Контрольные задания > Выполни умножение: a) 1\(\frac{1}{7}\) ⋅ 3\(\frac{1}{16}\); б) \(\frac{2}{9}\) ⋅ 1\(\frac{1}{2}\); в) 4\(\frac{1}{6}\) ⋅ 8\(\frac{2}{5}\); г) 3\(\frac{9}{13}\) ⋅ 1\(\frac{5}{8}\); д) \(\frac{7}{8}\) ⋅ 5\(\frac{1}{3}\); е) 7\(\frac{5}{7}\) ⋅ 1\(\frac{1}{6}\); ж) 1\(\frac{4}{5}\) ⋅ 6\(\frac{2}{3}\); з) 4\(\frac{1}{2}\) ⋅ 2\(\frac{4}{5}\); и) 3\(\frac{3}{11}\) ⋅ 7\(\frac{1}{3}\); к) 10\(\frac{2}{7}\) ⋅ 1\(\frac{2}{9}\); л) 2\(\frac{1}{2}\) ⋅ \(\frac{18}{25}\); м) 5\(\frac{1}{7}\) ⋅ 3\(\frac{8}{9}\); н) 4\(\frac{1}{2}\) ⋅ \(\frac{14}{45}\); о) 3\(\frac{3}{5}\) ⋅ 5\(\frac{5}{8}\); п) 1\(\frac{1}{24}\) ⋅ 11\(\frac{1}{5}\); р) 12\(\frac{4}{5}\) ⋅ 3\(\frac{1}{8}\);
Вопрос:

Выполни умножение: a) 1\(\frac{1}{7}\) ⋅ 3\(\frac{1}{16}\); б) \(\frac{2}{9}\) ⋅ 1\(\frac{1}{2}\); в) 4\(\frac{1}{6}\) ⋅ 8\(\frac{2}{5}\); г) 3\(\frac{9}{13}\) ⋅ 1\(\frac{5}{8}\); д) \(\frac{7}{8}\) ⋅ 5\(\frac{1}{3}\); е) 7\(\frac{5}{7}\) ⋅ 1\(\frac{1}{6}\); ж) 1\(\frac{4}{5}\) ⋅ 6\(\frac{2}{3}\); з) 4\(\frac{1}{2}\) ⋅ 2\(\frac{4}{5}\); и) 3\(\frac{3}{11}\) ⋅ 7\(\frac{1}{3}\); к) 10\(\frac{2}{7}\) ⋅ 1\(\frac{2}{9}\); л) 2\(\frac{1}{2}\) ⋅ \(\frac{18}{25}\); м) 5\(\frac{1}{7}\) ⋅ 3\(\frac{8}{9}\); н) 4\(\frac{1}{2}\) ⋅ \(\frac{14}{45}\); о) 3\(\frac{3}{5}\) ⋅ 5\(\frac{5}{8}\); п) 1\(\frac{1}{24}\) ⋅ 11\(\frac{1}{5}\); р) 12\(\frac{4}{5}\) ⋅ 3\(\frac{1}{8}\);

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Ответ:

Краткое пояснение: Переводим смешанные дроби в неправильные и выполняем умножение числителя на числитель, знаменателя на знаменатель.
  1. а) 1\(\frac{1}{7}\) ⋅ 3\(\frac{1}{16}\) = \(\frac{8}{7}\) ⋅ \(\frac{49}{16}\) = \(\frac{8 ⋅ 49}{7 ⋅ 16}\) = \(\frac{1 ⋅ 7}{1 ⋅ 2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)
  2. б) \(\frac{2}{9}\) ⋅ 1\(\frac{1}{2}\) = \(\frac{2}{9}\) ⋅ \(\frac{3}{2}\) = \(\frac{2 ⋅ 3}{9 ⋅ 2}\) = \(\frac{1 ⋅ 1}{3 ⋅ 1}\) = \(\frac{1}{3}\)
  3. в) 4\(\frac{1}{6}\) ⋅ 8\(\frac{2}{5}\) = \(\frac{25}{6}\) ⋅ \(\frac{42}{5}\) = \(\frac{25 ⋅ 42}{6 ⋅ 5}\) = \(\frac{5 ⋅ 7}{1 ⋅ 1}\) = 35
  4. г) 3\(\frac{9}{13}\) ⋅ 1\(\frac{5}{8}\) = \(\frac{48}{13}\) ⋅ \(\frac{13}{8}\) = \(\frac{48 ⋅ 13}{13 ⋅ 8}\) = \(\frac{6 ⋅ 1}{1 ⋅ 1}\) = 6
  5. д) \(\frac{7}{8}\) ⋅ 5\(\frac{1}{3}\) = \(\frac{7}{8}\) ⋅ \(\frac{16}{3}\) = \(\frac{7 ⋅ 16}{8 ⋅ 3}\) = \(\frac{7 ⋅ 2}{1 ⋅ 3}\) = \(\frac{14}{3}\) = 4\(\frac{2}{3}\)
  6. е) 7\(\frac{5}{7}\) ⋅ 1\(\frac{1}{6}\) = \(\frac{54}{7}\) ⋅ \(\frac{7}{6}\) = \(\frac{54 ⋅ 7}{7 ⋅ 6}\) = \(\frac{9 ⋅ 1}{1 ⋅ 1}\) = 9
  7. ж) 1\(\frac{4}{5}\) ⋅ 6\(\frac{2}{3}\) = \(\frac{9}{5}\) ⋅ \(\frac{20}{3}\) = \(\frac{9 ⋅ 20}{5 ⋅ 3}\) = \(\frac{3 ⋅ 4}{1 ⋅ 1}\) = 12
  8. з) 4\(\frac{1}{2}\) ⋅ 2\(\frac{4}{5}\) = \(\frac{9}{2}\) ⋅ \(\frac{14}{5}\) = \(\frac{9 ⋅ 14}{2 ⋅ 5}\) = \(\frac{9 ⋅ 7}{1 ⋅ 5}\) = \(\frac{63}{5}\) = 12\(\frac{3}{5}\)
  9. и) 3\(\frac{3}{11}\) ⋅ 7\(\frac{1}{3}\) = \(\frac{36}{11}\) ⋅ \(\frac{22}{3}\) = \(\frac{36 ⋅ 22}{11 ⋅ 3}\) = \(\frac{12 ⋅ 2}{1 ⋅ 1}\) = 24
  10. к) 10\(\frac{2}{7}\) ⋅ 1\(\frac{2}{9}\) = \(\frac{72}{7}\) ⋅ \(\frac{11}{9}\) = \(\frac{72 ⋅ 11}{7 ⋅ 9}\) = \(\frac{8 ⋅ 11}{7 ⋅ 1}\) = \(\frac{88}{7}\) = 12\(\frac{4}{7}\)
  11. л) 2\(\frac{1}{2}\) ⋅ \(\frac{18}{25}\) = \(\frac{5}{2}\) ⋅ \(\frac{18}{25}\) = \(\frac{5 ⋅ 18}{2 ⋅ 25}\) = \(\frac{1 ⋅ 9}{1 ⋅ 5}\) = \(\frac{9}{5}\) = 1\(\frac{4}{5}\)
  12. м) 5\(\frac{1}{7}\) ⋅ 3\(\frac{8}{9}\) = \(\frac{36}{7}\) ⋅ \(\frac{35}{9}\) = \(\frac{36 ⋅ 35}{7 ⋅ 9}\) = \(\frac{4 ⋅ 5}{1 ⋅ 1}\) = 20
  13. н) 4\(\frac{1}{2}\) ⋅ \(\frac{14}{45}\) = \(\frac{9}{2}\) ⋅ \(\frac{14}{45}\) = \(\frac{9 ⋅ 14}{2 ⋅ 45}\) = \(\frac{1 ⋅ 7}{1 ⋅ 5}\) = \(\frac{7}{5}\) = 1\(\frac{2}{5}\)
  14. о) 3\(\frac{3}{5}\) ⋅ 5\(\frac{5}{8}\) = \(\frac{18}{5}\) ⋅ \(\frac{45}{8}\) = \(\frac{18 ⋅ 45}{5 ⋅ 8}\) = \(\frac{9 ⋅ 9}{1 ⋅ 4}\) = \(\frac{81}{4}\) = 20\(\frac{1}{4}\)
  15. п) 1\(\frac{1}{24}\) ⋅ 11\(\frac{1}{5}\) = \(\frac{25}{24}\) ⋅ \(\frac{56}{5}\) = \(\frac{25 ⋅ 56}{24 ⋅ 5}\) = \(\frac{5 ⋅ 7}{3 ⋅ 1}\) = \(\frac{35}{3}\) = 11\(\frac{2}{3}\)
  16. р) 12\(\frac{4}{5}\) ⋅ 3\(\frac{1}{8}\) = \(\frac{64}{5}\) ⋅ \(\frac{25}{8}\) = \(\frac{64 ⋅ 25}{5 ⋅ 8}\) = \(\frac{8 ⋅ 5}{1 ⋅ 1}\) = 40

Ответ: а) 3\(\frac{1}{2}\); б) \(\frac{1}{3}\); в) 35; г) 6; д) 4\(\frac{2}{3}\); е) 9; ж) 12; з) 12\(\frac{3}{5}\); и) 24; к) 12\(\frac{4}{7}\); л) 1\(\frac{4}{5}\); м) 20; н) 1\(\frac{2}{5}\); о) 20\(\frac{1}{4}\); п) 11\(\frac{2}{3}\); р) 40

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