5. Все действия с обыкновенными дробями 51717681711 1). (+= 2). (+= 3). (\frac{1}{4}+\frac{5}{6}).\frac{5}{6} 144242559362321 343\frac{1}{3}5324523 4). (+= 5). (6-). 6. (2) 232442-1 11113712 7). (+= 8). (4+) (3+2). 9). (3.6-1): (4-2) 44782

5. Все действия с обыкновенными дробями

1) \[(\frac{5}{14} + \frac{17}{42}) \cdot \frac{17}{6} = (\frac{5 \cdot 3}{14 \cdot 3} + \frac{17}{42}) \cdot \frac{17}{6} = (\frac{15}{42} + \frac{17}{42}) \cdot \frac{17}{6} = \frac{32}{42} \cdot \frac{17}{6} = \frac{16}{21} \cdot \frac{17}{6} = \frac{16 \cdot 17}{21 \cdot 6} = \frac{272}{126} = \frac{136}{63}\]

2) \[(\frac{8}{9} + 1\frac{17}{36}) : \frac{5}{9} = (\frac{8}{9} + \frac{1 \cdot 36 + 17}{36}) : \frac{5}{9} = (\frac{8}{9} + \frac{53}{36}) : \frac{5}{9} = (\frac{8 \cdot 4}{9 \cdot 4} + \frac{53}{36}) : \frac{5}{9} = (\frac{32}{36} + \frac{53}{36}) : \frac{5}{9} = \frac{85}{36} \cdot \frac{9}{5} = \frac{85 \cdot 9}{36 \cdot 5} = \frac{17 \cdot 1}{4 \cdot 1} = \frac{17}{4}\]

3) \[(\frac{1}{4} + \frac{5}{6}) \cdot \frac{5}{6} = (\frac{1 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 2}{6 \cdot 2}) \cdot \frac{5}{6} = (\frac{3}{12} + \frac{10}{12}) \cdot \frac{5}{6} = \frac{13}{12} \cdot \frac{5}{6} = \frac{13 \cdot 5}{12 \cdot 6} = \frac{65}{72}\]

4) \[(1\frac{3}{4} + 3\frac{1}{3}) \div (5 - 3\frac{2}{3}) = (\frac{1 \cdot 4 + 3}{4} + \frac{3 \cdot 3 + 1}{3}) \div (5 - \frac{3 \cdot 3 + 2}{3}) = (\frac{7}{4} + \frac{10}{3}) \div (\frac{5 \cdot 3}{3} - \frac{11}{3}) = (\frac{7 \cdot 3}{4 \cdot 3} + \frac{10 \cdot 4}{3 \cdot 4}) \div (\frac{15}{3} - \frac{11}{3}) = (\frac{21}{12} + \frac{40}{12}) \div \frac{4}{3} = \frac{61}{12} \div \frac{4}{3} = \frac{61}{12} \cdot \frac{3}{4} = \frac{61 \cdot 3}{12 \cdot 4} = \frac{61}{16}\]

5) \[(6 - 2\frac{3}{4}) \div (4\frac{2}{3} - 1) = (6 - \frac{2 \cdot 4 + 3}{4}) \div (\frac{4 \cdot 3 + 2}{3} - 1) = (\frac{6 \cdot 4}{4} - \frac{11}{4}) \div (\frac{14}{3} - \frac{1 \cdot 3}{3}) = (\frac{24}{4} - \frac{11}{4}) \div (\frac{14}{3} - \frac{3}{3}) = \frac{13}{4} \div \frac{11}{3} = \frac{13}{4} \cdot \frac{3}{11} = \frac{13 \cdot 3}{4 \cdot 11} = \frac{39}{44}\]

6) \[(2\frac{5}{8} + 3) \div (4\frac{2}{3} - 1) = (\frac{2 \cdot 8 + 5}{8} + 3) \div (\frac{4 \cdot 3 + 2}{3} - 1) = (\frac{21}{8} + 3) \div (\frac{14}{3} - 1) = (\frac{21}{8} + \frac{3 \cdot 8}{8}) \div (\frac{14}{3} - \frac{1 \cdot 3}{3}) = (\frac{21}{8} + \frac{24}{8}) \div (\frac{14}{3} - \frac{3}{3}) = \frac{45}{8} \div \frac{11}{3} = \frac{45}{8} \cdot \frac{3}{11} = \frac{45 \cdot 3}{8 \cdot 11} = \frac{135}{88}\]

7) \[(1\frac{1}{4} + 2\frac{1}{3}) \div (7 - 1\frac{2}{3}) = (\frac{1 \cdot 4 + 1}{4} + \frac{2 \cdot 3 + 1}{3}) \div (7 - \frac{1 \cdot 3 + 2}{3}) = (\frac{5}{4} + \frac{7}{3}) \div (\frac{7 \cdot 3}{3} - \frac{5}{3}) = (\frac{5 \cdot 3}{4 \cdot 3} + \frac{7 \cdot 4}{3 \cdot 4}) \div (\frac{21}{3} - \frac{5}{3}) = (\frac{15}{12} + \frac{28}{12}) \div \frac{16}{3} = \frac{43}{12} \div \frac{16}{3} = \frac{43}{12} \cdot \frac{3}{16} = \frac{43 \cdot 3}{12 \cdot 16} = \frac{43}{64}\]

8) \[(4 + \frac{4}{7}) \div (3 + 2\frac{11}{8}) = (\frac{4 \cdot 7}{7} + \frac{4}{7}) \div (3 + \frac{2 \cdot 8 + 11}{8}) = (\frac{28}{7} + \frac{4}{7}) \div (3 + \frac{27}{8}) = \frac{32}{7} \div (\frac{3 \cdot 8}{8} + \frac{27}{8}) = \frac{32}{7} \div (\frac{24}{8} + \frac{27}{8}) = \frac{32}{7} \div \frac{51}{8} = \frac{32}{7} \cdot \frac{8}{51} = \frac{32 \cdot 8}{7 \cdot 51} = \frac{256}{357}\]

9) \[(3.6 - 1\frac{2}{3}) : (4\frac{1}{2} - 5\frac{3}{5}) = (\frac{36}{10} - \frac{1 \cdot 3 + 2}{3}) : (\frac{4 \cdot 2 + 1}{2} - \frac{5 \cdot 5 + 3}{5}) = (\frac{18}{5} - \frac{5}{3}) : (\frac{9}{2} - \frac{28}{5}) = (\frac{18 \cdot 3}{5 \cdot 3} - \frac{5 \cdot 5}{3 \cdot 5}) : (\frac{9 \cdot 5}{2 \cdot 5} - \frac{28 \cdot 2}{5 \cdot 2}) = (\frac{54}{15} - \frac{25}{15}) : (\frac{45}{10} - \frac{56}{10}) = \frac{29}{15} : (-\frac{11}{10}) = \frac{29}{15} \cdot -\frac{10}{11} = -\frac{29 \cdot 10}{15 \cdot 11} = -\frac{29 \cdot 2}{3 \cdot 11} = -\frac{58}{33}\]