5} = \frac{17}{12} \cdot \frac{5}{17} = \frac{5}{12}$ 3) $\frac{2}{5} \cdot \frac{11}{12} = \frac{1}{5} \cdot \frac{11}{6} = \frac{11}{30}$ 4) $\frac{5}{12} - \frac{11}{30} = \frac{25}{60} - \frac{22}{60} = \frac{3}{60} = \frac{1}{20}$ **Ответ: 1/20** 43. $-\frac{6}{5} + \frac{12}{35} \cdot 1\frac{13}{15} + 5 : 7\frac{1}{2}$ 1) $\frac{12}{35} \cdot \frac{28}{15} = \frac{4}{5} \cdot \frac{4}{5} = \frac{16}{25}$ 2) $5 : \frac{15}{2} = 5 \cdot \frac{2}{15} = \frac{2}{3}$ 3) $-\frac{6}{5} + \frac{16}{25} + \frac{2}{3} = -\frac{90}{75} + \frac{48}{75} + \frac{50}{75} = \frac{8}{75}$ **Ответ: 8/75** 44. $\frac{7}{30} + \frac{9}{8} : (4 - 3\frac{7}{22}) - 1\frac{5}{6}$ 1) $4 - 3\frac{7}{22} = \frac{15}{22}$ 2) $\frac{9}{8} : \frac{15}{22} = \frac{9}{8} \cdot \frac{22}{15} = \frac{3}{4} \cdot \frac{11}{5} = \frac{33}{20} = 1\frac{13}{20}$ 3) $\frac{7}{30} + 1\frac{13}{20} = \frac{14}{60} + 1\frac{39}{60} = 1\frac{53}{60}$ 4) $1\frac{53}{60} - 1\frac{5}{6} = 1\frac{53}{60} - 1\frac{50}{60} = \frac{3}{60} = \frac{1}{20}$ **Ответ: 1/20** 45. $\frac{25}{12} : 1\frac{7}{8} - \frac{3}{5} \cdot (4 - 2\frac{11}{18})$ 1) $4 - 2\frac{11}{18} = 1\frac{7}{18} = \frac{25}{18}$ 2) $\frac{25}{12} : \frac{15}{8} = \frac{25}{12} \cdot \frac{8}{15} = \frac{5}{3} \cdot \frac{2}{3} = \frac{10}{9}$ 3) $\frac{3}{5} \cdot \frac{25}{18} = \frac{1}{1} \cdot \frac{5}{6} = \frac{5}{6}$ 4) $\frac{10}{9} - \frac{5}{6} = \frac{20}{18} - \frac{15}{18} = \frac{5}{18}$ **Ответ: 5/18** 46. $-1 + (\frac{7}{12} + \frac{5}{6}) : \frac{5}{6} - \frac{2}{3}$ 1) $\frac{7}{12} + \frac{10}{12} = \frac{17}{12}$ 2) $\frac{17}{12} : \frac{5}{6} = \frac{17}{12} \cdot \frac{6}{5} = \frac{17}{10} = 1,7$ 3) $-1 + 1,7 - \frac{2}{3} = 0,7 - \frac{2}{3} = \frac{7}{10} - \frac{2}{3} = \frac{21}{30} - \frac{20}{30} = \frac{1}{30}$ **Ответ: 1/30** 47. $2\frac{1}{2} + \frac{9}{16} \cdot 1\frac{5}{27} - 3\frac{3}{7} : \frac{27}{28}$ 1) $\frac{9}{16} \cdot \frac{32}{27} = \frac{1}{1} \cdot \frac{2}{3} = \frac{2}{3}$ 2) $\frac{24}{7} : \frac{27}{28} = \frac{24}{7} \cdot \frac{28}{27} = \frac{8}{1} \cdot \frac{4}{9} = \frac{32}{9} = 3\frac{5}{9}$ 3) $2\frac{1}{2} + \frac{2}{3} - 3\frac{5}{9} = 2\frac{9}{18} + \frac{12}{18} - 3\frac{10}{18} = 2\frac{21}{18} - 3\frac{10}{18} = -\frac{7}{18}$ **Ответ: -7/18** 48. $-2 + (\frac{11}{24} + \frac{5}{6}) : 1\frac{15}{16} - \frac{2}{5}$ 1) $\frac{11}{24} + \frac{20}{24} = \frac{31}{24}$ 2) $\frac{31}{24} : \frac{31}{16} = \frac{31}{24} \cdot \frac{16}{31} = \frac{16}{24} = \frac{2}{3}$ 3) $-2 + \frac{2}{3} - \frac{2}{5} = -\frac{30}{15} + \frac{10}{15} - \frac{6}{15} = -\frac{26}{15} = -1\frac{11}{15}$ **Ответ: -1 11/15** 49. $\frac{3}{4} + 3\frac{3}{5} \cdot (\frac{5}{18} - \frac{7}{24}) - \frac{1}{5}$ 1) $\frac{5}{18} - \frac{7}{24} = \frac{20}{72} - \frac{21}{72} = -\frac{1}{72}$ 2) $\frac{18}{5} \cdot (-\frac{1}{72}) = -\frac{1}{5} \cdot \frac{1}{4} = -\frac{1}{20}$ 3) $\frac{3}{4} - \frac{1}{20} - \frac{1}{5} = \frac{15}{20} - \frac{1}{20} - \frac{4}{20} = \frac{10}{20} = \frac{1}{2}$ **Ответ: 1/2**