I 1) a) 3/4 * 8/9 б) 1 7/8 * 4/10 в) 1 3/7 + 4/7 * 1 1/3 2) a) 3/11 : 1 5/22 б) 15/16 : 3/10 в) 4 2/3 : 2/3 - 1 : 3 1/2 3) 18/49 : X = 6/35 4) (3 1/6 - 5 1/6 * 4 2/15) : 30 2/3

Решение:

1. 1) а) $$ \frac{3}{4} \cdot \frac{8}{9} = \frac{3 \cdot 8}{4 \cdot 9} = \frac{24}{36} = \frac{2}{3} $$

   б) $$ 1 \frac{7}{8} \cdot \frac{4}{10} = \frac{15}{8} \cdot \frac{4}{10} = \frac{15 \cdot 4}{8 \cdot 10} = \frac{60}{80} = \frac{3}{4} $$

   в) $$ 1 \frac{3}{7} + \frac{4}{7} \cdot 1 \frac{1}{3} = \frac{10}{7} + \frac{4}{7} \cdot \frac{4}{3} = \frac{10}{7} + \frac{16}{21} = \frac{10 \cdot 3 + 16}{21} = \frac{30 + 16}{21} = \frac{46}{21} = 2 \frac{4}{21} $$

2. 2) а) $$ \frac{3}{11} : 1 \frac{5}{22} = \frac{3}{11} : \frac{27}{22} = \frac{3}{11} \cdot \frac{22}{27} = \frac{3 \cdot 22}{11 \cdot 27} = \frac{66}{297} = \frac{2}{9} $$

   б) $$ \frac{15}{16} : \frac{3}{10} = \frac{15}{16} \cdot \frac{10}{3} = \frac{15 \cdot 10}{16 \cdot 3} = \frac{150}{48} = \frac{25}{8} = 3 \frac{1}{8} $$

   в) $$ 4 \frac{2}{3} : \frac{2}{3} - 1 : 3 \frac{1}{2} = \frac{14}{3} : \frac{2}{3} - \frac{1}{1} : \frac{7}{2} = \frac{14}{3} \cdot \frac{3}{2} - \frac{1}{1} \cdot \frac{2}{7} = \frac{14 \cdot 3}{3 \cdot 2} - \frac{1 \cdot 2}{1 \cdot 7} = \frac{42}{6} - \frac{2}{7} = \frac{7}{1} - \frac{2}{7} = \frac{7 \cdot 7 - 2}{7} = \frac{49 - 2}{7} = \frac{47}{7} = 6 \frac{5}{7} $$

3. 3) $$ \frac{18}{49} : x = \frac{6}{35} $$

   $$ x = \frac{18}{49} : \frac{6}{35} $$

   $$ x = \frac{18}{49} \cdot \frac{35}{6} $$

   $$ x = \frac{18 \cdot 35}{49 \cdot 6} $$

   $$ x = \frac{630}{294} $$

   $$ x = \frac{15}{7} = 2 \frac{1}{7} $$

4. 4) $$ (3 \frac{1}{6} - 5 \frac{1}{6} \cdot 4 \frac{2}{15}) : 30 \frac{2}{3} = (\frac{19}{6} - \frac{31}{6} \cdot \frac{62}{15}) : \frac{92}{3} = (\frac{19}{6} - \frac{31 \cdot 62}{6 \cdot 15}) : \frac{92}{3} = (\frac{19}{6} - \frac{1922}{90}) : \frac{92}{3} = (\frac{19 \cdot 15 - 1922}{90}) : \frac{92}{3} = (\frac{285 - 1922}{90}) : \frac{92}{3} = (\frac{-1637}{90}) : \frac{92}{3} = -\frac{1637}{90} \cdot \frac{3}{92} = -\frac{1637 \cdot 3}{90 \cdot 92} = -\frac{4911}{8280} = -\frac{545 \frac{2}{3}}{920} $$

Ответ: