Вычислите:
а) $(\frac{2}{15} + 1\frac{7}{12}) * \frac{30}{103} - 2 : 2\frac{1}{4} * \frac{9}{32} + 2\frac{1}{3}$;
б) $(7\frac{1}{2} * 2\frac{2}{3} - 12\frac{1}{4} : \frac{7}{9}) : 6 + 3\frac{1}{8} + 5\frac{2}{7}$;
в) $5\frac{1}{3} : 6\frac{2}{5} + (12 : 3\frac{3}{5} - \frac{2}{3}) * \frac{2}{3} + 7\frac{2}{5}$;
г) $21\frac{2}{59} - \frac{2}{5} * (3\frac{15}{28} : \frac{9}{28} - 1 : 1\frac{10}{49}) : 2$.

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Решение

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Математика 5 класс Никольский. Номер №1028

Решение а

$(\frac{2}{15} + 1\frac{7}{12}) * \frac{30}{103} - 2 : 2\frac{1}{4} * \frac{9}{32} + 2\frac{1}{3} = 2 : 2\frac{1}{4} * \frac{9}{32} + 2\frac{1}{3} = (\frac{8}{60} + 1\frac{35}{60}) * \frac{30}{103} - \frac{2}{1} * \frac{4}{9} * \frac{9}{32} + 2\frac{1}{3} = 1\frac{43}{60} * \frac{30}{103} - \frac{8}{9} * \frac{9}{8 * 4} + 2\frac{1}{3} = \frac{103}{60} * \frac{30}{103} - \frac{1}{4} + 2\frac{1}{3} = \frac{1}{2} - \frac{1}{4} + 2\frac{1}{3} = \frac{1}{2} - \frac{1}{4} + 2\frac{1}{3} = 2 + \frac{6 - 3 + 4}{12} = 2\frac{7}{12}$

Решение б

$(7\frac{1}{2} * 2\frac{2}{3} - 12\frac{1}{4} : \frac{7}{9}) : 6 + 3\frac{1}{8} + 5\frac{2}{7} = (20 - \frac{63}{4}) * \frac{1}{6} + 3\frac{1}{8} + 5\frac{2}{7} = \frac{20}{6} - \frac{63}{4 * 6} + 3\frac{1}{8} + 5\frac{2}{7} = \frac{80}{24} - \frac{63}{24} + 3\frac{1}{8} + 5\frac{2}{7} = \frac{17}{24} + 3\frac{1}{8} + 5\frac{2}{7} = 8 + \frac{119 + 21 + 48}{168} = 8 + \frac{188}{168} = 8 + 1\frac{20}{168} = 9\frac{5}{42}$

Решение в

$5\frac{1}{3} : 6\frac{2}{5} + (12 : 3\frac{3}{5} - \frac{2}{3}) * \frac{2}{3} + 7\frac{2}{5} = \frac{16}{3} * \frac{5}{32} + (\frac{12}{1} * \frac{5}{18} - \frac{2}{3}) * \frac{2}{3} + 7\frac{2}{5} = \frac{5}{6} + (\frac{10}{3} - \frac{2}{3}) * \frac{2}{3} + 7\frac{2}{5} = \frac{5}{6} + \frac{8}{3} * \frac{2}{3} + 7\frac{2}{5} = \frac{5}{6} + \frac{16}{9} + 7\frac{2}{5} = \frac{15}{18} + \frac{32}{18} + 7\frac{2}{5} = \frac{47}{18} + 7\frac{2}{5} = 7 + \frac{235 + 36}{90} = 7\frac{271}{90} = 10\frac{1}{90}$

Решение г

$21\frac{2}{59} - \frac{2}{5} * (3\frac{15}{28} : \frac{9}{28} - 1 : 1\frac{10}{49}) : 2 = 21\frac{2}{59} - \frac{2}{5} * (\frac{99}{28} * \frac{28}{9} - 1 * \frac{49}{59}) * \frac{1}{2} = 21\frac{5}{59} - \frac{2}{5} * (11 - \frac{49}{59}) * \frac{1}{2} = 21\frac{2}{59} - \frac{2}{5} * (10\frac{59}{59} - \frac{49}{59}) * \frac{1}{2} = 21\frac{2}{59} - \frac{2}{5} * 10\frac{10}{59} * \frac{1}{2} = 21\frac{2}{59} - \frac{2}{5} * \frac{600}{59} * \frac{1}{2} = 21\frac{2}{59} - \frac{1}{5} * \frac{5 * 120}{59} = 21\frac{2}{59} - \frac{120}{59} = 19\frac{120}{59} - \frac{120}{59} = 19$