Контрольные задания > Найдите произведение или частное: a) $$9 \div \frac{5}{10} \cdot \frac{5}{12}$$; б) $$3 \frac{11}{5} \div \frac{2}{15}$$; в) $$9 \div \frac{2}{22} \cdot 6$$; г) $$\frac{7}{8} \div \frac{7}{16}$$; д) $$\frac{27}{40} \div \frac{18}{35}$$; e) $$\frac{8}{9} \div 6$$; ж) $$15 \cdot \frac{5}{6}$$; з) $$3 \frac{1}{7} \cdot 12$$; и) $$2 \frac{1}{3}$$; к) $$2 \div \frac{18}{3}$$; л) $$8 \div \frac{36}{27}$$; м) $$10 \div \frac{4}{15}$$
Вопрос:

Найдите произведение или частное: a) $$9 \div \frac{5}{10} \cdot \frac{5}{12}$$; б) $$3 \frac{11}{5} \div \frac{2}{15}$$; в) $$9 \div \frac{2}{22} \cdot 6$$; г) $$\frac{7}{8} \div \frac{7}{16}$$; д) $$\frac{27}{40} \div \frac{18}{35}$$; e) $$\frac{8}{9} \div 6$$; ж) $$15 \cdot \frac{5}{6}$$; з) $$3 \frac{1}{7} \cdot 12$$; и) $$2 \frac{1}{3}$$; к) $$2 \div \frac{18}{3}$$; л) $$8 \div \frac{36}{27}$$; м) $$10 \div \frac{4}{15}$$

Ответ:

  1. a) $$9 \div \frac{5}{10} \cdot \frac{5}{12} = 9 \div \frac{1}{2} \cdot \frac{5}{12} = 9 \cdot 2 \cdot \frac{5}{12} = 18 \cdot \frac{5}{12} = \frac{18 \cdot 5}{12} = \frac{90}{12} = \frac{15}{2} = 7 \frac{1}{2}$$
  2. б) $$3 \frac{11}{5} \div \frac{2}{15} = \frac{26}{5} \div \frac{2}{15} = \frac{26}{5} \cdot \frac{15}{2} = \frac{26 \cdot 15}{5 \cdot 2} = \frac{26 \cdot 3}{2} = 13 \cdot 3 = 39$$
  3. в) $$9 \div \frac{2}{22} \cdot 6 = 9 \div \frac{1}{11} \cdot 6 = 9 \cdot 11 \cdot 6 = 99 \cdot 6 = 594$$
  4. г) $$\frac{7}{8} \div \frac{7}{16} = \frac{7}{8} \cdot \frac{16}{7} = \frac{7 \cdot 16}{8 \cdot 7} = \frac{16}{8} = 2$$
  5. д) $$\frac{27}{40} \div \frac{18}{35} = \frac{27}{40} \cdot \frac{35}{18} = \frac{27 \cdot 35}{40 \cdot 18} = \frac{3 \cdot 7}{8 \cdot 2} = \frac{21}{16} = 1 \frac{5}{16}$$
  6. e) $$\frac{8}{9} \div 6 = \frac{8}{9} \cdot \frac{1}{6} = \frac{8}{9 \cdot 6} = \frac{8}{54} = \frac{4}{27}$$
  7. ж) $$15 \cdot \frac{5}{6} = \frac{15 \cdot 5}{6} = \frac{75}{6} = \frac{25}{2} = 12 \frac{1}{2}$$
  8. з) $$3 \frac{1}{7} \cdot 12 = \frac{22}{7} \cdot 12 = \frac{22 \cdot 12}{7} = \frac{264}{7} = 37 \frac{5}{7}$$
  9. и) $$2 \frac{1}{3} = \frac{7}{3}$$
  10. к) $$2 \div \frac{18}{3} = 2 \div 6 = \frac{2}{6} = \frac{1}{3}$$
  11. л) $$8 \div \frac{36}{27} = 8 \div \frac{4}{3} = 8 \cdot \frac{3}{4} = \frac{8 \cdot 3}{4} = 2 \cdot 3 = 6$$
  12. м) $$10 \div \frac{4}{15} = 10 \cdot \frac{15}{4} = \frac{10 \cdot 15}{4} = \frac{5 \cdot 15}{2} = \frac{75}{2} = 37 \frac{1}{2}$$
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