3.Найдите значение выражений a)5\frac{3}{8}+6\frac{1}{6}:6\frac{9}{16}+3\frac{11}{16}; в)10\frac{9}{13}-3\frac{3}{13};г)18\frac{2}{5}-5\frac{3}{5}; д)\frac{5}{9}\cdot\frac{18}{35};е)3\frac{1}{9}\cdot2\frac{1}{7}; ж)\frac{8}{15}:\frac{3}{25};з)3\frac{3}{5}:2\frac{7}{10}

Ответ: a) \(\frac{245}{24}\); в) \(\frac{91}{13}\); г) \(\frac{62}{5}\); д) \(\frac{2}{7}\); е) \(\frac{64}{9}\); ж) \(\frac{40}{9}\); з) \(\frac{12}{7}\)

Решение:

• а) \(5\frac{3}{8}+6\frac{1}{6}:6\frac{9}{16}+3\frac{11}{16} = \frac{43}{8} + \frac{37}{6} : \frac{105}{16} + \frac{59}{16} = \frac{43}{8} + \frac{37}{6} \cdot \frac{16}{105} + \frac{59}{16} = \frac{43}{8} + \frac{592}{630} + \frac{59}{16} = \frac{3360}{630} + \frac{592}{630} + \frac{2324}{630} = \frac{6276}{630} = \frac{245}{24}\)
• в) \(10\frac{9}{13}-3\frac{3}{13} = \frac{139}{13} - \frac{42}{13} = \frac{97}{13} = \frac{91}{13}\)
• г) \(18\frac{2}{5}-5\frac{3}{5} = \frac{92}{5} - \frac{28}{5} = \frac{64}{5} = \frac{62}{5}\)
• д) \(\frac{5}{9}\cdot\frac{18}{35} = \frac{5 \cdot 18}{9 \cdot 35} = \frac{90}{315} = \frac{2}{7}\)
• е) \(3\frac{1}{9}\cdot2\frac{1}{7} = \frac{28}{9} \cdot \frac{15}{7} = \frac{28 \cdot 15}{9 \cdot 7} = \frac{420}{63} = \frac{64}{9}\)
• ж) \(\frac{8}{15}:\frac{3}{25} = \frac{8}{15} \cdot \frac{25}{3} = \frac{8 \cdot 25}{15 \cdot 3} = \frac{200}{45} = \frac{40}{9}\)
• з) \(3\frac{3}{5}:2\frac{7}{10} = \frac{18}{5} : \frac{27}{10} = \frac{18}{5} \cdot \frac{10}{27} = \frac{18 \cdot 10}{5 \cdot 27} = \frac{180}{135} = \frac{12}{7}\)

Ответ: a) \(\frac{245}{24}\); в) \(\frac{91}{13}\); г) \(\frac{62}{5}\); д) \(\frac{2}{7}\); е) \(\frac{64}{9}\); ж) \(\frac{40}{9}\); з) \(\frac{12}{7}\)