22. Вычислите, используя распределительный закон: a) $$97\frac{1}{58} \cdot 2 + 97\frac{1}{58} \cdot 3 + 97\frac{1}{58} \cdot 1$$; б) $$12\frac{4}{5} \cdot \frac{7}{20} + 12\frac{4}{5} \cdot \frac{2}{3} + 12\frac{4}{5} \cdot \frac{8}{15}$$; в) $$3\frac{5}{6} \cdot \frac{1}{3} + 3\frac{5}{6} \cdot \frac{7}{8} + 1\frac{1}{24} \cdot 3\frac{5}{6}$$; г) $$31 \cdot 26 + 31 \cdot 78 - 31 \cdot 24$$; д) $$27\frac{2}{3} \cdot \frac{5}{2} + 27\frac{2}{3} \cdot \frac{1}{2} - 27\frac{2}{3} \cdot \frac{5}{6}$$; e) $$1\frac{1}{2} \cdot 2\frac{1}{7} + 3\frac{1}{2} \cdot 2\frac{1}{7} - 2\frac{1}{2} \cdot 2\frac{1}{7} - 1\frac{5}{6} \cdot 2\frac{1}{7}$$

<h1>Решение задания 22</h1> <p>a) $$97\frac{1}{58} \cdot 2 + 97\frac{1}{58} \cdot 3 + 97\frac{1}{58} \cdot 1 = 97\frac{1}{58} \cdot (2 + 3 + 1) = 97\frac{1}{58} \cdot 6 = \frac{97 \cdot 58 + 1}{58} \cdot 6 = \frac{5626 + 1}{58} \cdot 6 = \frac{5627}{58} \cdot 6 = \frac{5627 \cdot 6}{58} = \frac{33762}{58} = 582\frac{6}{58} = 582\frac{3}{29}$$</p> <p><strong>Ответ: $$582\frac{3}{29}$$</strong></p> <p>б) $$12\frac{4}{5} \cdot \frac{7}{20} + 12\frac{4}{5} \cdot \frac{2}{3} + 12\frac{4}{5} \cdot \frac{8}{15} = 12\frac{4}{5} \cdot (\frac{7}{20} + \frac{2}{3} + \frac{8}{15}) = \frac{12 \cdot 5 + 4}{5} \cdot (\frac{7 \cdot 3}{20 \cdot 3} + \frac{2 \cdot 20}{3 \cdot 20} + \frac{8 \cdot 4}{15 \cdot 4}) = \frac{64}{5} \cdot (\frac{21}{60} + \frac{40}{60} + \frac{32}{60}) = \frac{64}{5} \cdot \frac{21 + 40 + 32}{60} = \frac{64}{5} \cdot \frac{93}{60} = \frac{64}{5} \cdot \frac{31}{20} = \frac{16}{5} \cdot \frac{31}{5} = \frac{16 \cdot 31}{5 \cdot 5} = \frac{496}{25} = 19\frac{21}{25}$$</p> <p><strong>Ответ: $$19\frac{21}{25}$$</strong></p> <p>в) $$3\frac{5}{6} \cdot \frac{1}{3} + 3\frac{5}{6} \cdot \frac{7}{8} + 1\frac{1}{24} \cdot 3\frac{5}{6} = 3\frac{5}{6} \cdot (\frac{1}{3} + \frac{7}{8} + 1\frac{1}{24}) = \frac{3 \cdot 6 + 5}{6} \cdot (\frac{1}{3} + \frac{7}{8} + \frac{25}{24}) = \frac{23}{6} \cdot (\frac{1 \cdot 8}{3 \cdot 8} + \frac{7 \cdot 3}{8 \cdot 3} + \frac{25}{24}) = \frac{23}{6} \cdot (\frac{8}{24} + \frac{21}{24} + \frac{25}{24}) = \frac{23}{6} \cdot \frac{8 + 21 + 25}{24} = \frac{23}{6} \cdot \frac{54}{24} = \frac{23}{6} \cdot \frac{9}{4} = \frac{23 \cdot 9}{6 \cdot 4} = \frac{23 \cdot 3}{2 \cdot 4} = \frac{69}{8} = 8\frac{5}{8}$$</p> <p><strong>Ответ: $$8\frac{5}{8}$$</strong></p> <p>г) $$31 \cdot 26 + 31 \cdot 78 - 31 \cdot 24 = 31 \cdot (26 + 78 - 24) = 31 \cdot (104 - 24) = 31 \cdot 80 = 2480$$</p> <p><strong>Ответ: $$2480$$</strong></p> <p>д) $$27\frac{2}{3} \cdot \frac{5}{2} + 27\frac{2}{3} \cdot \frac{1}{2} - 27\frac{2}{3} \cdot \frac{5}{6} = 27\frac{2}{3} \cdot (\frac{5}{2} + \frac{1}{2} - \frac{5}{6}) = \frac{27 \cdot 3 + 2}{3} \cdot (\frac{5}{2} + \frac{1}{2} - \frac{5}{6}) = \frac{83}{3} \cdot (\frac{6}{2} - \frac{5}{6}) = \frac{83}{3} \cdot (3 - \frac{5}{6}) = \frac{83}{3} \cdot (\frac{18}{6} - \frac{5}{6}) = \frac{83}{3} \cdot \frac{13}{6} = \frac{83 \cdot 13}{3 \cdot 6} = \frac{1079}{18} = 59\frac{17}{18}$$</p> <p><strong>Ответ: $$59\frac{17}{18}$$</strong></p> <p>e) $$1\frac{1}{2} \cdot 2\frac{1}{7} + 3\frac{1}{2} \cdot 2\frac{1}{7} - 2\frac{1}{2} \cdot 2\frac{1}{7} - 1\frac{5}{6} \cdot 2\frac{1}{7} = 2\frac{1}{7} \cdot (1\frac{1}{2} + 3\frac{1}{2} - 2\frac{1}{2} - 1\frac{5}{6}) = 2\frac{1}{7} \cdot (\frac{3}{2} + \frac{7}{2} - \frac{5}{2} - \frac{11}{6}) = \frac{15}{7} \cdot (\frac{10}{2} - \frac{11}{6}) = \frac{15}{7} \cdot (5 - \frac{11}{6}) = \frac{15}{7} \cdot (\frac{30}{6} - \frac{11}{6}) = \frac{15}{7} \cdot \frac{19}{6} = \frac{5}{7} \cdot \frac{19}{2} = \frac{5 \cdot 19}{7 \cdot 2} = \frac{95}{14} = 6\frac{11}{14}$$</p> <p><strong>Ответ: $$6\frac{11}{14}$$</strong></p>