Решение заданий

Задание 1. Найдите произведение:

а) $$rac{5}{6} cdot rac{7}{9} = rac{5 cdot 7}{6 cdot 9} = rac{35}{54}$$

б) $$rac{11}{28} cdot rac{7}{33} = rac{11 cdot 7}{28 cdot 33} = rac{11 cdot 7}{4 cdot 7 cdot 3 cdot 11} = rac{1}{4 cdot 3} = rac{1}{12}$$

в) $$1rac{8}{25} cdot 1rac{4}{11} = rac{25 + 8}{25} cdot rac{11 + 4}{11} = rac{33}{25} cdot rac{15}{11} = rac{3 cdot 11 cdot 3 cdot 5}{5 cdot 5 cdot 11} = rac{3 cdot 3}{5} = rac{9}{5} = 1rac{4}{5}$$

г) $$3rac{5}{7} cdot 1rac{1}{13} = rac{3 cdot 7 + 5}{7} cdot rac{1 cdot 13 + 1}{13} = rac{26}{7} cdot rac{14}{13} = rac{2 cdot 13 cdot 2 cdot 7}{7 cdot 13} = 2 cdot 2 = 4$$

д) $$2rac{2}{3} cdot 6 = rac{2 cdot 3 + 2}{3} cdot 6 = rac{8}{3} cdot 6 = rac{8 cdot 6}{3} = 8 cdot 2 = 16$$

Задание 2. Выполните действия:

а) $$1rac{5}{19} cdot (6 - 3rac{5}{8}) = rac{19 + 5}{19} cdot (6 - rac{3 cdot 8 + 5}{8}) = rac{24}{19} cdot (6 - rac{29}{8}) = rac{24}{19} cdot (rac{6 cdot 8}{8} - rac{29}{8}) = rac{24}{19} cdot (rac{48}{8} - rac{29}{8}) = rac{24}{19} cdot rac{48 - 29}{8} = rac{24}{19} cdot rac{19}{8} = rac{24 cdot 19}{19 cdot 8} = rac{3 cdot 8 cdot 19}{19 cdot 8} = 3$$

б) $$1,8 cdot (6,3 cdot 1,4 - 2,05) = 1,8 cdot (8,82 - 2,05) = 1,8 cdot 6,77 = 12,186$$

в) $$1rac{2}{23} cdot 2,07 cdot rac{2}{9} = rac{23 + 2}{23} cdot 2,07 cdot rac{2}{9} = rac{25}{23} cdot 2,07 cdot rac{2}{9} = rac{25}{23} cdot rac{207}{100} cdot rac{2}{9} = rac{25 cdot 207 cdot 2}{23 cdot 100 cdot 9} = rac{25 cdot 23 cdot 9 cdot 2}{23 cdot 25 cdot 4 cdot 9} = rac{2}{4} = rac{1}{2} = 0,5$$

г) $$3,2 cdot 2rac{5}{8} cdot rac{5}{7} cdot 3,2 = 3,2 cdot rac{2 cdot 8 + 5}{8} cdot rac{5}{7} cdot 3,2 = 3,2 cdot rac{21}{8} cdot rac{5}{7} cdot 3,2 = rac{32}{10} cdot rac{21}{8} cdot rac{5}{7} cdot rac{32}{10} = rac{1024 cdot 105}{560} = rac{107520}{5600} = rac{192}{10} = 19,2$$

д) $$1rac{5}{7} cdot 1rac{2}{3} cdot 4,2 = rac{7 + 5}{7} cdot rac{3 + 2}{3} cdot 4,2 = rac{12}{7} cdot rac{5}{3} cdot rac{42}{10} = rac{12 cdot 5 cdot 42}{7 cdot 3 cdot 10} = rac{12 cdot 5 cdot 6 cdot 7}{7 cdot 3 cdot 2 cdot 5} = rac{12 cdot 6}{3 cdot 2} = rac{72}{6} = 12$$

е) $$rac{8}{21} cdot 1,05 cdot 1rac{2}{3} = rac{8}{21} cdot 1,05 cdot rac{3 + 2}{3} = rac{8}{21} cdot rac{105}{100} cdot rac{5}{3} = rac{8 cdot 105 cdot 5}{21 cdot 100 cdot 3} = rac{8 cdot 5 cdot 21 cdot 5}{21 cdot 20 cdot 5 cdot 3} = rac{8 cdot 5}{20 cdot 3} = rac{40}{60} = rac{2}{3}$$