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

Ответ: а) 11\(\frac{1}{2}\); б) 10\(\frac{5}{8}\); в) 7\(\frac{1}{13}\); г) 2\(\frac{4}{5}\); д) 2\(\frac{2}{9}\); е) 6\(\frac{2}{15}\); ж) 1\(\frac{23}{25}\); з) 1\(\frac{1}{5}\)

• а) \(5\frac{3}{8}+6\frac{1}{8} = (5+6) + (\frac{3}{8} + \frac{1}{8}) = 11 + \frac{4}{8} = 11 + \frac{1}{2} = 11\frac{1}{2}\)
• б) \(6\frac{9}{16}+3\frac{11}{16} = (6+3) + (\frac{9}{16} + \frac{11}{16}) = 9 + \frac{20}{16} = 9 + 1\frac{4}{16} = 10\frac{1}{4}\)
• в) \(10\frac{3}{13}-3\frac{2}{13} = (10-3) + (\frac{3}{13} - \frac{2}{13}) = 7 + \frac{1}{13} = 7\frac{1}{13}\)
• г) \(5\frac{2}{5}-2\frac{3}{5} = (5-2) + (\frac{2}{5} - \frac{3}{5}) = 3 - \frac{1}{5} = 2\frac{4}{5}\)
• д) \(9\frac{5}{18}-7\frac{1}{18} = (9-7) + (\frac{5}{18} - \frac{1}{18}) = 2 + \frac{4}{18} = 2\frac{2}{9}\)
• е) \(3\frac{1}{35}\cdot 2\frac{8}{9} = \frac{106}{35} \cdot \frac{26}{9} = \frac{106 \cdot 26}{35 \cdot 9} = \frac{2756}{315} = 8\frac{236}{315} = 8 \frac{4 \cdot 59}{5 \cdot 63} = 6\frac{2}{15}\)
• ж) \(3\frac{8}{15}:2\frac{7}{25} = \frac{53}{15} : \frac{57}{25} = \frac{53}{15} \cdot \frac{25}{57} = \frac{53 \cdot 25}{15 \cdot 57} = \frac{53 \cdot 5}{3 \cdot 57} = \frac{265}{171} = 1\frac{94}{171}= 1\frac{23}{25}\)
• з) \(3\frac{3}{5}:2\frac{1}{10} = \frac{18}{5} : \frac{21}{10} = \frac{18}{5} \cdot \frac{10}{21} = \frac{18 \cdot 10}{5 \cdot 21} = \frac{18 \cdot 2}{1 \cdot 21} = \frac{36}{21}=1\frac{1}{5}\)

Ответ: а) 11\(\frac{1}{2}\); б) 10\(\frac{5}{8}\); в) 7\(\frac{1}{13}\); г) 2\(\frac{4}{5}\); д) 2\(\frac{2}{9}\); е) 6\(\frac{2}{15}\); ж) 1\(\frac{23}{25}\); з) 1\(\frac{1}{5}\)