1 вариант 1 уровень (на «3») 2 a) 8:- 6) 3 12 :4 B) 25 14 7 -:- 15 5 г) 4-:3 2 8 9 2 уровень (на «4») a) 14:21; 6) 4:2; в) 18:; 39 52 11 3 уровень (на «5») 19 22 9 14 г) 2:4·2 7 6 3 2 4 1 a) (11/3): 35; 6) 31 (2: 5); B) 2号: (34-11) , 4 15

1 уровень (на «3»)

а) \[8 : \frac{2}{3} = \frac{8}{1} \cdot \frac{3}{2} = \frac{8 \cdot 3}{1 \cdot 2} = \frac{24}{2} = 12\]

б) \[\frac{12}{25} : 4 = \frac{12}{25} : \frac{4}{1} = \frac{12}{25} \cdot \frac{1}{4} = \frac{12 \cdot 1}{25 \cdot 4} = \frac{12}{100} = \frac{3}{25}\]

в) \[\frac{14}{15} : \frac{7}{5} = \frac{14}{15} \cdot \frac{5}{7} = \frac{14 \cdot 5}{15 \cdot 7} = \frac{2 \cdot 1}{3 \cdot 1} = \frac{2}{3}\]

г) \[4 \frac{2}{3} : 3 \frac{8}{9} = \frac{4 \cdot 3 + 2}{3} : \frac{3 \cdot 9 + 8}{9} = \frac{14}{3} : \frac{35}{9} = \frac{14}{3} \cdot \frac{9}{35} = \frac{14 \cdot 9}{3 \cdot 35} = \frac{2 \cdot 3}{1 \cdot 5} = \frac{6}{5} = 1 \frac{1}{5}\]

2 уровень (на «4»)

а) \[\frac{14}{39} : \frac{21}{52} = \frac{14}{39} \cdot \frac{52}{21} = \frac{14 \cdot 52}{39 \cdot 21} = \frac{2 \cdot 4}{3 \cdot 3} = \frac{8}{9}\]

б) \[4 \frac{1}{11} : 2 \frac{19}{22} = \frac{4 \cdot 11 + 1}{11} : \frac{2 \cdot 22 + 19}{22} = \frac{45}{11} : \frac{63}{22} = \frac{45}{11} \cdot \frac{22}{63} = \frac{45 \cdot 22}{11 \cdot 63} = \frac{5 \cdot 2}{1 \cdot 7} = \frac{10}{7} = 1 \frac{3}{7}\]

в) \[18 : \frac{9}{14} = \frac{18}{1} \cdot \frac{14}{9} = \frac{18 \cdot 14}{1 \cdot 9} = \frac{2 \cdot 14}{1 \cdot 1} = 28\]

г) \[2 \frac{1}{7} : 4 \frac{1}{6} \cdot 2 \frac{1}{3} = \frac{2 \cdot 7 + 1}{7} : \frac{4 \cdot 6 + 1}{6} \cdot \frac{2 \cdot 3 + 1}{3} = \frac{15}{7} : \frac{25}{6} \cdot \frac{7}{3} = \frac{15}{7} \cdot \frac{6}{25} \cdot \frac{7}{3} = \frac{15 \cdot 6 \cdot 7}{7 \cdot 25 \cdot 3} = \frac{1 \cdot 2 \cdot 1}{1 \cdot 5 \cdot 1} = \frac{2}{5}\]

3 уровень (на «5»)

а) \[11 \frac{2}{5} : 3 \frac{4}{5} = \frac{11 \cdot 5 + 2}{5} : \frac{3 \cdot 5 + 4}{5} = \frac{57}{5} : \frac{19}{5} = \frac{57}{5} \cdot \frac{5}{19} = \frac{57 \cdot 5}{5 \cdot 19} = \frac{3 \cdot 1}{1 \cdot 1} = 3\]

б) \[3 \frac{1}{3} \cdot (2 \frac{3}{4} : 5 \frac{1}{2}) = \frac{3 \cdot 3 + 1}{3} \cdot (\frac{2 \cdot 4 + 3}{4} : \frac{5 \cdot 2 + 1}{2}) = \frac{10}{3} \cdot (\frac{11}{4} : \frac{11}{2}) = \frac{10}{3} \cdot (\frac{11}{4} \cdot \frac{2}{11}) = \frac{10}{3} \cdot (\frac{11 \cdot 2}{4 \cdot 11}) = \frac{10}{3} \cdot \frac{1}{2} = \frac{10 \cdot 1}{3 \cdot 2} = \frac{5}{3} = 1 \frac{2}{3}\]

в) \[2 \frac{2}{5} : (3 \frac{2}{4} - 1 \frac{11}{15}) = \frac{2 \cdot 5 + 2}{5} : (\frac{3 \cdot 4 + 2}{4} - \frac{1 \cdot 15 + 11}{15}) = \frac{12}{5} : (\frac{14}{4} - \frac{26}{15}) = \frac{12}{5} : (\frac{7}{2} - \frac{26}{15}) = \frac{12}{5} : (\frac{7 \cdot 15 - 26 \cdot 2}{30}) = \frac{12}{5} : (\frac{105 - 52}{30}) = \frac{12}{5} : \frac{53}{30} = \frac{12}{5} \cdot \frac{30}{53} = \frac{12 \cdot 30}{5 \cdot 53} = \frac{12 \cdot 6}{1 \cdot 53} = \frac{72}{53} = 1 \frac{19}{53}\]