№5. Найдите значение выражения: a) $$4\frac{11}{18}-1\frac{4}{9}$$; б) $$(1\frac{1}{2})^3 - 2\frac{1}{4} \cdot 1\frac{1}{3}$$; в) $$18\frac{3}{14} + (12 - 6\frac{2}{3}) \cdot 1\frac{2}{7}$$; г) $$4\frac{4}{5} \cdot 2\frac{1}{2} + 6\frac{3}{8} \cdot 16\frac{1}{17}$$; д) $$((1\frac{1}{4})^2 - \frac{5}{8}) \cdot 10\frac{2}{3} - 7\frac{1}{3}$$; e) $$1\frac{1}{22} \cdot 3\frac{2}{3} - (2\frac{5}{6} + 3\frac{5}{6} \cdot \frac{7}{23}) \cdot \frac{3}{5}$$; ж) $$(2,5 - 1\frac{1}{6})^2 \cdot \frac{27}{32} - 1\frac{6}{13}$$; з) $$(3\frac{1}{3} - 2\frac{1}{12})^2 \cdot 0,64 + 2\frac{7}{15}$$; н) $$(\frac{4}{5})^2$$; о) $$(\frac{2}{3})^3$$; п) $$(\frac{7}{8})^2$$; р) $$(\frac{5}{4})^3$$. №6. Используя распределительный закон умножения, вычислите: a) $$(4\frac{2}{3}+5\frac{1}{2}) \cdot 6$$; б) $$8\frac{5}{11} \cdot 4\frac{2}{9}+8\frac{5}{11} \cdot 6\frac{7}{9}$$;

Решение: №5 a) $$4\frac{11}{18}-1\frac{4}{9} = \frac{4 \cdot 18 + 11}{18} - \frac{1 \cdot 9 + 4}{9} = \frac{72 + 11}{18} - \frac{9 + 4}{9} = \frac{83}{18} - \frac{13}{9} = \frac{83}{18} - \frac{13 \cdot 2}{9 \cdot 2} = \frac{83}{18} - \frac{26}{18} = \frac{83 - 26}{18} = \frac{57}{18} = \frac{19}{6} = 3\frac{1}{6}$$ б) $$(1\frac{1}{2})^3 - 2\frac{1}{4} \cdot 1\frac{1}{3} = (\frac{3}{2})^3 - \frac{9}{4} \cdot \frac{4}{3} = \frac{27}{8} - \frac{36}{12} = \frac{27}{8} - 3 = \frac{27}{8} - \frac{3 \cdot 8}{8} = \frac{27 - 24}{8} = \frac{3}{8}$$ в) $$18\frac{3}{14} + (12 - 6\frac{2}{3}) \cdot 1\frac{2}{7} = 18\frac{3}{14} + (12 - \frac{20}{3}) \cdot \frac{9}{7} = 18\frac{3}{14} + (\frac{36}{3} - \frac{20}{3}) \cdot \frac{9}{7} = 18\frac{3}{14} + \frac{16}{3} \cdot \frac{9}{7} = 18\frac{3}{14} + \frac{16 \cdot 3}{7} = 18\frac{3}{14} + \frac{48}{7} = 18\frac{3}{14} + 6\frac{6}{7} = 18\frac{3}{14} + 6\frac{12}{14} = 24\frac{15}{14} = 25\frac{1}{14}$$ г) $$4\frac{4}{5} \cdot 2\frac{1}{2} + 6\frac{3}{8} \cdot 16\frac{1}{17} = \frac{24}{5} \cdot \frac{5}{2} + \frac{51}{8} \cdot \frac{273}{17} = \frac{24}{2} + \frac{3 \cdot 273}{8} = 12 + \frac{819}{8} = 12 + 102\frac{3}{8} = 114\frac{3}{8}$$ д) $$((\frac{5}{4})^2 - \frac{5}{8}) \cdot 10\frac{2}{3} - 7\frac{1}{3} = (\frac{25}{16} - \frac{5}{8}) \cdot \frac{32}{3} - \frac{22}{3} = (\frac{25}{16} - \frac{10}{16}) \cdot \frac{32}{3} - \frac{22}{3} = \frac{15}{16} \cdot \frac{32}{3} - \frac{22}{3} = \frac{15 \cdot 2}{3} - \frac{22}{3} = 10 - \frac{22}{3} = \frac{30}{3} - \frac{22}{3} = \frac{8}{3} = 2\frac{2}{3}$$ e) $$1\frac{1}{22} \cdot 3\frac{2}{3} - (2\frac{5}{6} + 3\frac{5}{6} \cdot \frac{7}{23}) \cdot \frac{3}{5} = \frac{23}{22} \cdot \frac{11}{3} - (\frac{17}{6} + \frac{23}{6} \cdot \frac{7}{23}) \cdot \frac{3}{5} = \frac{23}{2 \cdot 3} - (\frac{17}{6} + \frac{7}{6}) \cdot \frac{3}{5} = \frac{23}{6} - \frac{24}{6} \cdot \frac{3}{5} = \frac{23}{6} - 4 \cdot \frac{3}{5} = \frac{23}{6} - \frac{12}{5} = \frac{23 \cdot 5 - 12 \cdot 6}{30} = \frac{115 - 72}{30} = \frac{43}{30} = 1\frac{13}{30}$$ ж) $$(2,5 - 1\frac{1}{6})^2 \cdot \frac{27}{32} - 1\frac{6}{13} = (\frac{5}{2} - \frac{7}{6})^2 \cdot \frac{27}{32} - \frac{19}{13} = (\frac{15 - 7}{6})^2 \cdot \frac{27}{32} - \frac{19}{13} = (\frac{8}{6})^2 \cdot \frac{27}{32} - \frac{19}{13} = \frac{64}{36} \cdot \frac{27}{32} - \frac{19}{13} = \frac{2 \cdot 3}{4} - \frac{19}{13} = \frac{3}{2} - \frac{19}{13} = \frac{39 - 38}{26} = \frac{1}{26}$$ з) $$(3\frac{1}{3} - 2\frac{1}{12})^2 \cdot 0,64 + 2\frac{7}{15} = (\frac{10}{3} - \frac{25}{12})^2 \cdot \frac{64}{100} + \frac{37}{15} = (\frac{40 - 25}{12})^2 \cdot \frac{16}{25} + \frac{37}{15} = (\frac{15}{12})^2 \cdot \frac{16}{25} + \frac{37}{15} = \frac{225}{144} \cdot \frac{16}{25} + \frac{37}{15} = \frac{9}{9} \cdot \frac{1}{1} + \frac{37}{15} = 1 + \frac{37}{15} = \frac{15 + 37}{15} = \frac{52}{15} = 3\frac{7}{15}$$ н) $$(\frac{4}{5})^2 = \frac{4^2}{5^2} = \frac{16}{25}$$ о) $$(\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}$$ п) $$(\frac{7}{8})^2 = \frac{7^2}{8^2} = \frac{49}{64}$$ р) $$(\frac{5}{4})^3 = \frac{5^3}{4^3} = \frac{125}{64} = 1\frac{61}{64}$$ №6 a) $$(4\frac{2}{3}+5\frac{1}{2}) \cdot 6 = (\frac{14}{3} + \frac{11}{2}) \cdot 6 = (\frac{28 + 33}{6}) \cdot 6 = \frac{61}{6} \cdot 6 = 61$$ б) $$8\frac{5}{11} \cdot 4\frac{2}{9}+8\frac{5}{11} \cdot 6\frac{7}{9} = 8\frac{5}{11} \cdot (4\frac{2}{9}+6\frac{7}{9}) = 8\frac{5}{11} \cdot (4 + 6 + \frac{2}{9} + \frac{7}{9}) = 8\frac{5}{11} \cdot (10 + \frac{9}{9}) = 8\frac{5}{11} \cdot 11 = \frac{93}{11} \cdot 11 = 93$$