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) $$x + 3\frac{8}{13} = 6$$; в) $$a - 7\frac{5}{8} = \frac{7}{12}$$; д) $$5\frac{25}{36} - t = 1\frac{1}{12}+2\frac{3}{8}$$; б) $$14\frac{4}{9} + y = 23$$; г) $$12\frac{1}{6} - b = 4\frac{8}{15}$$; e) $$\frac{4}{7} - \frac{1}{3} + z = \frac{13}{14} - \frac{7}{8}$$.

Решение задания 2.214: а) $$(12\frac{1}{3}-11\frac{1}{4})+(14-9\frac{8}{15})$$ $$12\frac{1}{3} - 11\frac{1}{4} = \frac{37}{3} - \frac{45}{4} = \frac{148 - 135}{12} = \frac{13}{12} = 1\frac{1}{12}$$ $$14 - 9\frac{8}{15} = \frac{210}{15} - \frac{143}{15} = \frac{67}{15} = 4\frac{7}{15}$$ $$1\frac{1}{12} + 4\frac{7}{15} = \frac{13}{12} + \frac{67}{15} = \frac{65+268}{60} = \frac{333}{60} = \frac{111}{20} = 5\frac{11}{20}$$ Ответ: $$5\frac{11}{20}$$ б) $$(15-12\frac{5}{8}) - (13\frac{1}{2}-11\frac{2}{9})$$ $$15 - 12\frac{5}{8} = \frac{120}{8} - \frac{101}{8} = \frac{19}{8} = 2\frac{3}{8}$$ $$13\frac{1}{2} - 11\frac{2}{9} = \frac{27}{2} - \frac{101}{9} = \frac{243-202}{18} = \frac{41}{18} = 2\frac{5}{18}$$ $$2\frac{3}{8} - 2\frac{5}{18} = \frac{19}{8} - \frac{41}{18} = \frac{171 - 164}{72} = \frac{7}{72}$$ Ответ: $$\frac{7}{72}$$ в) $$(14\frac{2}{3}-5\frac{5}{9}) - (3\frac{7}{8}+4\frac{5}{6})+(10\frac{3}{4}-4\frac{4}{9})$$ $$14\frac{2}{3} - 5\frac{5}{9} = \frac{44}{3} - \frac{50}{9} = \frac{132-50}{9} = \frac{82}{9} = 9\frac{1}{9}$$ $$3\frac{7}{8} + 4\frac{5}{6} = \frac{31}{8} + \frac{29}{6} = \frac{93+116}{24} = \frac{209}{24} = 8\frac{17}{24}$$ $$10\frac{3}{4} - 4\frac{4}{9} = \frac{43}{4} - \frac{40}{9} = \frac{387-160}{36} = \frac{227}{36} = 6\frac{11}{36}$$ $$9\frac{1}{9} - 8\frac{17}{24} + 6\frac{11}{36} = \frac{82}{9} - \frac{209}{24} + \frac{227}{36} = \frac{656-627+227}{72} = \frac{256}{72} = \frac{32}{9} = 3\frac{5}{9}$$ Ответ: $$3\frac{5}{9}$$ г) $$(14\frac{5}{7}-14) + (30-29\frac{5}{7}) + (3\frac{1}{7}-\frac{23}{28})$$ $$14\frac{5}{7} - 14 = \frac{5}{7}$$ $$30 - 29\frac{5}{7} = \frac{210}{7} - \frac{208}{7} = \frac{2}{7}$$ $$3\frac{1}{7} - \frac{23}{28} = \frac{22}{7} - \frac{23}{28} = \frac{88-23}{28} = \frac{65}{28} = 2\frac{9}{28}$$ $$\frac{5}{7} + \frac{2}{7} + 2\frac{9}{28} = \frac{7}{7} + 2\frac{9}{28} = 1 + 2\frac{9}{28} = 3\frac{9}{28}$$ Ответ: $$3\frac{9}{28}$$ Решение задания 2.215: а) $$2\frac{3}{4} + 3,4$$ $$2\frac{3}{4} + 3,4 = 2,75 + 3,4 = 6,15$$ Ответ: 6,15 б) $$4\frac{7}{25} -3,3$$ $$4\frac{7}{25} - 3,3 = 4,28 - 3,3 = 0,98$$ Ответ: 0,98 в) $$7,2-6\frac{5}{6}$$ $$7,2 - 6\frac{5}{6} = 7,2 - 6,8333 = 0,3667$$ Ответ: 0,3667 (округленно) г) $$5\frac{7}{12} - 1,6$$ $$5\frac{7}{12} - 1,6 = 5,5833 - 1,6 = 3,9833$$ Ответ: 3,9833 (округленно) Решение задания 2.216: a) $$x + 3\frac{8}{13} = 6$$ $$x = 6 - 3\frac{8}{13} = 6 - \frac{47}{13} = \frac{78 - 47}{13} = \frac{31}{13} = 2\frac{5}{13}$$ Ответ: $$2\frac{5}{13}$$ б) $$14\frac{4}{9} + y = 23$$ $$y = 23 - 14\frac{4}{9} = 23 - \frac{130}{9} = \frac{207 - 130}{9} = \frac{77}{9} = 8\frac{5}{9}$$ Ответ: $$8\frac{5}{9}$$ в) $$a - 7\frac{5}{8} = \frac{7}{12}$$ $$a = \frac{7}{12} + 7\frac{5}{8} = \frac{7}{12} + \frac{61}{8} = \frac{14+183}{24} = \frac{197}{24} = 8\frac{5}{24}$$ Ответ: $$8\frac{5}{24}$$ г) $$12\frac{1}{6} - b = 4\frac{8}{15}$$ $$b = 12\frac{1}{6} - 4\frac{8}{15} = \frac{73}{6} - \frac{68}{15} = \frac{365-136}{30} = \frac{229}{30} = 7\frac{19}{30}$$ Ответ: $$7\frac{19}{30}$$ д) $$5\frac{25}{36} - t = 1\frac{1}{12}+2\frac{3}{8}$$ $$1\frac{1}{12} + 2\frac{3}{8} = \frac{13}{12} + \frac{19}{8} = \frac{26+57}{24} = \frac{83}{24} = 3\frac{11}{24}$$ $$5\frac{25}{36} - t = 3\frac{11}{24}$$ $$t = 5\frac{25}{36} - 3\frac{11}{24} = \frac{205}{36} - \frac{83}{24} = \frac{410-249}{72} = \frac{161}{72} = 2\frac{17}{72}$$ Ответ: $$2\frac{17}{72}$$ e) $$\frac{4}{7} - \frac{1}{3} + z = \frac{13}{14} - \frac{7}{8}$$ $$\frac{4}{7} - \frac{1}{3} = \frac{12-7}{21} = \frac{5}{21}$$ $$\frac{13}{14} - \frac{7}{8} = \frac{52-49}{56} = \frac{3}{56}$$ $$\frac{5}{21} + z = \frac{3}{56}$$ $$z = \frac{3}{56} - \frac{5}{21} = \frac{9-40}{168} = -\frac{31}{168}$$ Ответ: $$-\frac{31}{168}$$