Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаДействия с рациональными числами 1 вариант 1).2\frac{1}{3}:(\frac{5}{8}:\frac{8}{3})-2.1\frac{1}{7} 2). (7-\frac{1}{9}:\frac{5}{24}):\frac{20}{27} 4). (\frac{5}{16}-\frac{1}{8}):(\frac{5}{6}+\frac{3}{14}). 5). (\frac{13}{48}+2\frac{5}{12}):3\frac{3}{4}-9\frac{3}{4}:12. 6). 4\frac{1}{3}\cdot 5+2,4: (-0,1)-\frac{14}{15}:1\frac{2}{5}. 7). 3\frac{1}{7}\cdot (-4)-1,8: (-0,1)+\frac{20}{21}:1\frac{2}{3}. 8). \frac{7}{9}:1\frac{1}{6}+2,7: (-0,1)-4\frac{1}{3}\cdot (-4). 2 вариант 1). \frac{7}{15}: (\frac{6}{10}-\frac{8}{3})+19\frac{2}{31}. 2). (1\frac{1}{35}:\frac{5}{5}-\frac{4}{35}):3\frac{1}{3}. 3). 2\frac{7}{9}:2\frac{18}{25}+\frac{9}{60}:(\frac{7}{12}-\frac{3}{5}) 4). (\frac{4}{5}+\frac{4}{7}):(3\frac{3}{8}+2\frac{1}{4}). 5). -3\frac{1}{7}\cdot (-8)-2,9:0,1+\frac{11}{21}:(-3\frac{2}{3}). 6). (6-2\frac{4}{5}):\frac{3}{8}-1\frac{3}{5}:\frac{1}{4}. 7). 4\frac{1}{6}:(1\frac{1}{2}-\frac{3}{5})+(\frac{3}{4}+\frac{5}{6})\cdot 6. 8). 7\cdot 2\frac{6}{7}+\frac{53}{12}:(\frac{7}{9}-\frac{9}{4}).
Ответ:
1 вариант
1) 2\frac{1}{3}:(\frac{5}{8}:\frac{8}{3})-2.1\frac{1}{7} = \frac{7}{3}:(\frac{5}{8}\cdot \frac{3}{8})-\frac{15}{7} = \frac{7}{3}:\frac{15}{64}-\frac{15}{7} = \frac{7}{3}\cdot \frac{64}{15}-\frac{15}{7} = \frac{448}{45}-\frac{15}{7} = \frac{3136-675}{315} = \frac{2461}{315} = 7\frac{256}{315}
2) (7-\frac{1}{9}:\frac{5}{24}):\frac{20}{27} = (7-\frac{1}{9}\cdot \frac{24}{5}):\frac{20}{27} = (7-\frac{8}{15}):\frac{20}{27} = (\frac{105-8}{15}):\frac{20}{27} = \frac{97}{15}:\frac{20}{27} = \frac{97}{15}\cdot \frac{27}{20} = \frac{97}{5}\cdot \frac{9}{20} = \frac{873}{100} = 8.73
3) (нет в задании)
4) (\frac{5}{16}-\frac{1}{8}):(\frac{5}{6}+\frac{3}{14}) = (\frac{5}{16}-\frac{2}{16}):(\frac{35+9}{42}) = \frac{3}{16}:\frac{44}{42} = \frac{3}{16}:\frac{22}{21} = \frac{3}{16}\cdot \frac{21}{22} = \frac{63}{352}
5) (\frac{13}{48}+2\frac{5}{12}):3\frac{3}{4}-9\frac{3}{4}:12. = (\frac{13}{48}+\frac{29}{12}):\frac{15}{4}-\frac{39}{4}:12 = (\frac{13+116}{48}):\frac{15}{4}-\frac{39}{4}\cdot \frac{1}{12} = \frac{129}{48}:\frac{15}{4}-\frac{13}{4}\cdot \frac{1}{4} = \frac{43}{16}\cdot \frac{4}{15}-\frac{13}{16} = \frac{43}{4}\cdot \frac{1}{15}-\frac{13}{16} = \frac{43}{60}-\frac{13}{16} = \frac{172-195}{240} = -\frac{23}{240}
6) 4\frac{1}{3}\cdot 5+2,4: (-0,1)-\frac{14}{15}:1\frac{2}{5} = \frac{13}{3}\cdot 5+2,4: (-0,1)-\frac{14}{15}:\frac{7}{5} = \frac{65}{3}-24-\frac{14}{15}\cdot \frac{5}{7} = \frac{65}{3}-24-\frac{2}{3} = \frac{63}{3}-24 = 21-24 = -3
7) 3\frac{1}{7}\cdot (-4)-1,8: (-0,1)+\frac{20}{21}:1\frac{2}{3} = \frac{22}{7}\cdot (-4)-1,8: (-0,1)+\frac{20}{21}:\frac{5}{3} = -\frac{88}{7}+18+\frac{20}{21}\cdot \frac{3}{5} = -\frac{88}{7}+18+\frac{4}{7} = -\frac{84}{7}+18 = -12+18 = 6
8) \frac{7}{9}:1\frac{1}{6}+2,7: (-0,1)-4\frac{1}{3}\cdot (-4) = \frac{7}{9}:\frac{7}{6}+2,7: (-0,1)-\frac{13}{3}\cdot (-4) = \frac{7}{9}\cdot \frac{6}{7}-27+\frac{52}{3} = \frac{2}{3}-27+\frac{52}{3} = \frac{54}{3}-27 = 18-27 = -9
2 вариант
1) \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}
2) (1\frac{1}{35}:\frac{5}{5}-\frac{4}{35}):3\frac{1}{3} = (\frac{36}{35}- \frac{4}{35}):\frac{10}{3} = \frac{32}{35}:\frac{10}{3} = \frac{32}{35}\cdot \frac{3}{10} = \frac{16}{35}\cdot \frac{3}{5} = \frac{48}{175}
3) 2\frac{7}{9}:2\frac{18}{25}+\frac{9}{60}:(\frac{7}{12}-\frac{3}{5}) = \frac{25}{9}:\frac{68}{25}+\frac{3}{20}:(\frac{35-36}{60}) = \frac{25}{9}\cdot \frac{25}{68}+\frac{3}{20}:(-\frac{1}{60}) = \frac{625}{612}+\frac{3}{20}\cdot (-60) = \frac{625}{612}-9 = \frac{625-5508}{612} = -\frac{4883}{612}
4) (\frac{4}{5}+\frac{4}{7}):(3\frac{3}{8}+2\frac{1}{4}) = (\frac{28+20}{35}):(\frac{27}{8}+\frac{9}{4}) = \frac{48}{35}:(\frac{27+18}{8}) = \frac{48}{35}:\frac{45}{8} = \frac{48}{35}\cdot \frac{8}{45} = \frac{16}{35}\cdot \frac{8}{15} = \frac{128}{525}
5) -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}) = \frac{176}{7}-29-\frac{1}{7} = \frac{175}{7}-29 = 25-29 = -4
6) (6-2\frac{4}{5}):\frac{3}{8}-1\frac{3}{5}:\frac{1}{4} = (6-\frac{14}{5}):\frac{3}{8}-\frac{8}{5}:\frac{1}{4} = (\frac{30-14}{5}):\frac{3}{8}-\frac{8}{5}\cdot 4 = \frac{16}{5}:\frac{3}{8}-\frac{32}{5} = \frac{16}{5}\cdot \frac{8}{3}-\frac{32}{5} = \frac{128}{15}-\frac{32}{5} = \frac{128-96}{15} = \frac{32}{15}
7) 4\frac{1}{6}:(1\frac{1}{2}-\frac{3}{5})+(\frac{3}{4}+\frac{5}{6})\cdot 6 = \frac{25}{6}:(\frac{5}{2}-\frac{3}{5})+(\frac{9+10}{12})\cdot 6 = \frac{25}{6}:(\frac{25-6}{10})+\frac{19}{12}\cdot 6 = \frac{25}{6}:\frac{19}{10}+\frac{19}{2} = \frac{25}{6}\cdot \frac{10}{19}+\frac{19}{2} = \frac{125}{3}\cdot \frac{1}{19}+\frac{19}{2} = \frac{125}{57}+\frac{19}{2} = \frac{250+1083}{114} = \frac{1333}{114}
8) 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
Проверка за 10 секунд: Убедись, что правильно применила порядок действий и не ошиблась в арифметике. Пересчитай примеры, в которых сомневаешься!
Редфлаг: Будь особенно внимательна при работе с отрицательными числами и делением дробей. Помни, что деление на дробь - это умножение на её перевёрнутую версию.
