Карточки по заданию 6 ОГЭ по математике. Действия с обыкновенными дробями.

Решаю все задания по карточкам. Карточка №1 1) $$\frac{1}{5} + \frac{19}{20} = \frac{4}{20} + \frac{19}{20} = \frac{23}{20} = 1 \frac{3}{20}$$ 2) $$\frac{3}{4} + \frac{4}{5} = \frac{15}{20} + \frac{16}{20} = \frac{31}{20} = 1 \frac{11}{20}$$ 3) $$\frac{27}{5 \cdot 4} = \frac{27}{20} = 1 \frac{7}{20}$$ 4) $$\frac{0.9}{1 + \frac{1}{8}} = \frac{0.9}{\frac{9}{8}} = 0.9 \cdot \frac{8}{9} = \frac{9}{10} \cdot \frac{8}{9} = \frac{8}{10} = 0.8$$ 5) $$\frac{1}{\frac{1}{18} + \frac{1}{21}} = \frac{1}{\frac{7}{126} + \frac{6}{126}} = \frac{1}{\frac{13}{126}} = \frac{126}{13} = 9 \frac{9}{13}$$ 6) $$\left( \frac{11}{18} + \frac{1}{9} \right) \div \frac{5}{48} = \left( \frac{11}{18} + \frac{2}{18} \right) \div \frac{5}{48} = \frac{13}{18} \cdot \frac{48}{5} = \frac{13 \cdot 8}{3 \cdot 5} = \frac{104}{15} = 6 \frac{14}{15}$$ 7) $$\left( 1 \frac{3}{13} - 2 \frac{3}{4} \right) \cdot 26 = \left( \frac{16}{13} - \frac{11}{4} \right) \cdot 26 = \left( \frac{64}{52} - \frac{143}{52} \right) \cdot 26 = -\frac{79}{52} \cdot 26 = -\frac{79}{2} = -39.5$$ 8) $$4 \frac{3}{13} \div \left( \frac{6}{17} - 2 \frac{8}{13} \right) = \frac{55}{13} \div \left( \frac{6}{17} - \frac{34}{13} \right) = \frac{55}{13} \div \left( \frac{78}{221} - \frac{578}{221} \right) = \frac{55}{13} \div \left( -\frac{500}{221} \right) = \frac{55}{13} \cdot \left( -\frac{221}{500} \right) = \frac{11}{1} \cdot \left( -\frac{17}{100} \right) = -\frac{187}{100} = -1.87$$ 9) $$18 \cdot \left( \frac{1}{9} \right)^2 - 20 \cdot \frac{1}{9} = 18 \cdot \frac{1}{81} - \frac{20}{9} = \frac{2}{9} - \frac{20}{9} = -\frac{18}{9} = -2$$ 10) $$\left( \frac{13}{30} + \frac{11}{20} \right) \div \frac{9}{5} = \left( \frac{26}{60} + \frac{33}{60} \right) \div \frac{9}{5} = \frac{59}{60} \cdot \frac{5}{9} = \frac{59}{12 \cdot 9} = \frac{59}{108}$$ Карточка №2 1) $$\frac{1}{2} + \frac{33}{50} = \frac{25}{50} + \frac{33}{50} = \frac{58}{50} = \frac{29}{25} = 1 \frac{4}{25}$$ 2) $$\frac{19}{2} + \frac{7}{25} = \frac{475}{50} + \frac{14}{50} = \frac{489}{50} = 9 \frac{39}{50}$$ 3) $$\frac{15}{3.2} = \frac{150}{32} = \frac{75}{16} = 4 \frac{11}{16}$$ 4) $$\frac{1.6}{1 + \frac{1}{9}} = \frac{1.6}{\frac{10}{9}} = 1.6 \cdot \frac{9}{10} = \frac{16}{10} \cdot \frac{9}{10} = \frac{144}{100} = 1.44$$ 5) $$\frac{1}{\frac{1}{30} + \frac{1}{42}} = \frac{1}{\frac{7}{210} + \frac{5}{210}} = \frac{1}{\frac{12}{210}} = \frac{210}{12} = \frac{105}{6} = \frac{35}{2} = 17.5$$ 6) $$\left( \frac{11}{30} + \frac{17}{36} \right) \div \frac{19}{45} = \left( \frac{66}{180} + \frac{85}{180} \right) \div \frac{19}{45} = \frac{151}{180} \cdot \frac{45}{19} = \frac{151}{4 \cdot 19} = \frac{151}{76} = 1 \frac{75}{76}$$ 7) $$4 \frac{7}{8} \div \left( 2 \frac{3}{4} + 1 \frac{10}{19} \right) = \frac{39}{8} \div \left( \frac{11}{4} + \frac{29}{19} \right) = \frac{39}{8} \div \left( \frac{209}{76} + \frac{116}{76} \right) = \frac{39}{8} \div \frac{325}{76} = \frac{39}{8} \cdot \frac{76}{325} = \frac{39}{2} \cdot \frac{19}{325} = \frac{3 \cdot 19}{2 \cdot 25} = \frac{57}{50} = 1.14$$ 8) $$6 \cdot \left( \frac{1}{3} \right)^2 - 11 \cdot \frac{1}{3} = 6 \cdot \frac{1}{9} - \frac{11}{3} = \frac{2}{3} - \frac{11}{3} = -\frac{9}{3} = -3$$ 9) $$\left( \frac{13}{12} + \frac{11}{20} \right) \div \frac{12}{5} = \left( \frac{65}{60} + \frac{33}{60} \right) \div \frac{12}{5} = \frac{98}{60} \cdot \frac{5}{12} = \frac{49}{12} \cdot \frac{1}{12} = \frac{49}{144}$$ Карточка №3 1) $$\frac{1}{10} + \frac{21}{50} = \frac{5}{50} + \frac{21}{50} = \frac{26}{50} = \frac{13}{25}$$ 2) $$\frac{3}{2} - \frac{9}{5} = \frac{15}{10} - \frac{18}{10} = -\frac{3}{10}$$ 3) $$\frac{19}{5.4} = \frac{190}{54} = \frac{95}{27} = 3 \frac{14}{27}$$ 4) $$\frac{1.3}{1 + \frac{1}{4}} = \frac{1.3}{\frac{5}{4}} = \frac{13}{10} \cdot \frac{4}{5} = \frac{13 \cdot 2}{5 \cdot 5} = \frac{26}{25} = 1.04$$ 5) $$\frac{1}{\frac{1}{9} - \frac{1}{12}} = \frac{1}{\frac{4}{36} - \frac{3}{36}} = \frac{1}{\frac{1}{36}} = 36$$ 6) $$\left( \frac{7}{16} - \frac{1}{32} \right) \div \frac{11}{24} = \left( \frac{14}{32} - \frac{1}{32} \right) \div \frac{11}{24} = \frac{13}{32} \cdot \frac{24}{11} = \frac{13 \cdot 3}{4 \cdot 11} = \frac{39}{44}$$ 7) $$\left( \frac{4}{9} - 3 \frac{1}{15} \right) \cdot 9 = \left( \frac{4}{9} - \frac{46}{15} \right) \cdot 9 = \left( \frac{20}{45} - \frac{138}{45} \right) \cdot 9 = -\frac{118}{45} \cdot 9 = -\frac{118}{5} = -23.6$$ 8) $$2 \frac{2}{5} \cdot \left( \frac{9}{10} - 1 \frac{5}{14} \right) = \frac{12}{5} \cdot \left( \frac{9}{10} - \frac{19}{14} \right) = \frac{12}{5} \cdot \left( \frac{63}{70} - \frac{95}{70} \right) = \frac{12}{5} \cdot \left( -\frac{32}{70} \right) = \frac{12}{5} \cdot \left( -\frac{16}{35} \right) = -\frac{192}{175}$$ 9) $$6 \cdot \left( \frac{1}{3} \right)^2 - 8 \cdot \frac{1}{3} = 6 \cdot \frac{1}{9} - \frac{8}{3} = \frac{2}{3} - \frac{8}{3} = -\frac{6}{3} = -2$$ 10) $$\frac{5}{33} - \frac{8}{15} \div \frac{11}{5} = \frac{5}{33} - \frac{8}{15} \cdot \frac{5}{11} = \frac{5}{33} - \frac{8}{3 \cdot 11} = \frac{5}{33} - \frac{8}{33} = -\frac{3}{33} = -\frac{1}{11}$$ Карточка №4 1) $$\frac{1}{5} - \frac{27}{20} = \frac{4}{20} - \frac{27}{20} = -\frac{23}{20} = -1 \frac{3}{20}$$ 2) $$\frac{2}{25} + \frac{1}{4} = \frac{8}{100} + \frac{25}{100} = \frac{33}{100} = 0.33$$ 3) $$\frac{14}{5.4} = \frac{140}{54} = \frac{70}{27} = 2 \frac{16}{27}$$ 4) $$\frac{1.8}{1 + \frac{1}{11}} = \frac{1.8}{\frac{12}{11}} = \frac{18}{10} \cdot \frac{11}{12} = \frac{3}{5} \cdot \frac{11}{2} = \frac{33}{10} = 3.3$$ 5) $$\frac{1}{\frac{1}{63} + \frac{1}{72}} = \frac{1}{\frac{8}{504} + \frac{7}{504}} = \frac{1}{\frac{15}{504}} = \frac{504}{15} = \frac{168}{5} = 33.6$$ 6) $$\left( \frac{17}{35} + \frac{3}{8} \right) \div \frac{5}{28} = \left( \frac{136}{280} + \frac{105}{280} \right) \div \frac{5}{28} = \frac{241}{280} \cdot \frac{28}{5} = \frac{241}{10 \cdot 5} = \frac{241}{50} = 4.82$$ 7) $$3 \frac{7}{11} \div \frac{2}{11} + 2 \frac{4}{19} = \frac{40}{11} \cdot \frac{11}{2} + \frac{42}{19} = 20 + \frac{42}{19} = \frac{380}{19} + \frac{42}{19} = \frac{422}{19} = 22 \frac{4}{19}$$ 8) $$7 \cdot \left( \frac{1}{7} \right)^2 - 8 \cdot \frac{1}{7} = 7 \cdot \frac{1}{49} - \frac{8}{7} = \frac{1}{7} - \frac{8}{7} = -\frac{7}{7} = -1$$ 9) $$\left( \frac{1}{20} + \frac{11}{8} \right) \div \frac{18}{5} = \left( \frac{2}{40} + \frac{55}{40} \right) \div \frac{18}{5} = \frac{57}{40} \cdot \frac{5}{18} = \frac{57}{8 \cdot 18} = \frac{19}{8 \cdot 6} = \frac{19}{48}$$ 10) $$\left( \frac{14}{11} + \frac{5}{22} \right) \div \frac{9}{10} = \left( \frac{28}{22} + \frac{5}{22} \right) \div \frac{9}{10} = \frac{33}{22} \cdot \frac{10}{9} = \frac{3}{2} \cdot \frac{10}{9} = \frac{1}{1} \cdot \frac{5}{3} = \frac{5}{3} = 1 \frac{2}{3}$$ Карточка №5 1) $$\frac{1}{2} - \frac{13}{50} = \frac{25}{50} - \frac{13}{50} = \frac{12}{50} = \frac{6}{25}$$ 2) $$\frac{1}{2} + \frac{16}{5} = \frac{5}{10} + \frac{32}{10} = \frac{37}{10} = 3.7$$ 3) $$\frac{27}{3.2} = \frac{270}{32} = \frac{135}{16} = 8 \frac{7}{16}$$ 4) $$\frac{0.7}{1 + \frac{1}{3}} = \frac{0.7}{\frac{4}{3}} = \frac{7}{10} \cdot \frac{3}{4} = \frac{21}{40}$$ 5) $$\frac{1}{\frac{1}{36} - \frac{1}{44}} = \frac{1}{\frac{11}{396} - \frac{9}{396}} = \frac{1}{\frac{2}{396}} = \frac{396}{2} = 198$$ 6) $$\left( \frac{17}{10} + \frac{10}{11} \right) \div \frac{5}{44} = \left( \frac{187}{110} + \frac{100}{110} \right) \div \frac{5}{44} = \frac{287}{110} \cdot \frac{44}{5} = \frac{287 \cdot 2}{5 \cdot 5} = \frac{574}{25} = 22.96$$ 7) $$16 + 2 \frac{3}{8} = 16 + \frac{19}{8} = \frac{128}{8} + \frac{19}{8} = \frac{147}{8} = 18 \frac{3}{8}$$ 8) $$1 \frac{1}{12} \cdot \left( \frac{13}{18} - 2 \frac{5}{9} \right) = \frac{13}{12} \cdot \left( \frac{13}{18} - \frac{23}{9} \right) = \frac{13}{12} \cdot \left( \frac{13}{18} - \frac{46}{18} \right) = \frac{13}{12} \cdot \left( -\frac{33}{18} \right) = \frac{13}{4} \cdot \left( -\frac{11}{6} \right) = -\frac{143}{24} = -5 \frac{23}{24}$$ 9) $$6 \cdot \left( \frac{1}{3} \right)^2 - 14 \cdot \frac{1}{3} = 6 \cdot \frac{1}{9} - \frac{14}{3} = \frac{2}{3} - \frac{14}{3} = -\frac{12}{3} = -4$$ 10) $$\left( \frac{14}{11} + \frac{5}{22} \right) \div \frac{9}{10} = \left( \frac{28}{22} + \frac{5}{22} \right) \div \frac{9}{10} = \frac{33}{22} \cdot \frac{10}{9} = \frac{3}{2} \cdot \frac{10}{9} = \frac{1}{1} \cdot \frac{5}{3} = \frac{5}{3} = 1 \frac{2}{3}$$