1. Выполните действия. 4 3 a) • 9 32 9 6) 42 28 8 в) 1:— 17 5 г) :— 56 7 4 д) :— 9 8 9 е) —: 16 25 5 ж) 5.3 26 3) 9:27 28 7 и) 22:1— 9 36

Ответ:

1. а) \[\frac{4}{9} \cdot \frac{3}{32} = \frac{4 \cdot 3}{9 \cdot 32} = \frac{1 \cdot 1}{3 \cdot 8} = \frac{1}{24}\]
2. б) \[\frac{9}{28} \cdot 42 = \frac{9 \cdot 42}{28} = \frac{9 \cdot 3 \cdot 14}{2 \cdot 14} = \frac{9 \cdot 3}{2} = \frac{27}{2} = 13 \frac{1}{2}\]
3. в) \[1 \frac{8}{17} = \frac{1 \cdot 17 + 8}{17} = \frac{25}{17}\] \[\frac{25}{17} : \frac{8}{1} = \frac{25}{17} \cdot \frac{1}{8} = \frac{25 \cdot 1}{17 \cdot 8} = \frac{25}{136}\]
4. г) \[\frac{25}{56} : \frac{5}{7} = \frac{25}{56} \cdot \frac{7}{5} = \frac{5 \cdot 5 \cdot 7}{8 \cdot 7 \cdot 5} = \frac{5}{8}\]
5. д) \[\frac{4}{9} : \frac{7}{8} = \frac{4}{9} \cdot \frac{8}{7} = \frac{4 \cdot 8}{9 \cdot 7} = \frac{32}{63}\]
6. е) \[\frac{9}{16} : \frac{36}{1} = \frac{9}{16} \cdot \frac{1}{36} = \frac{9 \cdot 1}{16 \cdot 9 \cdot 4} = \frac{1}{64}\]
7. ж) \[5 \cdot \frac{3}{26} = \frac{5}{1} \cdot \frac{3}{26} = \frac{5 \cdot 3}{1 \cdot 26} = \frac{15}{26}\]
8. з) \[9 : \frac{27}{28} = \frac{9}{1} \cdot \frac{28}{27} = \frac{9 \cdot 28}{1 \cdot 9 \cdot 3} = \frac{28}{3} = 9 \frac{1}{3}\]
9. и) \[2 \frac{2}{9} : 1 \frac{7}{9} = \frac{2 \cdot 9 + 2}{9} : \frac{1 \cdot 9 + 7}{9} = \frac{20}{9} : \frac{16}{9} = \frac{20}{9} \cdot \frac{9}{16} = \frac{20 \cdot 9}{9 \cdot 16} = \frac{4 \cdot 5}{4 \cdot 4} = \frac{5}{4} = 1 \frac{1}{4}\]

Ответ: а) \(\frac{1}{24}\), б) \(13 \frac{1}{2}\), в) \(\frac{25}{136}\), г) \(\frac{5}{8}\), д) \(\frac{32}{63}\), е) \(\frac{1}{64}\), ж) \(\frac{15}{26}\), з) \(9 \frac{1}{3}\), и) \(1 \frac{1}{4}\)