Выполните действия в 16 математических примерах с обыкновенными и десятичными дробями.

Решим примеры по порядку, соблюдая правила действий с обыкновенными и десятичными дробями. 1). $2\frac{1}{3} : (\frac{5}{8} - \frac{8}{3}) - 2 \cdot 1\frac{3}{7} = \frac{7}{3} : (\frac{15-64}{24}) - 2 \cdot \frac{10}{7} = \frac{7}{3} : (-\frac{49}{24}) - \frac{20}{7} = \frac{7}{3} \cdot (-\frac{24}{49}) - \frac{20}{7} = -\frac{8}{7} - \frac{20}{7} = -\frac{28}{7} = -4$ 2). $\frac{7}{15} : (\frac{6}{10} - \frac{8}{3}) + 19 \cdot \frac{2}{31} = \frac{7}{15} : (\frac{3}{5} - \frac{8}{3}) + \frac{38}{31} = \frac{7}{15} : (\frac{9-40}{15}) + \frac{38}{31} = \frac{7}{15} : (-\frac{31}{15}) + \frac{38}{31} = -\frac{7}{31} + \frac{38}{31} = \frac{31}{31} = 1$ 3). $(7 - 1\frac{5}{9} : \frac{7}{24}) : \frac{20}{27} = (7 - \frac{14}{9} \cdot \frac{24}{7}) : \frac{20}{27} = (7 - \frac{2 \cdot 8}{3}) : \frac{20}{27} = (7 - \frac{16}{3}) : \frac{20}{27} = (\frac{21-16}{3}) : \frac{20}{27} = \frac{5}{3} \cdot \frac{27}{20} = \frac{9}{4} = 2,25$ 4). $(1\frac{1}{35} : \frac{4}{5} - 1\frac{8}{35}) \cdot 3\frac{1}{3} = (\frac{36}{35} \cdot \frac{5}{4} - \frac{43}{35}) \cdot \frac{10}{3} = (\frac{9}{7} - \frac{43}{35}) \cdot \frac{10}{3} = (\frac{45-43}{35}) \cdot \frac{10}{3} = \frac{2}{35} \cdot \frac{10}{3} = \frac{2 \cdot 2}{7 \cdot 3} = \frac{4}{21}$ 5). $1\frac{31}{35} : (2 - \frac{8}{9} : 1\frac{19}{45}) = \frac{66}{35} : (2 - \frac{8}{9} : \frac{64}{45}) = \frac{66}{35} : (2 - \frac{8}{9} \cdot \frac{45}{64}) = \frac{66}{35} : (2 - \frac{5}{8}) = \frac{66}{35} : \frac{11}{8} = \frac{66}{35} \cdot \frac{8}{11} = \frac{6 \cdot 8}{35} = \frac{48}{35} = 1\frac{13}{35}$ 6). $2\frac{7}{9} \cdot \frac{18}{25} + \frac{9}{60} : (\frac{7}{12} - \frac{3}{5}) = \frac{25}{9} \cdot \frac{18}{25} + \frac{3}{20} : (\frac{35-36}{60}) = 2 + \frac{3}{20} : (-\frac{1}{60}) = 2 + \frac{3}{20} \cdot (-60) = 2 - 9 = -7$ 7). $(5\frac{1}{16} - 1\frac{1}{8}) (\frac{5}{6} + \frac{3}{14}) = (5\frac{1}{16} - 1\frac{2}{16}) (\frac{35+9}{42}) = 3\frac{15}{16} \cdot \frac{44}{42} = \frac{63}{16} \cdot \frac{22}{21} = \frac{3 \cdot 11}{8} = \frac{33}{8} = 4\frac{1}{8} = 4,125$ 8). $(\frac{4}{5} + \frac{4}{7}) (3\frac{3}{8} + 2\frac{11}{4}) = (\frac{28+20}{35}) (3\frac{3}{8} + 4\frac{6}{8}) = \frac{48}{35} \cdot 7\frac{9}{8} = \frac{48}{35} \cdot 8\frac{1}{8} = \frac{48}{35} \cdot \frac{65}{8} = \frac{6 \cdot 13}{7} = \frac{78}{7} = 11\frac{1}{7}$ 9). (2\frac{13}{48} + 2\frac{5}{12}) : 3\frac{3}{4} - 9\frac{3}{4} : 12 = (2\frac{13}{48} + 2\frac{20}{48}) : \frac{15}{4} - \frac{39}{4} \cdot \frac{1}{12} = 4\frac{33}{48} : \frac{15}{4} - \frac{13}{16} = 4\frac{11}{16} \cdot \frac{4}{15} - \frac{13}{16} = \frac{75}{16} \cdot \frac{4}{15} - \frac{13}{16} = \frac{5}{4} - \frac{13}{16} = \frac{20-13}{16} = \frac{7}{16}$ 10). $-3\frac{1}{7} \cdot (-8) - 2,9 : 0,1 + \frac{11}{21} : (-3\frac{2}{3}) = \frac{22}{7} \cdot 8 - 29 + \frac{11}{21} : (-\frac{11}{3}) = \frac{176}{7} - 29 - \frac{11}{21} \cdot \frac{3}{11} = 25\frac{1}{7} - 29 - \frac{1}{7} = 25 - 29 = -4$ 11). $4\frac{1}{3} \cdot 5 + 2,4 : (-0,1) - \frac{14}{15} : 1\frac{2}{5} = \frac{13}{3} \cdot 5 - 24 - \frac{14}{15} : \frac{7}{5} = \frac{65}{3} - 24 - \frac{14}{15} \cdot \frac{5}{7} = 21\frac{2}{3} - 24 - \frac{2}{3} = 21 - 24 = -3$ 12). (6 - 2\frac{4}{5}) \cdot 3\frac{1}{8} - 1\frac{3}{5} : \frac{1}{4} = 3\frac{1}{5} \cdot \frac{25}{8} - \frac{8}{5} \cdot 4 = \frac{16}{5} \cdot \frac{25}{8} - \frac{32}{5} = 2 \cdot 5 - 6,4 = 10 - 6,4 = 3,6$ 13). $3\frac{1}{7} \cdot (-4) - 1,8 : (-0,1) + \frac{20}{21} : 1\frac{2}{3} = -\frac{22}{7} \cdot 4 + 18 + \frac{20}{21} : \frac{5}{3} = -\frac{88}{7} + 18 + \frac{20}{21} \cdot \frac{3}{5} = -12\frac{4}{7} + 18 + \frac{4}{7} = -12 + 18 = 6$ 14). $4\frac{1}{6} \cdot (1\frac{1}{2} - \frac{3}{5}) + (\frac{3}{4} + \frac{5}{6}) \cdot 6 = \frac{25}{6} \cdot (\frac{15-6}{10}) + (\frac{9+10}{12}) \cdot 6 = \frac{25}{6} \cdot \frac{9}{10} + \frac{19}{12} \cdot 6 = \frac{5 \cdot 3}{2 \cdot 2} + \frac{19}{2} = \frac{15}{4} + \frac{38}{4} = \frac{53}{4} = 13,25$ 15). $\frac{7}{9} : 1\frac{1}{6} + 2,7 : (-0,1) - 4\frac{1}{3} \cdot (-4) = \frac{7}{9} \cdot \frac{6}{7} - 27 + \frac{13}{3} \cdot 4 = \frac{2}{3} - 27 + \frac{52}{3} = \frac{54}{3} - 27 = 18 - 27 = -9$ 16). $7,2 \cdot \frac{6}{7} + \frac{53}{12} : (\frac{7}{9} - \frac{9}{4}) = \frac{36}{5} \cdot \frac{6}{7} + \frac{53}{12} : (\frac{28-81}{36}) = \frac{216}{35} + \frac{53}{12} : (-\frac{53}{36}) = \frac{216}{35} - \frac{53}{12} \cdot \frac{36}{53} = 6\frac{6}{35} - 3 = 3\frac{6}{35}$