Контрольные задания > Выполните действия: 1) $90 \cdot \frac{4}{63}$; 2) $\frac{15}{34} \cdot 16$; 3) $\frac{11}{26} \cdot \frac{1}{2}$; 4) $\frac{1}{3} \cdot \frac{1}{5}$; 5) $\frac{5}{66} \cdot \frac{9}{20}$; 6) $\frac{2}{55} \cdot \frac{35}{4}$; 7) $2\frac{14}{15} \cdot 5\frac{7}{16}$; 8) $8\frac{3}{4} \cdot 1\frac{11}{15}$; 9) $12 : \frac{10}{11}$; 10) $\frac{2}{7} : 16$; 11) $\frac{9}{32} : \frac{3}{4}$; 12) $3\frac{1}{4} : 4\frac{1}{3}$; 13) $1\frac{1}{10} : 6\frac{1}{2}$; 14) $0,5 \cdot \frac{1}{2}$; 15) $\frac{3}{8} : 0,75$; 16) $0,3 : \frac{3}{4}$.
Вопрос:

Выполните действия: 1) $$90 \cdot \frac{4}{63}$$; 2) $$\frac{15}{34} \cdot 16$$; 3) $$\frac{11}{26} \cdot \frac{1}{2}$$; 4) $$\frac{1}{3} \cdot \frac{1}{5}$$; 5) $$\frac{5}{66} \cdot \frac{9}{20}$$; 6) $$\frac{2}{55} \cdot \frac{35}{4}$$; 7) $$2\frac{14}{15} \cdot 5\frac{7}{16}$$; 8) $$8\frac{3}{4} \cdot 1\frac{11}{15}$$; 9) $$12 : \frac{10}{11}$$; 10) $$\frac{2}{7} : 16$$; 11) $$\frac{9}{32} : \frac{3}{4}$$; 12) $$3\frac{1}{4} : 4\frac{1}{3}$$; 13) $$1\frac{1}{10} : 6\frac{1}{2}$$; 14) $$0,5 \cdot \frac{1}{2}$$; 15) $$\frac{3}{8} : 0,75$$; 16) $$0,3 : \frac{3}{4}$$.

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Ответ:

Решение:

  1. $$90 \cdot \frac{4}{63} = \frac{90 \cdot 4}{63} = \frac{360}{63} = \frac{40}{7} = 5\frac{5}{7}$$
  2. $$\frac{15}{34} \cdot 16 = \frac{15 \cdot 16}{34} = \frac{240}{34} = \frac{120}{17} = 7\frac{1}{17}$$
  3. $$\frac{11}{26} \cdot \frac{1}{2} = \frac{11 \cdot 1}{26 \cdot 2} = \frac{11}{52}$$
  4. $$\frac{1}{3} \cdot \frac{1}{5} = \frac{1 \cdot 1}{3 \cdot 5} = \frac{1}{15}$$
  5. $$\frac{5}{66} \cdot \frac{9}{20} = \frac{5 \cdot 9}{66 \cdot 20} = \frac{45}{1320} = \frac{3}{88}$$
  6. $$\frac{2}{55} \cdot \frac{35}{4} = \frac{2 \cdot 35}{55 \cdot 4} = \frac{70}{220} = \frac{7}{22}$$
  7. $$2\frac{14}{15} \cdot 5\frac{7}{16} = \frac{2 \cdot 15 + 14}{15} \cdot \frac{5 \cdot 16 + 7}{16} = \frac{44}{15} \cdot \frac{87}{16} = \frac{44 \cdot 87}{15 \cdot 16} = \frac{3828}{240} = \frac{319}{20} = 15\frac{19}{20}$$
  8. $$8\frac{3}{4} \cdot 1\frac{11}{15} = \frac{8 \cdot 4 + 3}{4} \cdot \frac{1 \cdot 15 + 11}{15} = \frac{35}{4} \cdot \frac{26}{15} = \frac{35 \cdot 26}{4 \cdot 15} = \frac{910}{60} = \frac{91}{6} = 15\frac{1}{6}$$
  9. $$12 : \frac{10}{11} = 12 \cdot \frac{11}{10} = \frac{12 \cdot 11}{10} = \frac{132}{10} = \frac{66}{5} = 13\frac{1}{5}$$
  10. $$\frac{2}{7} : 16 = \frac{2}{7} \cdot \frac{1}{16} = \frac{2 \cdot 1}{7 \cdot 16} = \frac{2}{112} = \frac{1}{56}$$
  11. $$\frac{9}{32} : \frac{3}{4} = \frac{9}{32} \cdot \frac{4}{3} = \frac{9 \cdot 4}{32 \cdot 3} = \frac{36}{96} = \frac{3}{8}$$
  12. $$3\frac{1}{4} : 4\frac{1}{3} = \frac{3 \cdot 4 + 1}{4} : \frac{4 \cdot 3 + 1}{3} = \frac{13}{4} : \frac{13}{3} = \frac{13}{4} \cdot \frac{3}{13} = \frac{13 \cdot 3}{4 \cdot 13} = \frac{39}{52} = \frac{3}{4}$$
  13. $$1\frac{1}{10} : 6\frac{1}{2} = \frac{1 \cdot 10 + 1}{10} : \frac{6 \cdot 2 + 1}{2} = \frac{11}{10} : \frac{13}{2} = \frac{11}{10} \cdot \frac{2}{13} = \frac{11 \cdot 2}{10 \cdot 13} = \frac{22}{130} = \frac{11}{65}$$
  14. $$0,5 \cdot \frac{1}{2} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4}$$
  15. $$\frac{3}{8} : 0,75 = \frac{3}{8} : \frac{75}{100} = \frac{3}{8} : \frac{3}{4} = \frac{3}{8} \cdot \frac{4}{3} = \frac{3 \cdot 4}{8 \cdot 3} = \frac{12}{24} = \frac{1}{2}$$
  16. $$0,3 : \frac{3}{4} = \frac{3}{10} : \frac{3}{4} = \frac{3}{10} \cdot \frac{4}{3} = \frac{3 \cdot 4}{10 \cdot 3} = \frac{12}{30} = \frac{2}{5}$$
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