Вопрос:

Вычислите: 1) 2 1/2 * 48 - 3 2/3 : 1 1/18 + 5 5/12 : 7/36

Вычислите: 1) 2 1/2 * 48 - 3 2/3 : 1 1/18 + 5 5/12 : 7/36
Фотография

Ответ ассистента

1) $2 \frac{1}{2} \cdot 48 - 3 \frac{2}{3} : 1 \frac{1}{18} + 5 \frac{5}{12} : \frac{7}{36} = \frac{5}{2} \cdot 48 - \frac{11}{3} \cdot \frac{18}{19} + \frac{65}{12} \cdot \frac{36}{7} = 120 - \frac{66}{19} + \frac{195}{7} = 120 - 3 \frac{9}{19} + 27 \frac{6}{7} = 116 \frac{10}{19} + 27 \frac{6}{7} = 143 + \frac{70 + 114}{133} = 144 \frac{51}{133}$ 2) $(1 \frac{8}{13} \cdot \frac{13}{42} + 5 \frac{5}{7} \cdot \frac{8}{21}) : (8 \frac{1}{8} + 3 \frac{1}{2}) = (\frac{21}{13} \cdot \frac{13}{42} + \frac{40}{7} \cdot \frac{8}{21}) : (\frac{65}{8} + \frac{7}{2}) = (\frac{1}{2} + \frac{320}{147}) : \frac{65 + 28}{8} = \frac{147 + 640}{294} : \frac{93}{8} = \frac{787}{294} \cdot \frac{8}{93} = \frac{787 \cdot 4}{147 \cdot 93} = \frac{3148}{13671}$ 3) $[(3 \frac{2}{5} + 1 \frac{7}{10}) \cdot 1 \frac{3}{17} - (2 \frac{7}{23} - 1 \frac{45}{46}) \cdot \frac{69}{80}] \cdot \frac{4}{9} = [(4 + \frac{4+7}{10}) \cdot \frac{20}{17} - (\frac{53}{23} - \frac{91}{46}) \cdot \frac{69}{80}] \cdot \frac{4}{9} = [5 \frac{1}{10} \cdot \frac{20}{17} - \frac{106-91}{46} \cdot \frac{69}{80}] \cdot \frac{4}{9} = [\frac{51}{10} \cdot \frac{20}{17} - \frac{15}{46} \cdot \frac{69}{80}] \cdot \frac{4}{9} = [6 - \frac{3 \cdot 3}{2 \cdot 16}] \cdot \frac{4}{9} = [6 - \frac{9}{32}] \cdot \frac{4}{9} = 5 \frac{23}{32} \cdot \frac{4}{9} = \frac{183}{32} \cdot \frac{4}{9} = \frac{61}{8 \cdot 3} = \frac{61}{24} = 2 \frac{13}{24}$ 4) $[(4 \frac{5}{12} - 3 \frac{13}{24}) : 1 \frac{3}{4} + (3 \frac{5}{8} - 2 \frac{5}{6}) : 1 \frac{2}{12}] : 2 \frac{3}{5} = [(4 \frac{10}{24} - 3 \frac{13}{24}) : \frac{7}{4} + (3 \frac{15}{24} - 2 \frac{20}{24}) : \frac{14}{12}] : \frac{13}{5} = [\frac{21}{24} : \frac{7}{4} + \frac{19}{24} : \frac{7}{6}] : \frac{13}{5} = [\frac{21 \cdot 4}{24 \cdot 7} + \frac{19 \cdot 6}{24 \cdot 7}] : \frac{13}{5} = [\frac{1}{2} + \frac{19}{28}] : \frac{13}{5} = \frac{14+19}{28} \cdot \frac{5}{13} = \frac{33}{28} \cdot \frac{5}{13} = \frac{165}{364}$

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