1. Найдите значение выражения: 1)3::1: 2)3(:1): 48 5 1 7) + 1288 8) : 7 ; 7 15 19 3) 3) 1- :1 5) 9 32 36 7 9 15 19 :1 32 34:12.2: 73 7 36 2 6):(1): 3 7 73 51.3 1288 5 9 9) 2윽:(-) 6 9 10) 2윽:-: ; 76 14' 11) 2:1- 3.7 12) 3-5:4 6 6 2 3 15 92

Решение:

1) \(3 \frac{3}{4} : \frac{3}{8} : 1 \frac{3}{7} = \frac{15}{4} : \frac{3}{8} : \frac{10}{7} = \frac{15}{4} \cdot \frac{8}{3} \cdot \frac{7}{10} = \frac{15 \cdot 8 \cdot 7}{4 \cdot 3 \cdot 10} = \frac{3 \cdot 5 \cdot 4 \cdot 2 \cdot 7}{4 \cdot 3 \cdot 5 \cdot 2} = 7\) 2) \(3 \frac{3}{4} : (\frac{3}{8} : 1 \frac{3}{7}) = \frac{15}{4} : (\frac{3}{8} : \frac{10}{7}) = \frac{15}{4} : (\frac{3}{8} \cdot \frac{7}{10}) = \frac{15}{4} : \frac{21}{80} = \frac{15}{4} \cdot \frac{80}{21} = \frac{15 \cdot 80}{4 \cdot 21} = \frac{3 \cdot 5 \cdot 4 \cdot 20}{4 \cdot 3 \cdot 7} = \frac{100}{7} = 14 \frac{2}{7}\) 3) \(1 \frac{7}{9} \cdot \frac{15}{32} : 1 \frac{19}{36} = \frac{16}{9} \cdot \frac{15}{32} : \frac{55}{36} = \frac{16}{9} \cdot \frac{15}{32} \cdot \frac{36}{55} = \frac{16 \cdot 15 \cdot 36}{9 \cdot 32 \cdot 55} = \frac{16 \cdot 3 \cdot 5 \cdot 9 \cdot 4}{9 \cdot 16 \cdot 2 \cdot 5 \cdot 11} = \frac{3 \cdot 4}{2 \cdot 11} = \frac{6}{11}\) 4) \(1 \frac{7}{9} \cdot (\frac{15}{32} : 1 \frac{19}{36}) = \frac{16}{9} \cdot (\frac{15}{32} : \frac{55}{36}) = \frac{16}{9} \cdot (\frac{15}{32} \cdot \frac{36}{55}) = \frac{16}{9} \cdot \frac{15 \cdot 36}{32 \cdot 55} = \frac{16}{9} \cdot \frac{3 \cdot 5 \cdot 9 \cdot 4}{16 \cdot 2 \cdot 5 \cdot 11} = \frac{16}{9} \cdot \frac{36}{32} \cdot \frac{15}{55} = \frac{4}{9} \cdot \frac{3}{2} \cdot \frac{3}{11} = \frac{2}{1} \cdot \frac{1}{1} \cdot \frac{1}{11} = \frac{6}{11}\) 5) \(3 \frac{4}{7} : 1 \frac{1}{7} \cdot \frac{2}{3} = \frac{25}{7} : \frac{8}{7} \cdot \frac{2}{3} = \frac{25}{7} \cdot \frac{7}{8} \cdot \frac{2}{3} = \frac{25 \cdot 7 \cdot 2}{7 \cdot 8 \cdot 3} = \frac{25 \cdot 1 \cdot 1}{1 \cdot 4 \cdot 3} = \frac{25}{12} = 2 \frac{1}{12}\) 6) \(3 \frac{4}{7} : (1 \frac{1}{7} \cdot \frac{2}{3}) = \frac{25}{7} : (\frac{8}{7} \cdot \frac{2}{3}) = \frac{25}{7} : \frac{16}{21} = \frac{25}{7} \cdot \frac{21}{16} = \frac{25 \cdot 21}{7 \cdot 16} = \frac{25 \cdot 3}{1 \cdot 16} = \frac{75}{16} = 4 \frac{11}{16}\) 7) \((\frac{5}{12} + \frac{1}{8}) : \frac{3}{8} = (\frac{10}{24} + \frac{3}{24}) : \frac{3}{8} = \frac{13}{24} : \frac{3}{8} = \frac{13}{24} \cdot \frac{8}{3} = \frac{13 \cdot 8}{24 \cdot 3} = \frac{13 \cdot 1}{3 \cdot 3} = \frac{13}{9} = 1 \frac{4}{9}\) 8) \(\frac{5}{12} + \frac{1}{8} : \frac{3}{8} = \frac{5}{12} + \frac{1}{8} \cdot \frac{8}{3} = \frac{5}{12} + \frac{1}{3} = \frac{5}{12} + \frac{4}{12} = \frac{9}{12} = \frac{3}{4}\) 9) \(2 \frac{6}{7} : (\frac{5}{6} - \frac{9}{14}) = \frac{20}{7} : (\frac{35}{42} - \frac{27}{42}) = \frac{20}{7} : \frac{8}{42} = \frac{20}{7} \cdot \frac{42}{8} = \frac{20 \cdot 42}{7 \cdot 8} = \frac{20 \cdot 6}{1 \cdot 8} = \frac{10 \cdot 3}{1 \cdot 2} = \frac{30}{2} = 15\) 10) \(2 \frac{6}{7} : \frac{5}{6} - \frac{9}{14} = \frac{20}{7} : \frac{5}{6} - \frac{9}{14} = \frac{20}{7} \cdot \frac{6}{5} - \frac{9}{14} = \frac{20 \cdot 6}{7 \cdot 5} - \frac{9}{14} = \frac{4 \cdot 6}{7 \cdot 1} - \frac{9}{14} = \frac{24}{7} - \frac{9}{14} = \frac{48}{14} - \frac{9}{14} = \frac{39}{14} = 2 \frac{11}{14}\) 11) \(2 \frac{1}{4} : 1 \frac{4}{11} - \frac{3}{8} \cdot \frac{7}{8} = \frac{9}{4} : \frac{15}{11} - \frac{3}{8} \cdot \frac{7}{8} = \frac{9}{4} \cdot \frac{11}{15} - \frac{21}{64} = \frac{99}{60} - \frac{21}{64} = \frac{33}{20} - \frac{21}{64} = \frac{33 \cdot 16}{20 \cdot 16} - \frac{21 \cdot 5}{64 \cdot 5} = \frac{528}{320} - \frac{105}{320} = \frac{423}{320} = 1 \frac{103}{320}\) 12) \((3 \frac{1}{6} - 5 \frac{1}{6}) : 4 \frac{2}{15}) \cdot \frac{3}{92} = (\frac{19}{6} - \frac{31}{6}) : \frac{62}{15} \cdot \frac{3}{92} = \frac{-12}{6} : \frac{62}{15} \cdot \frac{3}{92} = -2 : \frac{62}{15} \cdot \frac{3}{92} = -2 \cdot \frac{15}{62} \cdot \frac{3}{92} = -2 \cdot \frac{15}{62} \cdot \frac{3}{92} = \frac{-2 \cdot 15 \cdot 3}{62 \cdot 92} = \frac{-90}{5704} = -\frac{45}{2852}\)

Ответ: 1) 7; 2) 14 \frac{2}{7}; 3) \frac{6}{11}; 4) \frac{6}{11}; 5) 2 \frac{1}{12}; 6) 4 \frac{11}{16}; 7) 1 \frac{4}{9}; 8) \frac{3}{4}; 9) 15; 10) 2 \frac{11}{14}; 11) 1 \frac{103}{320}; 12) -\frac{45}{2852}