3.Найдите значение выражений a)5\frac{3}{8}+6\frac{1}{8}:б)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}{3} \cdot 2\frac{2}{7};ж)\frac{1}{15}:\frac{8}{25};з)3\frac{3}{5}:2\frac{7}{10}

Ответ: а) \(11\frac{1}{2}\); б) 10\frac{5}{8}; в) 7\frac{6}{13}; г) 12\frac{4}{5}; д) \(\frac{2}{7}\); е) 8; ж) \(\frac{5}{24}\); з) \(\frac{36}{27} = \frac{4}{3} = 1\frac{1}{3}\)

a) \(5\frac{3}{8}+6\frac{1}{8} = (5+6) + (\frac{3}{8} + \frac{1}{8}) = 11 + \frac{4}{8} = 11 + \frac{1}{2} = 11\frac{1}{2}\)

б) \(6\frac{9}{16}+3\frac{11}{16} = (6+3) + (\frac{9}{16} + \frac{11}{16}) = 9 + \frac{20}{16} = 9 + 1\frac{4}{16} = 10\frac{4}{16} = 10\frac{1}{4}\)

в) \(10\frac{9}{13}-3\frac{3}{13} = (10-3) + (\frac{9}{13} - \frac{3}{13}) = 7 + \frac{6}{13} = 7\frac{6}{13}\)

г) \(18\frac{2}{5}-5\frac{3}{5} = (18-5) + (\frac{2}{5} - \frac{3}{5}) = 13 - \frac{1}{5} = 12 + 1 - \frac{1}{5} = 12 + \frac{5}{5} - \frac{1}{5} = 12\frac{4}{5}\)

д) \(\frac{5}{9} \cdot \frac{18}{35} = \frac{5 \cdot 18}{9 \cdot 35} = \frac{5 \cdot 2 \cdot 9}{9 \cdot 5 \cdot 7} = \frac{2}{7}\)

е) \(3\frac{1}{3} \cdot 2\frac{2}{7} = \frac{10}{3} \cdot \frac{16}{7} = \frac{10 \cdot 16}{3 \cdot 7} = \frac{160}{21} = 7\frac{13}{21}\)

ж) \(\frac{1}{15}:\frac{8}{25} = \frac{1}{15} \cdot \frac{25}{8} = \frac{1 \cdot 25}{15 \cdot 8} = \frac{1 \cdot 5 \cdot 5}{3 \cdot 5 \cdot 8} = \frac{5}{24}\)

з) \(3\frac{3}{5}:2\frac{7}{10} = \frac{18}{5} : \frac{27}{10} = \frac{18}{5} \cdot \frac{10}{27} = \frac{18 \cdot 10}{5 \cdot 27} = \frac{2 \cdot 9 \cdot 2 \cdot 5}{5 \cdot 3 \cdot 9} = \frac{4}{3} = 1\frac{1}{3}\)

Ответ: а) \(11\frac{1}{2}\); б) 10\frac{5}{8}; в) 7\frac{6}{13}; г) 12\frac{4}{5}; д) \(\frac{2}{7}\); е) 8; ж) \(\frac{5}{24}\); з) \(\frac{36}{27} = \frac{4}{3} = 1\frac{1}{3}\)