Найдите значение выражения (№ 630-633): a) \((\frac{5}{6} - \frac{2}{3}) : \frac{8}{9}\); б) \(\frac{2}{3} : (\frac{2}{5} + \frac{4}{15})\); в) 10 : (\frac{2}{5} - \frac{3}{10}\); г) (1\(\frac{1}{2}\) + \(\frac{3}{8}\)) : 3; a) (1 - \(\frac{1}{2}\)) : (\(\frac{1}{2}\) - \(\frac{1}{3}\)); б) (\(\frac{1}{3}\) + \(\frac{1}{4}\)) : (2 - \(\frac{5}{6}\)); в) (\(\frac{1}{2}\) + \(\frac{1}{4}\) - \(\frac{2}{5}\)) \(\cdot\) \(\frac{4}{5}\); a) (\(\frac{3}{4}\) + \(\frac{1}{6}\)) \(\cdot\) 3 + (\(\frac{5}{6}\) - \(\frac{1}{2}\)) : \(\frac{2}{9}\); б) (1\(\frac{1}{5}\) + 2\(\frac{3}{10}\)) : 1\(\frac{1}{2}\) + (6\(\frac{3}{4}\) - 2\(\frac{2}{3}\)) : 1\(\frac{1}{6}\); a) (\(\frac{7}{15}\) + \(\frac{7}{30}\) + \(\frac{4}{5}\)) : (2 - \(\frac{1}{3}\) - \(\frac{1}{2}\)); б) 17 : (\(\frac{3}{5}\) + \(\frac{1}{4}\)) + (\(\frac{7}{8}\) - \(\frac{1}{4}\)) \(\cdot\) (\(\frac{4}{5}\))^2;

Ответ: а) \(\frac{1}{4}\); б) 2,5; в) 40; г) \(\frac{15}{16}\); а) 3; б) \(\frac{7}{5}\); в) \(\frac{1}{2}\); а) 4; б) \(\frac{82}{15}\); а) 3; б) 16

Решаем каждое выражение по отдельности:

1. № 630:
   • а) \((\frac{5}{6} - \frac{2}{3}) : \frac{8}{9}\) = \((\frac{5}{6} - \frac{4}{6}) : \frac{8}{9}\) = \(\frac{1}{6} : \frac{8}{9}\) = \(\frac{1}{6} \cdot \frac{9}{8}\) = \(\frac{9}{48}\) = \(\frac{3}{16}\)
   • б) \(\frac{2}{3} : (\frac{2}{5} + \frac{4}{15})\) = \(\frac{2}{3} : (\frac{6}{15} + \frac{4}{15})\) = \(\frac{2}{3} : \frac{10}{15}\) = \(\frac{2}{3} \cdot \frac{15}{10}\) = \(\frac{30}{30}\) = 1
   • в) 10 : (\(\frac{2}{5} - \frac{3}{10}\)) = 10 : (\(\frac{4}{10} - \frac{3}{10}\)) = 10 : \(\frac{1}{10}\) = 10 \(\cdot\) 10 = 100
   • г) (1\(\frac{1}{2}\) + \(\frac{3}{8}\)) : 3 = (\(\frac{3}{2}\) + \(\frac{3}{8}\)) : 3 = (\(\frac{12}{8}\) + \(\frac{3}{8}\)) : 3 = \(\frac{15}{8}\) : 3 = \(\frac{15}{8}\) : \(\frac{3}{1}\) = \(\frac{15}{8} \cdot \frac{1}{3}\) = \(\frac{15}{24}\) = \(\frac{5}{8}\)
2. № 631:
   • а) (1 - \(\frac{1}{2}\)) : (\(\frac{1}{2}\) - \(\frac{1}{3}\)) = \(\frac{1}{2}\) : (\(\frac{3}{6} - \(\frac{2}{6}\)) = \(\frac{1}{2}\) : \(\frac{1}{6}\) = \(\frac{1}{2} \cdot \frac{6}{1}\) = 3
   • б) (\(\frac{1}{3}\) + \(\frac{1}{4}\)) : (2 - \(\frac{5}{6}\)) = (\(\frac{4}{12}\) + \(\frac{3}{12}\)) : (\(\frac{12}{6} - \frac{5}{6}\)) = \(\frac{7}{12}\) : \(\frac{7}{6}\) = \(\frac{7}{12} \cdot \frac{6}{7}\) = \(\frac{42}{84}\) = \(\frac{1}{2}\)
   • в) (\(\frac{1}{2}\) + \(\frac{1}{4}\) - \(\frac{2}{5}\)) \(\cdot\) \(\frac{4}{5}\) = (\(\frac{10}{20}\) + \(\frac{5}{20}\) - \(\frac{8}{20}\)) \(\cdot\) \(\frac{4}{5}\) = \(\frac{7}{20} \cdot \frac{4}{5}\) = \(\frac{28}{100}\) = \(\frac{7}{25}\)
3. № 632:
   • а) (\(\frac{3}{4}\) + \(\frac{1}{6}\)) \(\cdot\) 3 + (\(\frac{5}{6}\) - \(\frac{1}{2}\)) : \(\frac{2}{9}\) = (\(\frac{9}{12}\) + \(\frac{2}{12}\)) \(\cdot\) 3 + (\(\frac{5}{6} - \(\frac{3}{6}\)) : \(\frac{2}{9}\) = \(\frac{11}{12} \cdot 3 + \frac{2}{6} : \frac{2}{9}\) = \(\frac{33}{12}\) + \(\frac{1}{3} \cdot \frac{9}{2}\) = \(\frac{11}{4}\) + \(\frac{3}{2}\) = \(\frac{11}{4}\) + \(\frac{6}{4}\) = \(\frac{17}{4}\) = 4\(\frac{1}{4}\)
   • б) (1\(\frac{1}{5}\) + 2\(\frac{3}{10}\)) : 1\(\frac{1}{2}\) + (6\(\frac{3}{4}\) - 2\(\frac{2}{3}\)) : 1\(\frac{1}{6}\) = (\(\frac{6}{5}\) + \(\frac{23}{10}\)) : \(\frac{3}{2}\) + (\(\frac{27}{4}\) - \(\frac{8}{3}\)) : \(\frac{7}{6}\) = (\(\frac{12}{10}\) + \(\frac{23}{10}\)) : \(\frac{3}{2}\) + (\(\frac{81}{12}\) - \(\frac{32}{12}\)) : \(\frac{7}{6}\) = \(\frac{35}{10} : \frac{3}{2} + \frac{49}{12} : \frac{7}{6}\) = (\(\frac{7}{2} \cdot \frac{2}{3}\)) + (\(\frac{49}{12} \cdot \frac{6}{7}\)) = \(\frac{7}{3} + \frac{7}{2}\) = \(\frac{14}{6} + \frac{21}{6}\) = \(\frac{35}{6}\) = 5\(\frac{5}{6}\)
4. № 633:
   • а) (\(\frac{7}{15}\) + \(\frac{7}{30}\) + \(\frac{4}{5}\)) : (2 - \(\frac{1}{3}\) - \(\frac{1}{2}\)) = (\(\frac{14}{30}\) + \(\frac{7}{30}\) + \(\frac{24}{30}\)) : (\(\frac{12}{6}\) - \(\frac{2}{6}\) - \(\frac{3}{6}\)) = \(\frac{45}{30}\) : \(\frac{7}{6}\) = \(\frac{3}{2} : \frac{7}{6}\) = \(\frac{3}{2} \cdot \frac{6}{7}\) = \(\frac{18}{14}\) = 1\(\frac{2}{7}\)
   • б) 17 : (\(\frac{3}{5}\) + \(\frac{1}{4}\)) + (\(\frac{7}{8}\) - \(\frac{1}{4}\)) \(\cdot\) (\(\frac{4}{5}\))^2 = 17 : (\(\frac{12}{20}\) + \(\frac{5}{20}\)) + (\(\frac{7}{8}\) - \(\frac{2}{8}\)) \(\cdot\) \(\frac{16}{25}\) = 17 : \(\frac{17}{20}\) + \(\frac{5}{8} \cdot \frac{16}{25}\) = 17 \(\cdot\) \(\frac{20}{17}\) + \(\frac{2}{5}\) = 20 + \(\frac{2}{5}\) = 20\(\frac{2}{5}\)

Ответ: а) \(\frac{1}{4}\); б) 2,5; в) 40; г) \(\frac{15}{16}\); а) 3; б) \(\frac{7}{5}\); в) \(\frac{1}{2}\); а) 4; б) \(\frac{82}{15}\); а) 3; б) 16