Краткое пояснение: Чтобы умножить смешанные дроби, нужно перевести их в неправильные дроби, а затем умножить числители и знаменатели.
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a) $$1\frac{1}{2} \cdot 3 = \frac{3}{2} \cdot \frac{3}{1} = \frac{3 \cdot 3}{2 \cdot 1} = \frac{9}{2} = 4\frac{1}{2}$$
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b) $$3\frac{1}{2} \cdot 5 = \frac{7}{2} \cdot \frac{5}{1} = \frac{7 \cdot 5}{2 \cdot 1} = \frac{35}{2} = 17\frac{1}{2}$$
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c) $$2\frac{1}{5} \cdot 5 = \frac{11}{5} \cdot \frac{5}{1} = \frac{11 \cdot 5}{5 \cdot 1} = \frac{55}{5} = 11$$
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d) $$(3\frac{1}{2})^2 = (\frac{7}{2})^2 = \frac{7}{2} \cdot \frac{7}{2} = \frac{7 \cdot 7}{2 \cdot 2} = \frac{49}{4} = 12\frac{1}{4}$$
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e) $$(1\frac{1}{3})^3 = (\frac{4}{3})^3 = \frac{4}{3} \cdot \frac{4}{3} \cdot \frac{4}{3} = \frac{4 \cdot 4 \cdot 4}{3 \cdot 3 \cdot 3} = \frac{64}{27} = 2\frac{10}{27}$$
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f) $$1\frac{3}{5} \cdot \frac{5}{7} = \frac{8}{5} \cdot \frac{5}{7} = \frac{8 \cdot 5}{5 \cdot 7} = \frac{40}{35} = \frac{8}{7} = 1\frac{1}{7}$$
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g) $$5\frac{1}{4} \cdot \frac{2}{7} = \frac{21}{4} \cdot \frac{2}{7} = \frac{21 \cdot 2}{4 \cdot 7} = \frac{42}{28} = \frac{3}{2} = 1\frac{1}{2}$$
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h) $$\frac{2}{9} \cdot 3\frac{3}{5} = \frac{2}{9} \cdot \frac{18}{5} = \frac{2 \cdot 18}{9 \cdot 5} = \frac{36}{45} = \frac{4}{5}$$
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i) $$5\frac{1}{6} \cdot 2\frac{1}{3} = \frac{31}{6} \cdot \frac{7}{3} = \frac{31 \cdot 7}{6 \cdot 3} = \frac{217}{18} = 12\frac{1}{18}$$
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j) $$\frac{3}{7} \cdot 3\frac{1}{2} = \frac{3}{7} \cdot \frac{7}{2} = \frac{3 \cdot 7}{7 \cdot 2} = \frac{21}{14} = \frac{3}{2} = 1\frac{1}{2}$$
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k) $$3\frac{1}{3} \cdot 2\frac{1}{10} = \frac{10}{3} \cdot \frac{21}{10} = \frac{10 \cdot 21}{3 \cdot 10} = \frac{210}{30} = 7$$
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l) $$3\frac{1}{3} \cdot 2\frac{1}{10} = \frac{10}{3} \cdot \frac{21}{10} = \frac{10 \cdot 21}{3 \cdot 10} = \frac{210}{30} = 7$$
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m) $$3\frac{1}{9} \cdot 1\frac{2}{7} = \frac{28}{9} \cdot \frac{9}{7} = \frac{28 \cdot 9}{9 \cdot 7} = \frac{252}{63} = 4$$
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n) $$2\frac{5}{7} \cdot 2\frac{1}{3} = \frac{19}{7} \cdot \frac{7}{3} = \frac{19 \cdot 7}{7 \cdot 3} = \frac{133}{21} = 6\frac{7}{21} = 6\frac{1}{3}$$
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o) $$3\frac{3}{5} \cdot 3\frac{3}{4} = \frac{18}{5} \cdot \frac{15}{4} = \frac{18 \cdot 15}{5 \cdot 4} = \frac{270}{20} = \frac{27}{2} = 13\frac{1}{2}$$
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p) $$1\frac{6}{2} \cdot \frac{4}{11} \cdot \frac{1}{9} = \frac{8}{2} \cdot \frac{4}{11} \cdot \frac{1}{9} = \frac{8 \cdot 4 \cdot 1}{2 \cdot 11 \cdot 9} = \frac{32}{198} = \frac{16}{99}$$
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q) $$1\frac{7}{25} \cdot 9 \cdot \frac{4}{11} \cdot \frac{1}{2} = \frac{32}{25} \cdot \frac{9}{1} \cdot \frac{4}{11} \cdot \frac{1}{2} = \frac{32 \cdot 9 \cdot 4 \cdot 1}{25 \cdot 1 \cdot 11 \cdot 2} = \frac{1152}{550} = \frac{576}{275} = 2\frac{26}{275}$$
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r) $$27 \cdot (\frac{2}{3})^2 \cdot \frac{7}{8} = \frac{27}{1} \cdot \frac{4}{9} \cdot \frac{7}{8} = \frac{27 \cdot 4 \cdot 7}{1 \cdot 9 \cdot 8} = \frac{756}{72} = \frac{21}{2} = 10\frac{1}{2}$$
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s) $$1\frac{1}{12} \cdot 1\frac{1}{13} \cdot 1\frac{1}{14} = \frac{13}{12} \cdot \frac{14}{13} \cdot \frac{15}{14} = \frac{13 \cdot 14 \cdot 15}{12 \cdot 13 \cdot 14} = \frac{2730}{2184} = \frac{5}{4} = 1\frac{1}{4}$$
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t) $$1\frac{2}{15} \cdot 1\frac{2}{17} \cdot 1\frac{2}{19} = \frac{17}{15} \cdot \frac{19}{17} \cdot \frac{21}{19} = \frac{17 \cdot 19 \cdot 21}{15 \cdot 17 \cdot 19} = \frac{6783}{4845} = \frac{21}{15} = \frac{7}{5} = 1\frac{2}{5}$$
Ответ: См. подробное решение выше