2.214 Вычислите значение выражения: a) $$(12\frac{1}{3}-11\frac{1}{4})+(14-9\frac{8}{15});$$ б) $$(15-12\frac{5}{8})-(13\frac{1}{2}-11\frac{2}{9});$$ в) $$(14\frac{2}{3}-5\frac{5}{9})-(3\frac{7}{8}+4\frac{5}{6})+(10\frac{3}{4}-4\frac{4}{9});$$ г) $$(14\frac{5}{7}-14)+(30-29\frac{5}{7})+(3\frac{1}{7}-\frac{23}{28});$$ 2.215 Вычислите: a) $$2\frac{3}{4}+3,4;$$ б) $$4\frac{7}{25}-3,3;$$ в) $$7,2-6\frac{5}{6};$$ г) $$5\frac{7}{12}-1,6.$$ 2.216 Найдите корень уравнения: a) $$x + 3\frac{8}{13} = 6;$$ б) $$14\frac{4}{9} + y = 23;$$ в) $$a - 7\frac{5}{8} = \frac{7}{12};$$ г) $$12\frac{1}{6} - b = 4\frac{8}{15};$$ д) $$5\frac{25}{36} - t = 1\frac{1}{12} + 2\frac{3}{8};$$ e) $$\frac{4}{7} - \frac{1}{3} + z = \frac{13}{14} - \frac{7}{8}.$$

2.214 а) $$(12\frac{1}{3}-11\frac{1}{4})+(14-9\frac{8}{15}) = (\frac{37}{3}-\frac{45}{4})+(14-\frac{143}{15}) = (\frac{148-135}{12})+(\frac{210-143}{15})=\frac{13}{12}+\frac{67}{15}=\frac{65+268}{60}=\frac{333}{60}=\frac{111}{20}=5\frac{11}{20}$$ б) $$(15-12\frac{5}{8})-(13\frac{1}{2}-11\frac{2}{9}) = (15-\frac{101}{8})-(\frac{27}{2}-\frac{101}{9}) = (\frac{120-101}{8})-(\frac{243-202}{18})=\frac{19}{8}-\frac{41}{18}=\frac{171-164}{72}=\frac{7}{72}$$ в) $$(14\frac{2}{3}-5\frac{5}{9})-(3\frac{7}{8}+4\frac{5}{6})+(10\frac{3}{4}-4\frac{4}{9}) = (\frac{44}{3}-\frac{50}{9})-(\frac{31}{8}+ \frac{29}{6})+(\frac{43}{4}-\frac{40}{9}) = (\frac{132-50}{9})-(\frac{93+116}{24})+(\frac{387-160}{36}) = \frac{82}{9}-\frac{209}{24}+\frac{227}{36} = \frac{328\cdot 4 - 209\cdot 3 + 227}{36} = \frac{1312 - 627 + 227}{36} = \frac{912}{36} = \frac{228}{9} = \frac{76}{3} = 25\frac{1}{3}$$ г) $$(14\frac{5}{7}-14)+(30-29\frac{5}{7})+(3\frac{1}{7}-\frac{23}{28}) = (\frac{103}{7}-14)+(30-\frac{208}{7})+(\frac{22}{7}-\frac{23}{28}) = (\frac{103-98}{7})+(\frac{210-208}{7})+(\frac{88-23}{28}) = \frac{5}{7}+\frac{2}{7}+\frac{65}{28} = \frac{20+8+65}{28} = \frac{93}{28} = 3\frac{9}{28}$$ 2.215 a) $$2\frac{3}{4}+3,4 = 2,75 + 3,4 = 6,15$$ б) $$4\frac{7}{25}-3,3 = 4,28 - 3,3 = 0,98$$ в) $$7,2-6\frac{5}{6} = 7,2 - 6,8333... = 0,3666... = 0,(36)$$ г) $$5\frac{7}{12}-1,6 = 5,58333... - 1,6 = 3,98333... = 3,98(3)$$ 2.216 a) $$x + 3\frac{8}{13} = 6$$ $$x = 6 - 3\frac{8}{13}$$ $$x = 6 - \frac{47}{13}$$ $$x = \frac{78 - 47}{13}$$ $$x = \frac{31}{13}$$ $$x = 2\frac{5}{13}$$ б) $$14\frac{4}{9} + y = 23$$ $$y = 23 - 14\frac{4}{9}$$ $$y = 23 - \frac{130}{9}$$ $$y = \frac{207 - 130}{9}$$ $$y = \frac{77}{9}$$ $$y = 8\frac{5}{9}$$ в) $$a - 7\frac{5}{8} = \frac{7}{12}$$ $$a = \frac{7}{12} + 7\frac{5}{8}$$ $$a = \frac{7}{12} + \frac{61}{8}$$ $$a = \frac{14 + 183}{24}$$ $$a = \frac{197}{24}$$ $$a = 8\frac{5}{24}$$ г) $$12\frac{1}{6} - b = 4\frac{8}{15}$$ $$b = 12\frac{1}{6} - 4\frac{8}{15}$$ $$b = \frac{73}{6} - \frac{68}{15}$$ $$b = \frac{365 - 136}{30}$$ $$b = \frac{229}{30}$$ $$b = 7\frac{19}{30}$$ д) $$5\frac{25}{36} - t = 1\frac{1}{12} + 2\frac{3}{8}$$ $$5\frac{25}{36} - t = \frac{13}{12} + \frac{19}{8}$$ $$5\frac{25}{36} - t = \frac{26 + 57}{24}$$ $$5\frac{25}{36} - t = \frac{83}{24}$$ $$t = 5\frac{25}{36} - \frac{83}{24}$$ $$t = \frac{205}{36} - \frac{83}{24}$$ $$t = \frac{410 - 249}{72}$$ $$t = \frac{161}{72}$$ $$t = 2\frac{17}{72}$$ e) $$\frac{4}{7} - \frac{1}{3} + z = \frac{13}{14} - \frac{7}{8}$$ $$z = \frac{13}{14} - \frac{7}{8} - \frac{4}{7} + \frac{1}{3}$$ $$z = \frac{13}{14} - \frac{4}{7} - \frac{7}{8} + \frac{1}{3}$$ $$z = \frac{13}{14} - \frac{8}{14} - \frac{7}{8} + \frac{1}{3}$$ $$z = \frac{5}{14} - \frac{7}{8} + \frac{1}{3}$$ $$z = \frac{60 - 147 + 56}{168}$$ $$z = \frac{-31}{168}$$