Вычисли значения выражений с дробями в заданиях 3 и 4

Задание 3 1) $1\frac{5}{36} + 5\frac{1}{9} = \frac{41}{36} + \frac{46}{9} = \frac{41}{36} + \frac{23 \cdot 4}{9 \cdot 4} = \frac{41 + 92}{36} = \frac{133}{36} = 3\frac{25}{36}$ 6) $3\frac{2}{15} - 1\frac{21}{36} = \frac{47}{15} - \frac{57}{36} = \frac{47 \cdot 12}{15 \cdot 12} - \frac{57 \cdot 5}{36 \cdot 5} = \frac{564 - 285}{180} = \frac{279}{180} = \frac{93}{60} = \frac{31}{20} = 1\frac{11}{20}$ 11) $6\frac{1}{4} \cdot 2\frac{9}{10} = \frac{25}{4} \cdot \frac{29}{10} = \frac{5 \cdot 5}{2 \cdot 2} \cdot \frac{29}{5 \cdot 2} = \frac{5 \cdot 29}{2 \cdot 2 \cdot 2} = \frac{145}{8} = 18\frac{1}{8}$ 2) $1\frac{20}{32} + 3\frac{1}{2} = 1\frac{5}{8} + 3\frac{1}{2} = \frac{13}{8} + \frac{7}{2} = \frac{13}{8} + \frac{7 \cdot 4}{2 \cdot 4} = \frac{13 + 28}{8} = \frac{41}{8} = 5\frac{1}{8}$ 7) $9\frac{1}{4} - 1\frac{8}{25} = \frac{37}{4} - \frac{33}{25} = \frac{37 \cdot 25}{4 \cdot 25} - \frac{33 \cdot 4}{25 \cdot 4} = \frac{925 - 132}{100} = \frac{793}{100} = 7\frac{93}{100}$ 12) $3\frac{1}{6} \cdot 3\frac{9}{12} = \frac{19}{6} \cdot \frac{45}{12} = \frac{19}{2 \cdot 3} \cdot \frac{3 \cdot 15}{3 \cdot 4} = \frac{19 \cdot 15}{2 \cdot 4 \cdot 3} = \frac{285}{8} = 11\frac{7}{8}$ 3) $2\frac{28}{35} + 6\frac{1}{8} = 2\frac{4}{5} + 6\frac{1}{8} = \frac{14}{5} + \frac{49}{8} = \frac{14 \cdot 8}{5 \cdot 8} + \frac{49 \cdot 5}{8 \cdot 5} = \frac{112 + 245}{40} = \frac{357}{40} = 8\frac{37}{40}$ 8) $2\frac{1}{4} - 3\frac{2}{5} = \frac{9}{4} - \frac{17}{5} = \frac{9 \cdot 5}{4 \cdot 5} - \frac{17 \cdot 4}{5 \cdot 4} = \frac{45 - 68}{20} = -\frac{23}{20} = -1\frac{3}{20}$ 13) $2\frac{1}{20} : 1\frac{12}{13} = \frac{41}{20} : \frac{25}{13} = \frac{41}{20} \cdot \frac{13}{25} = \frac{41 \cdot 13}{20 \cdot 25} = \frac{533}{500} $ 4) $1\frac{7}{16} + 2\frac{5}{25} = 1\frac{7}{16} + 2\frac{1}{5} = \frac{23}{16} + \frac{11}{5} = \frac{23 \cdot 5}{16 \cdot 5} + \frac{11 \cdot 16}{5 \cdot 16} = \frac{115 + 176}{80} = \frac{291}{80} = 3\frac{51}{80}$ 9) $1\frac{30}{32} - 2\frac{3}{4} = 1\frac{15}{16} - 2\frac{3}{4} = \frac{31}{16} - \frac{11}{4} = \frac{31}{16} - \frac{11 \cdot 4}{4 \cdot 4} = \frac{31 - 44}{16} = -\frac{13}{16}$ 14) $6\frac{2}{7} : 2\frac{12}{14} = 6\frac{2}{7} : 2\frac{6}{7} = \frac{44}{7} : \frac{20}{7} = \frac{44}{7} \cdot \frac{7}{20} = \frac{44}{20} = \frac{11}{5} = 2\frac{1}{5}$ 5) $1\frac{11}{20} + 10\frac{5}{8} = \frac{31}{20} + \frac{85}{8} = \frac{31 \cdot 2}{20 \cdot 2} + \frac{85 \cdot 5}{8 \cdot 5} = \frac{62 + 425}{40} = \frac{487}{40} = 12\frac{7}{40}$ 10) $3\frac{19}{24} - 1\frac{3}{30} = 3\frac{19}{24} - 1\frac{1}{10} = \frac{91}{24} - \frac{11}{10} = \frac{91 \cdot 5}{24 \cdot 5} - \frac{11 \cdot 12}{10 \cdot 12} = \frac{455 - 132}{120} = \frac{323}{120} = 2\frac{83}{120}$ 15) $3\frac{3}{5} : 1\frac{5}{35} = 3\frac{3}{5} : 1\frac{1}{7} = \frac{18}{5} : \frac{8}{7} = \frac{18}{5} \cdot \frac{7}{8} = \frac{9}{5} \cdot \frac{7}{4} = \frac{63}{20} = 3\frac{3}{20}$ Задание 4. 1) $(\frac{14}{20} + 2\frac{15}{27}) \cdot 27 = (\frac{7}{10} + 2\frac{5}{9}) \cdot 27 = (\frac{7}{10} + \frac{23}{9}) \cdot 27 = (\frac{7 \cdot 9}{10 \cdot 9} + \frac{23 \cdot 10}{9 \cdot 10}) \cdot 27 = (\frac{63 + 230}{90}) \cdot 27 = \frac{293}{90} \cdot 27 = \frac{293 \cdot 3}{10} = \frac{879}{10} = 87\frac{9}{10}$ 6) $1\frac{8}{16} : (4\frac{13}{14} + \frac{3}{7}) = 1\frac{1}{2} : (4\frac{13}{14} + \frac{6}{14}) = \frac{3}{2} : 4\frac{19}{14} = \frac{3}{2} : \frac{75}{14} = \frac{3}{2} \cdot \frac{14}{75} = \frac{3 \cdot 7}{75} = \frac{21}{75} = \frac{7}{25}$ 2) $(2\frac{1}{2} - \frac{12}{15}) \cdot \frac{1}{34} = (2\frac{1}{2} - \frac{4}{5}) \cdot \frac{1}{34} = (\frac{5}{2} - \frac{4}{5}) \cdot \frac{1}{34} = (\frac{5 \cdot 5}{2 \cdot 5} - \frac{4 \cdot 2}{5 \cdot 2}) \cdot \frac{1}{34} = (\frac{25 - 8}{10}) \cdot \frac{1}{34} = \frac{17}{10} \cdot \frac{1}{34} = \frac{1}{10 \cdot 2} = \frac{1}{20}$ 7) $1\frac{17}{34} : (8\frac{1}{6} + 2\frac{6}{24}) = 1\frac{1}{2} : (8\frac{1}{6} + 2\frac{1}{4}) = \frac{3}{2} : (\frac{49}{6} + \frac{9}{4}) = \frac{3}{2} : (\frac{49 \cdot 2}{6 \cdot 2} + \frac{9 \cdot 3}{4 \cdot 3}) = \frac{3}{2} : (\frac{98 + 27}{12}) = \frac{3}{2} : \frac{125}{12} = \frac{3}{2} \cdot \frac{12}{125} = \frac{3 \cdot 6}{125} = \frac{18}{125}$ 3) $(2\frac{4}{10} + 1\frac{13}{20}) \cdot \frac{4}{9} = (2\frac{2}{5} + 1\frac{13}{20}) \cdot \frac{4}{9} = (\frac{12}{5} + \frac{33}{20}) \cdot \frac{4}{9} = (\frac{12 \cdot 4}{5 \cdot 4} + \frac{33}{20}) \cdot \frac{4}{9} = (\frac{48 + 33}{20}) \cdot \frac{4}{9} = \frac{81}{20} \cdot \frac{4}{9} = \frac{9 \cdot 1}{5 \cdot 1} = \frac{9}{5} = 1\frac{4}{5}$ 8) $2\frac{11}{36} : (1\frac{3}{27} + 3\frac{10}{20}) = 2\frac{11}{36} : (1\frac{1}{9} + 3\frac{1}{2}) = \frac{83}{36} : (\frac{10}{9} + \frac{7}{2}) = \frac{83}{36} : (\frac{10 \cdot 2}{9 \cdot 2} + \frac{7 \cdot 9}{2 \cdot 9}) = \frac{83}{36} : (\frac{20 + 63}{18}) = \frac{83}{36} : \frac{83}{18} = \frac{83}{36} \cdot \frac{18}{83} = \frac{1}{2}$ 4) $(\frac{8}{16} - 3\frac{3}{18}) \cdot 12 = (\frac{1}{2} - 3\frac{1}{6}) \cdot 12 = (\frac{1}{2} - \frac{19}{6}) \cdot 12 = (\frac{1 \cdot 3}{2 \cdot 3} - \frac{19}{6}) \cdot 12 = (\frac{3 - 19}{6}) \cdot 12 = -\frac{16}{6} \cdot 12 = -\frac{8}{3} \cdot 12 = -8 \cdot 4 = -32$ 9) $2\frac{3}{5} : (1\frac{12}{30} - 1\frac{10}{27}) = 2\frac{3}{5} : (1\frac{2}{5} - 1\frac{10}{27}) = \frac{13}{5} : (\frac{7}{5} - \frac{37}{27}) = \frac{13}{5} : (\frac{7 \cdot 27}{5 \cdot 27} - \frac{37 \cdot 5}{27 \cdot 5}) = \frac{13}{5} : (\frac{189 - 185}{135}) = \frac{13}{5} : \frac{4}{135} = \frac{13}{5} \cdot \frac{135}{4} = \frac{13 \cdot 27}{4} = \frac{351}{4} = 87\frac{3}{4}$ 5) $(1\frac{3}{20} + 2\frac{7}{10}) \cdot \frac{3}{11} = (1\frac{3}{20} + 2\frac{14}{20}) \cdot \frac{3}{11} = (\frac{23}{20} + \frac{54}{20}) \cdot \frac{3}{11} = \frac{77}{20} \cdot \frac{3}{11} = \frac{7 \cdot 3}{20} = \frac{21}{20} = 1\frac{1}{20}$ 10) $18\frac{1}{5} : (2\frac{12}{30} - 2\frac{5}{6}) = 18\frac{1}{5} : (2\frac{2}{5} - 2\frac{5}{6}) = \frac{91}{5} : (\frac{12}{5} - \frac{17}{6}) = \frac{91}{5} : (\frac{12 \cdot 6}{5 \cdot 6} - \frac{17 \cdot 5}{6 \cdot 5}) = \frac{91}{5} : (\frac{72 - 85}{30}) = \frac{91}{5} : (-\frac{13}{30}) = - \frac{91}{5} \cdot \frac{30}{13} = - \frac{91 \cdot 6}{13} = - 7 \cdot 6 = -42$