Математика 5 класс Никольский, Потапов, Решетников

Учебник по математике 5 класс Никольский

авторы: , , .
издательство: Просвещение 2017 год

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Номер №1136

Выполните действия:
а)
$(3\frac{1}{2} : 4\frac{2}{3} + 4\frac{2}{3} : 3\frac{1}{2}) * 4\frac{4}{5}$
;
б)
$3\frac{1}{8} : ((4\frac{5}{12} - 3\frac{13}{24}) * \frac{4}{7} + (3\frac{1}{18} - 2\frac{7}{12}) * 1\frac{10}{17})$
;
в)
$2\frac{3}{4} : ((4\frac{5}{7} - 1\frac{11}{14}) * 4\frac{2}{3} + (3\frac{2}{9} - 1\frac{5}{6}) * \frac{18}{25})$
;
г)
$(15 : 3\frac{3}{4} - (10\frac{1}{2} : 1\frac{1}{2}) * \frac{3}{14}) : (1\frac{23}{52} - 1\frac{1}{4})$
;
д)
$\frac{(\frac{7}{15} + \frac{14}{45} + \frac{2}{9}) * 10\frac{1}{3} - 1\frac{1}{11} * (2\frac{2}{3} - 1\frac{3}{4})}{(\frac{3}{7} - \frac{1}{4}) : \frac{3}{28} - 1}$
;
е)
$\frac{15 : \frac{5}{18} : 3\frac{3}{8} * (\frac{1}{16} + \frac{11}{36} + \frac{5}{48} + \frac{5}{18})}{(11\frac{5}{11} - 8\frac{21}{22}) : 1\frac{2}{3}}$
.

Решение а

$(3\frac{1}{2} : 4\frac{2}{3} + 4\frac{2}{3} : 3\frac{1}{2}) * 4\frac{4}{5} = (\frac{7}{2} : \frac{14}{3} + \frac{14}{3} : \frac{7}{2}) * \frac{24}{5} = (\frac{7}{2} * \frac{3}{14} + \frac{14}{3} * \frac{2}{7}) * \frac{24}{5} = \frac{7}{2} * \frac{3}{14} * \frac{24}{5} + \frac{14}{3} * \frac{2}{7} * \frac{24}{5} = \frac{7}{2} * \frac{3}{7 * 2} * \frac{2 * 12}{5} + \frac{7 * 2}{3} * \frac{2}{7} * \frac{3 * 8}{5} = \frac{3 * 6}{5} + \frac{4 * 8}{5} = \frac{18 + 32}{5} = \frac{50}{5} = 10$

Решение б

$3\frac{1}{8} : ((4\frac{5}{12} - 3\frac{13}{24}) * \frac{4}{7} + (3\frac{1}{18} - 2\frac{7}{12}) * 1\frac{10}{17}) = \frac{25}{8} : ((1\frac{5}{12} - \frac{13}{24}) * \frac{4}{7} + (1\frac{1}{18} - \frac{7}{12}) * \frac{27}{17}) = \frac{25}{8} : ((\frac{34}{24} - \frac{13}{24}) * \frac{4}{7} + (\frac{38}{36} - \frac{21}{36}) * \frac{27}{17}) = \frac{25}{8} : (\frac{21}{24} * \frac{4}{7} + \frac{17}{36} * \frac{27}{17}) = \frac{25}{8} : (\frac{3 * 7}{4 * 6} * \frac{4}{7} + \frac{17}{9 * 4} * \frac{3 * 9}{17}) = \frac{25}{8} : (\frac{3}{6} + \frac{3}{4}) = \frac{25}{8} : \frac{3 * 2 + 3 * 3}{12} = \frac{25}{8} * \frac{6 + 9}{12} = \frac{25}{8} * \frac{12}{15} = \frac{5 * 5}{4 * 2} * \frac{4 * 3}{5 * 3} = \frac{5}{2} = 2\frac{1}{2}$

Решение в

$2\frac{3}{4} : ((4\frac{5}{7} - 1\frac{11}{14}) * 4\frac{2}{3} + (3\frac{2}{9} - 1\frac{5}{6}) * \frac{18}{25}) = \frac{11}{4} : ((3\frac{5}{7} - \frac{11}{14}) * \frac{14}{3} + (2\frac{2}{9} - \frac{5}{6}) * \frac{18}{25}) = \frac{11}{4} : ((2\frac{24}{14} - \frac{11}{14}) * \frac{14}{3} + (1\frac{22}{18} - \frac{15}{18}) * \frac{18}{25}) = \frac{11}{4} : (2\frac{13}{14} * \frac{14}{3} + 1\frac{7}{18} * \frac{18}{25}) = \frac{11}{4} : (\frac{41}{14} * \frac{14}{3} + \frac{25}{18} * \frac{18}{25}) = \frac{11}{4} : (\frac{41}{3} + 1) = \frac{11}{4} : \frac{44}{3} = \frac{11}{4} * \frac{3}{44} = \frac{11}{4} * \frac{3}{4 * 11} = \frac{3}{16}$

Решение г

$(15 : 3\frac{3}{4} - (10\frac{1}{2} : 1\frac{1}{2}) * \frac{3}{14}) : (1\frac{23}{52} - 1\frac{1}{4}) = (15 : \frac{15}{4} - (\frac{21}{2} : \frac{3}{2}) * \frac{3}{14}) : (\frac{75}{52} - \frac{5}{4}) = (15 * \frac{4}{15} - (\frac{21}{2} * \frac{2}{3}) * \frac{3}{14}) : \frac{75 - 5 * 13}{52} = (4 - 7 * \frac{3}{14}) : \frac{75 - 65}{52} = (4 - \frac{3}{2}) : \frac{10}{52} = (4 - 1\frac{1}{2}) * \frac{52}{10} = (3 - \frac{1}{2}) * \frac{26 * 2}{5 * 2} = 2\frac{1}{2} * \frac{26}{5} = \frac{5}{2} * \frac{26}{5} = 13$

Решение д

$\frac{(\frac{7}{15} + \frac{14}{45} + \frac{2}{9}) * 10\frac{1}{3} - 1\frac{1}{11} * (2\frac{2}{3} - 1\frac{3}{4})}{(\frac{3}{7} - \frac{1}{4}) : \frac{3}{28} - 1} = \frac{\frac{7 * 3 + 14 + 2 * 5}{45} * 10\frac{1}{3} - \frac{12}{11} * (1\frac{2}{3} - \frac{3}{4})}{\frac{3 * 4 - 1 * 7}{28} : \frac{3}{28} - 1} = \frac{\frac{21 + 14 + 10}{42} * 10\frac{1}{3} - \frac{12}{11} * (\frac{20}{12} - \frac{9}{12})}{\frac{12 - 7}{28} * \frac{28}{3} - 1} = \frac{\frac{45}{45} * \frac{31}{3} - \frac{12}{11} * \frac{11}{12}}{\frac{5}{28} * \frac{28}{3} - 1} = \frac{10\frac{1}{3} - 1}{\frac{5}{3} - 1} = \frac{9\frac{1}{3}}{1\frac{2}{3} - 1} = \frac{9\frac{1}{3}}{\frac{2}{3}} = \frac{28}{3} * \frac{3}{2} = 14$

Решение е

$\frac{15 : \frac{5}{18} : 3\frac{3}{8} * (\frac{1}{16} + \frac{11}{36} + \frac{5}{48} + \frac{5}{18})}{(11\frac{5}{11} - 8\frac{21}{22}) : 1\frac{2}{3}} = \frac{15 * \frac{18}{5} : \frac{27}{8} * ((\frac{1}{16} + \frac{5}{48}) + (\frac{11}{36} + \frac{5}{18}))}{(3\frac{5}{11} - \frac{21}{22}) : \frac{5}{3}} = \frac{15 * \frac{18}{5} * \frac{8}{27} * (\frac{1 * 3 + 5}{48} + \frac{11 + 5 * 2}{36})}{(2\frac{32}{22} - \frac{21}{22}) : \frac{5}{3}} = \frac{3 * 5 * \frac{2 * 9}{5} * \frac{8}{3 * 9} * (\frac{3 + 5}{48} + \frac{11 + 10}{36})}{2\frac{11}{22} : \frac{5}{3}} = \frac{2 * 8 * (\frac{8}{48} + \frac{21}{36})}{\frac{55}{22} : \frac{5}{3}} = \frac{16 * (\frac{1}{6} + \frac{7}{12})}{\frac{5}{2} * \frac{3}{5}} = \frac{16 * \frac{1 * 2 + 7}{12}}{\frac{3}{2}} = \frac{4 * 4 * \frac{3 * 3}{3 * 4}}{\frac{3}{2}} = 12 * \frac{2}{3} = 4 * 2 = 8$
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