Зачётная работа №5. по теме «Примеры на порядок действий» 1.2:(-)-2.1 3).(7-10:24): 31 57 20 8 19 945 3 7 6 8 2.15:(1-3)+193 14 355 8 27.189 7 7. (5-1)(+). 8).(+) (3+2). 9). (2+2):30-9:12. 10). -3-(-8)-2,90,1+(-3). 142 11), 4-5+2,4: (-0,1)-1:13 12). (6-2)-3-1 46 13). 37-(-4)-1,8: (-0,1)+21 14). 4. (12-3)+(+8).6. 71 3 653 15):1+2,7: (-0,1)-4-(-4). 16). 7.2+:(3-4).

1) \[2 \frac{1}{3} : (\frac{5}{8} - 2 \frac{2}{3}) - 2.1 \cdot \frac{3}{7} = \frac{7}{3} : (\frac{5}{8} - \frac{8}{3}) - \frac{21}{10} \cdot \frac{3}{7} = \frac{7}{3} : (\frac{15 - 64}{24}) - \frac{3}{10} \cdot 3 = \frac{7}{3} : (\frac{-49}{24}) - \frac{9}{10} = \frac{7}{3} \cdot \frac{24}{-49} - \frac{9}{10} = \frac{1}{1} \cdot \frac{8}{-7} - \frac{9}{10} = -\frac{8}{7} - \frac{9}{10} = \frac{-80 - 63}{70} = \frac{-143}{70} = -2 \frac{3}{70}\]

2) \[\frac{7}{15} : (\frac{6}{10} - \frac{8}{3}) + 19 \frac{2}{31} = \frac{7}{15} : (\frac{18-80}{30}) + \frac{591}{31} = \frac{7}{15} : (\frac{-62}{30}) + \frac{591}{31} = \frac{7}{15} \cdot \frac{30}{-62} + \frac{591}{31} = \frac{7}{1} \cdot \frac{2}{-62} + \frac{591}{31} = \frac{-7}{31} + \frac{591}{31} = \frac{584}{31} = 18 \frac{26}{31}\]

3) \[(7 - 1 \frac{5}{9} : \frac{2}{24}) : \frac{7}{20} = (7 - \frac{14}{9} \cdot \frac{24}{2}) : \frac{7}{20} = (7 - \frac{14}{9} \cdot \frac{12}{1}) : \frac{7}{20} = (7 - \frac{168}{9}) : \frac{7}{20} = (7 - \frac{56}{3}) : \frac{7}{20} = (\frac{21-56}{3}) : \frac{7}{20} = \frac{-35}{3} \cdot \frac{20}{7} = \frac{-5}{3} \cdot \frac{20}{1} = \frac{-100}{3} = -33 \frac{1}{3}\]

4) \[(\frac{1}{35} \cdot \frac{4}{5} - \frac{8}{35}) \cdot \frac{1}{3 \frac{1}{3}} = (\frac{4}{175} - \frac{8}{35}) \cdot \frac{1}{\frac{10}{3}} = (\frac{4}{175} - \frac{40}{175}) \cdot \frac{3}{10} = (\frac{-36}{175}) \cdot \frac{3}{10} = \frac{-18}{175} \cdot \frac{3}{5} = \frac{-54}{875}\]

5) \[\frac{31}{35} : (2 - \frac{8}{9} \cdot \frac{19}{45}) = \frac{31}{35} : (2 - \frac{152}{405}) = \frac{31}{35} : (\frac{810 - 152}{405}) = \frac{31}{35} : (\frac{658}{405}) = \frac{31}{35} \cdot \frac{405}{658} = \frac{31}{7} \cdot \frac{81}{658} = \frac{2511}{4506} = \frac{81}{14 \cdot 154}\]

6) \[2 \frac{7}{9} \cdot \frac{18}{25} + \frac{9}{60} : (\frac{7}{12} \cdot \frac{3}{5}) = \frac{25}{9} \cdot \frac{18}{25} + \frac{3}{20} : (\frac{7}{20}) = \frac{1}{1} \cdot \frac{2}{1} + \frac{3}{20} \cdot \frac{20}{7} = 2 + \frac{3}{7} = \frac{14+3}{7} = \frac{17}{7} = 2 \frac{3}{7}\]

7) \[(\frac{4}{5} + \frac{4}{7}) \cdot (\frac{5}{16} - \frac{1}{8}) : (\frac{5}{6} + \frac{3}{14}) = (\frac{28 + 20}{35}) \cdot (\frac{5-2}{16}) : (\frac{35 + 9}{42}) = (\frac{48}{35}) \cdot (\frac{3}{16}) : (\frac{44}{42}) = (\frac{3}{35}) \cdot (\frac{3}{1}) : (\frac{22}{21}) = (\frac{9}{35}) \cdot (\frac{21}{22}) = (\frac{9}{5}) \cdot (\frac{3}{22}) = \frac{27}{110}\]

8) \[(\frac{3}{8} + 2 \frac{1}{4}) \cdot (\frac{4}{5} + \frac{11}{7}) = (\frac{3}{8} + \frac{9}{4}) \cdot (\frac{28 + 55}{35}) = (\frac{3+18}{8}) \cdot (\frac{83}{35}) = (\frac{21}{8}) \cdot (\frac{83}{35}) = (\frac{3}{8}) \cdot (\frac{83}{5}) = \frac{249}{40} = 6 \frac{9}{40}\]

9) \[ (\frac{13}{48} + 2 \frac{5}{12}) \cdot \frac{3}{4} - 9 \frac{3}{4} : 12 = (\frac{13}{48} + \frac{29}{12}) \cdot \frac{3}{4} - \frac{39}{4} \cdot \frac{1}{12} = (\frac{13 + 116}{48}) \cdot \frac{3}{4} - \frac{13}{4} \cdot \frac{1}{4} = (\frac{129}{48}) \cdot \frac{3}{4} - \frac{13}{16} = (\frac{43}{16}) \cdot \frac{3}{4} - \frac{13}{16} = \frac{129}{64} - \frac{13}{16} = \frac{129 - 52}{64} = \frac{77}{64} = 1 \frac{13}{64}\]

10) \[-3 \frac{1}{7} \cdot (-8) - 2,9 : 0,1 + \frac{11}{21} : (-3 \frac{2}{3}) = - \frac{22}{7} \cdot (-8) - \frac{29}{10} : \frac{1}{10} + \frac{11}{21} : (- \frac{11}{3}) = \frac{176}{7} - \frac{29}{10} \cdot 10 + \frac{11}{21} \cdot (- \frac{3}{11}) = \frac{176}{7} - 29 - \frac{1}{7} = \frac{175}{7} - 29 = 25 - 29 = -4\]

11) \[4 \frac{1}{3} \cdot 5 + 2,4 : (-0,1) - \frac{14}{15} : 1 \frac{2}{5} = \frac{13}{3} \cdot 5 + \frac{24}{10} : (- \frac{1}{10}) - \frac{14}{15} : \frac{7}{5} = \frac{65}{3} + \frac{12}{5} \cdot (-10) - \frac{2}{3} \cdot \frac{1}{1} = \frac{65}{3} - 24 - \frac{2}{3} = \frac{63}{3} - 24 = 21 - 24 = -3\]

12) \[(6 - 2 \frac{4}{5}) \cdot \frac{3}{4} - 1 \frac{3}{8} : \frac{1}{5} \cdot 4 = (6 - \frac{14}{5}) \cdot \frac{3}{4} - \frac{11}{8} \cdot 5 \cdot 4 = (\frac{30 - 14}{5}) \cdot \frac{3}{4} - \frac{11}{8} \cdot 20 = \frac{16}{5} \cdot \frac{3}{4} - \frac{11}{2} \cdot 5 = \frac{4}{5} \cdot 3 - \frac{55}{2} = \frac{12}{5} - \frac{55}{2} = \frac{24 - 275}{10} = \frac{-251}{10} = -25 \frac{1}{10}\]

13) \[3 \frac{1}{7} \cdot (-4) - 1,8 : (-0,1) + \frac{20}{21} : 1 \frac{2}{3} = \frac{22}{7} \cdot (-4) - \frac{18}{10} : (- \frac{1}{10}) + \frac{20}{21} : \frac{5}{3} = \frac{-88}{7} - \frac{9}{5} \cdot (-10) + \frac{4}{7} \cdot 1 = \frac{-88}{7} + 18 + \frac{4}{1} = \frac{-88 + 4}{7} + 18 = \frac{-84}{7} + 18 = -12 + 18 = 6\]

14) \[4 \frac{1}{6} \cdot (\frac{1}{2} - \frac{1}{5}) + (\frac{3}{4} + \frac{5}{6}) \cdot 6 = \frac{25}{6} \cdot (\frac{5-2}{10}) + (\frac{9 + 10}{12}) \cdot 6 = \frac{25}{6} \cdot (\frac{3}{10}) + (\frac{19}{12}) \cdot 6 = \frac{5}{2} \cdot (\frac{1}{2}) + (\frac{19}{2}) \cdot 1 = \frac{5}{4} + \frac{19}{2} = \frac{5+38}{4} = \frac{43}{4} = 10 \frac{3}{4}\]

15) \[1 \frac{7}{9} : 1 \frac{1}{6} + 2,7 : (-0,1) - 4 \frac{1}{3} \cdot (-4) = \frac{16}{9} : \frac{7}{6} + \frac{27}{10} : (- \frac{1}{10}) - \frac{13}{3} \cdot (-4) = \frac{16}{9} \cdot \frac{6}{7} + \frac{27}{10} \cdot (-10) - \frac{13}{3} \cdot (-4) = \frac{16}{3} \cdot \frac{2}{7} - 27 + \frac{52}{3} = \frac{32}{21} - \frac{567}{21} + \frac{364}{21} = \frac{32 - 567 + 364}{21} = \frac{-171}{21} = \frac{-57}{7} = -8 \frac{1}{7}\]

16) \[7 \cdot 2 \frac{6}{7} + \frac{53}{12} : (\frac{7}{9} - \frac{9}{4}) = 7 \cdot \frac{20}{7} + \frac{53}{12} : (\frac{28 - 81}{36}) = 20 + \frac{53}{12} : (\frac{-53}{36}) = 20 + \frac{53}{12} \cdot (\frac{36}{-53}) = 20 - 3 = 17\]