№1 Выполните действия: а) 5 1/3 : 1 1/3

### Решение №1 a) $5 \frac{1}{3} : 1 \frac{1}{3} = \frac{16}{3} : \frac{4}{3} = \frac{16}{3} \cdot \frac{3}{4} = 4$ б) $5,2 - 3 \frac{1}{3} = 5,2 - 3,333... = \frac{26}{5} - \frac{10}{3} = \frac{78-50}{15} = \frac{28}{15} = 1 \frac{13}{15}$ в) $2 \frac{1}{7} \cdot 1 \frac{1}{20} = \frac{15}{7} \cdot \frac{21}{20} = \frac{3 \cdot 3}{1 \cdot 4} = \frac{9}{4} = 2,25$ г) $3 \frac{2}{9} + 4 \frac{1}{6} = 3 \frac{4}{18} + 4 \frac{3}{18} = 7 \frac{7}{18}$ д) $7 \frac{16}{21} + 1 \frac{5}{14} = 7 \frac{32}{42} + 1 \frac{15}{42} = 8 \frac{47}{42} = 9 \frac{5}{42}$ е) $2 \frac{9}{13} \cdot 1,3 = \frac{35}{13} \cdot \frac{13}{10} = \frac{35}{10} = 3,5$ ### Решение №2 a) $3,75 : (\frac{3}{8} : 1 \frac{3}{7}) = 3,75 : (\frac{3}{8} : \frac{10}{7}) = 3,75 : (\frac{3}{8} \cdot \frac{7}{10}) = \frac{15}{4} : \frac{21}{80} = \frac{15}{4} \cdot \frac{80}{21} = \frac{5}{1} \cdot \frac{20}{7} = \frac{100}{7} = 14 \frac{2}{7}$ б) $11 - 6 \frac{2}{3} - 3 \frac{5}{7} = 11 - \frac{20}{3} - \frac{26}{7} = \frac{231 - 140 - 78}{21} = \frac{13}{21}$ ### Решение №3 a) $(9,2 : 0,23 - 29,4) \cdot 6,5 + 3,5 = (40 - 29,4) \cdot 6,5 + 3,5 = 10,6 \cdot 6,5 + 3,5 = 68,9 + 3,5 = 72,4$ б) $30 \frac{5}{6} - (7 \frac{1}{3} + 2 \frac{1}{4}) : \frac{1}{4} = 30 \frac{5}{6} - (\frac{44}{6} + \frac{9}{4}) : \frac{1}{4} = 30 \frac{5}{6} - (\frac{88 + 27}{12}) \cdot 4 = 30 \frac{5}{6} - \frac{115}{3} = \frac{185}{6} - \frac{230}{6} = -\frac{45}{6} = -7,5$ в) $(2,5 - 1 \frac{1}{6})^2 \cdot \frac{27}{32} - 1 \frac{6}{13} = (2 \frac{1}{2} - 1 \frac{1}{6})^2 \cdot \frac{27}{32} - 1 \frac{6}{13} = (\frac{8}{6})^2 \cdot \frac{27}{32} - 1 \frac{6}{13} = (\frac{4}{3})^2 \cdot \frac{27}{32} - 1 \frac{6}{13} = \frac{16}{9} \cdot \frac{27}{32} - 1 \frac{6}{13} = 1,5 - 1 \frac{6}{13} = \frac{3}{2} - \frac{19}{13} = \frac{39 - 38}{26} = \frac{1}{26}$ г) $\frac{(4-2,26) : 1 \frac{1}{5}}{(2 \frac{2}{3} + 1 \frac{1}{5}) \cdot 1,5} = \frac{1,74 : 1,2}{(\frac{40+18}{15}) \cdot \frac{3}{2}} = \frac{1,45}{\frac{58}{15} \cdot \frac{3}{2}} = \frac{1,45}{5,8} = 0,25$ ### Решение №4 a) $2,8 + (4 \frac{1}{5} - (1,7 + (2 \frac{1}{3} - 1 \frac{5}{6}))) = 2,8 + (4,2 - (1,7 + (\frac{14-11}{6}))) = 2,8 + (4,2 - (1,7 + 0,5)) = 2,8 + (4,2 - 2,2) = 2,8 + 2 = 4,8$ б) $\frac{1}{1 + \frac{1}{2 + \frac{1}{3}}} = \frac{1}{1 + \frac{1}{\frac{7}{3}}} = \frac{1}{1 + \frac{3}{7}} = \frac{1}{\frac{10}{7}} = 0,7$