Вопрос:

(\(\frac{3}{4}+3\frac{5}{6}\)):(\(\frac{3}{4}-3\frac{2}{3}\)) (\(\frac{4}{5}-2\frac{3}{4}\)):(\(\frac{16}{21}+3\frac{2}{3}\)) (\(\frac{3}{8}+3\frac{7}{24}\)):(\(\frac{2}{3}-1\frac{1}{8}\)) 7). (1\(\frac{3}{4}+2\frac{1}{3}\)):(7\(\frac{1}{2}-1\frac{2}{3}\))

Смотреть решения всех заданий с листа

Ответ:

4) \((3\frac{1}{4}+3\frac{5}{6}\)):(5\frac{3}{4}-3\frac{2}{3})=(\frac{13}{4}+3\frac{5}{6}):(\frac{23}{4}-\frac{11}{3})=(\frac{13\cdot3}{4\cdot3}+\frac{23\cdot2}{6\cdot2}):(\frac{23\cdot3}{4\cdot3}-\frac{11\cdot4}{3\cdot4})=(\frac{39}{12}+\frac{46}{12}):(\frac{69}{12}-\frac{44}{12})=\frac{85}{12}:\frac{25}{12}=\frac{85}{12}\cdot\frac{12}{25}=\frac{17}{5}=3\frac{2}{5}\)

5) \((6\frac{4}{5}-2\frac{3}{4}\)):(2\frac{16}{21}+3\frac{2}{3})=(\frac{34}{5}-\frac{11}{4}):(\frac{58}{21}+\frac{11}{3})=(\frac{34\cdot4}{5\cdot4}-\frac{11\cdot5}{4\cdot5}):(\frac{58}{21}+\frac{11\cdot7}{3\cdot7})=(\frac{136}{20}-\frac{55}{20}):(\frac{58}{21}+\frac{77}{21})=\frac{81}{20}:\frac{135}{21}=\frac{81}{20}\cdot\frac{21}{135}=\frac{9}{20}\cdot\frac{21}{15}=\frac{3}{20}\cdot\frac{21}{5}=\frac{63}{100}\)

6) \((2\frac{3}{8}+3\frac{7}{24}\)):(4\frac{2}{3}-1\frac{1}{8})=(\frac{19}{8}+\frac{79}{24}):(\frac{14}{3}-\frac{9}{8})=(\frac{19\cdot3}{8\cdot3}+\frac{79}{24}):(\frac{14\cdot8}{3\cdot8}-\frac{9\cdot3}{8\cdot3})=(\frac{57}{24}+\frac{79}{24}):(\frac{112}{24}-\frac{27}{24})=\frac{136}{24}:\frac{85}{24}=\frac{136}{24}\cdot\frac{24}{85}=\frac{8}{5}=1\frac{3}{5}\)

7) \((1\frac{3}{4}+2\frac{1}{3}\)):(7\frac{1}{2}-1\frac{2}{3})=(\frac{7}{4}+\frac{7}{3}):(\frac{15}{2}-\frac{5}{3})=(\frac{7\cdot3}{4\cdot3}+\frac{7\cdot4}{3\cdot4}):(\frac{15\cdot3}{2\cdot3}-\frac{5\cdot2}{3\cdot2})=(\frac{21}{12}+\frac{28}{12}):(\frac{45}{6}-\frac{10}{6})=\frac{49}{12}:\frac{35}{6}=\frac{49}{12}\cdot\frac{6}{35}=\frac{7}{2}\cdot\frac{1}{5}=\frac{7}{10}\)

Ответ: 4) \(3\frac{2}{5}\), 5) \(\frac{63}{100}\), 6) \(1\frac{3}{5}\), 7) \(\frac{7}{10}\)

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