Помоги решить примеры с дробями: 0.5 + 9/13

1. $0.5 + \frac{9}{13} = \frac{1}{2} + \frac{9}{13} = \frac{13}{26} + \frac{18}{26} = \frac{31}{26} = 1\frac{5}{26}$ 2. $6\frac{3}{8} + 5\frac{7}{25} + 6\frac{1}{8} + 1\frac{3}{25} = (6\frac{3}{8} + 6\frac{1}{8}) + (5\frac{7}{25} + 1\frac{3}{25}) = 12\frac{4}{8} + 6\frac{10}{25} = 12\frac{1}{2} + 6\frac{2}{5} = 12\frac{5}{10} + 6\frac{4}{10} = 18\frac{9}{10}$ 3. Решим уравнение: $$9\frac{2}{5} - (b + 1\frac{21}{40}) = 6\frac{7}{10}$$ $$9\frac{2}{5} - b - 1\frac{21}{40} = 6\frac{7}{10}$$ $$-b = 6\frac{7}{10} - 9\frac{2}{5} + 1\frac{21}{40}$$ $$-b = 6\frac{28}{40} - 9\frac{16}{40} + 1\frac{21}{40}$$ $$-b = 7\frac{49}{40} - 9\frac{16}{40}$$ $$-b = -2\frac{33}{40}$$ $$b = 2\frac{33}{40}$$ 4. $44 \cdot \frac{13}{72} = \frac{44 \cdot 13}{72} = \frac{11 \cdot 13}{18} = \frac{143}{18} = 7\frac{17}{18}$ 5. $\frac{56}{45} \cdot \frac{27}{64} = \frac{7 \cdot 3}{5 \cdot 8} = \frac{21}{40}$ 6. $1\frac{1}{2} \cdot 5\frac{1}{2} \cdot 2\frac{6}{11} = \frac{3}{2} \cdot \frac{11}{2} \cdot \frac{28}{11} = \frac{3 \cdot 1 \cdot 14}{1 \cdot 1 \cdot 2} = 3 \cdot 7 = 21$ 7. $7\frac{15}{22} + 1\frac{8}{11} \cdot 2\frac{1}{2} = 7\frac{15}{22} + \frac{19}{11} \cdot \frac{5}{2} = 7\frac{15}{22} + \frac{95}{22} = 7\frac{15}{22} + 4\frac{7}{22} = 11\frac{22}{22} = 12$ 8. а) $(\frac{1}{2} + \frac{5}{7})(1\frac{9}{10} - 1\frac{1}{5}) = (\frac{7}{14} + \frac{10}{14})(\frac{19}{10} - \frac{6}{5}) = \frac{17}{14}(\frac{19}{10} - \frac{12}{10}) = \frac{17}{14} \cdot \frac{7}{10} = \frac{17}{2} \cdot \frac{1}{10} = \frac{17}{20}$ б) $\frac{1}{2} + \frac{5}{7}(1\frac{9}{10} - 1\frac{1}{5}) = \frac{1}{2} + \frac{5}{7}(\frac{19}{10} - \frac{6}{5}) = \frac{1}{2} + \frac{5}{7}(\frac{19}{10} - \frac{12}{10}) = \frac{1}{2} + \frac{5}{7} \cdot \frac{7}{10} = \frac{1}{2} + \frac{1}{2} = 1$ 9. $\frac{5}{6} \cdot \frac{21}{40} \cdot \frac{25}{49} \cdot \frac{8}{15} = \frac{1 \cdot 3 \cdot 5 \cdot 8}{6 \cdot 8 \cdot 7 \cdot 3} = \frac{5}{42}$ 10. а) $(\frac{1}{2})^2 = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$ б) $(1\frac{1}{2})^2 = (\frac{3}{2})^2 = \frac{3}{2} \cdot \frac{3}{2} = \frac{9}{4} = 2\frac{1}{4}$ 11. $(\frac{13}{14} + \frac{4}{7})^2 \cdot 1\frac{7}{9} = (\frac{13}{14} + \frac{8}{14})^2 \cdot \frac{16}{9} = (\frac{21}{14})^2 \cdot \frac{16}{9} = (\frac{3}{2})^2 \cdot \frac{16}{9} = \frac{9}{4} \cdot \frac{16}{9} = \frac{1}{1} \cdot \frac{4}{1} = 4$ 12. $\frac{16}{9} \cdot (\frac{15}{16} + \frac{3}{4}) = \frac{16}{9} \cdot \frac{15}{16} + \frac{16}{9} \cdot \frac{3}{4} = \frac{1}{9} \cdot 15 + \frac{4}{3} \cdot \frac{1}{1} = \frac{15}{9} + \frac{4}{3} = \frac{5}{3} + \frac{4}{3} = \frac{9}{3} = 3$ 13. $6 : \frac{6}{7} = 6 \cdot \frac{7}{6} = \frac{1}{1} \cdot \frac{7}{1} = 7$ 14. $\frac{5}{7} : \frac{4}{11} = \frac{5}{7} \cdot \frac{11}{4} = \frac{55}{28} = 1\frac{27}{28}$ 15. $6\frac{4}{5} : 8\frac{2}{3} = \frac{34}{5} : \frac{26}{3} = \frac{34}{5} \cdot \frac{3}{26} = \frac{17}{5} \cdot \frac{3}{13} = \frac{51}{65}$