Решение задания 21

<p>a) $$36\frac{1}{13}-6\frac{10}{13}-9\frac{11}{13}-7\frac{7}{13} = (36 - 6 - 9 - 7) + (\frac{1}{13} - \frac{10}{13} - \frac{11}{13} - \frac{7}{13}) = 14 + \frac{1 - 10 - 11 - 7}{13} = 14 + \frac{-27}{13} = 14 - \frac{27}{13} = 14 - 2\frac{1}{13} = 11\frac{13}{13} + 2\frac{13}{13} - 2\frac{1}{13} = 11\frac{13-1}{13} = 11\frac{12}{13}$$</p> <p><strong>Ответ: $$11\frac{12}{13}$$</strong></p> <p>б) $$16\frac{4}{9}+8\frac{7}{9}-6\frac{2}{9}-7\frac{8}{9} = (16 + 8 - 6 - 7) + (\frac{4}{9} + \frac{7}{9} - \frac{2}{9} - \frac{8}{9}) = 11 + \frac{4 + 7 - 2 - 8}{9} = 11 + \frac{1}{9} = 11\frac{1}{9}$$</p> <p><strong>Ответ: $$11\frac{1}{9}$$</strong></p> <p>в) $$55\frac{5}{20}-6\frac{13}{20}+11\frac{14}{20}-37\frac{19}{20} = (55 - 6 + 11 - 37) + (\frac{5}{20} - \frac{13}{20} + \frac{14}{20} - \frac{19}{20}) = 23 + \frac{5 - 13 + 14 - 19}{20} = 23 + \frac{-13}{20} = 23 - \frac{13}{20} = 22\frac{20}{20} - \frac{13}{20} = 22\frac{7}{20}$$</p> <p><strong>Ответ: $$22\frac{7}{20}$$</strong></p> <p>г) $$8\frac{6}{7}+7\frac{1}{3}+8\frac{1}{7}+9\frac{2}{3} = (8 + 7 + 8 + 9) + (\frac{6}{7} + \frac{1}{3} + \frac{1}{7} + \frac{2}{3}) = 32 + (\frac{6}{7} + \frac{1}{7}) + (\frac{1}{3} + \frac{2}{3}) = 32 + \frac{7}{7} + \frac{3}{3} = 32 + 1 + 1 = 34$$</p> <p><strong>Ответ: $$34$$</strong></p> <p>д) $$11\frac{2}{3}-7\frac{5}{17}+12\frac{1}{3}-7\frac{12}{17} = (11 - 7 + 12 - 7) + (\frac{2}{3} - \frac{5}{17} + \frac{1}{3} - \frac{12}{17}) = 9 + (\frac{2}{3} + \frac{1}{3}) + ( -\frac{5}{17} - \frac{12}{17}) = 9 + \frac{3}{3} - \frac{17}{17} = 9 + 1 - 1 = 9$$</p> <p><strong>Ответ: $$9$$</strong></p> <p>e) $$7\frac{5}{9}-9\frac{90}{101}+10\frac{4}{9}-4\frac{11}{101} = (7 - 9 + 10 - 4) + (\frac{5}{9} - \frac{90}{101} + \frac{4}{9} - \frac{11}{101}) = 4 + (\frac{5}{9} + \frac{4}{9}) + (-\frac{90}{101} - \frac{11}{101}) = 4 + \frac{9}{9} - \frac{101}{101} = 4 + 1 - 1 = 4$$</p> <p><strong>Ответ: $$4$$</strong></p>