Задание №1. Выполните действие:

Ответ: Решения представлены ниже.

1. а) \[ \frac{3}{4} : \frac{5}{7} = \frac{3}{4} \cdot \frac{7}{5} = \frac{3 \cdot 7}{4 \cdot 5} = \frac{21}{20} = 1 \frac{1}{20} \]
2. б) \[ \frac{1}{8} : \frac{3}{4} = \frac{1}{8} \cdot \frac{4}{3} = \frac{1 \cdot 4}{8 \cdot 3} = \frac{4}{24} = \frac{1}{6} \]
3. в) \[ \frac{11}{12} : \frac{8}{9} = \frac{11}{12} \cdot \frac{9}{8} = \frac{11 \cdot 9}{12 \cdot 8} = \frac{99}{96} = \frac{33}{32} = 1 \frac{1}{32} \]
4. г) \[ \frac{3}{11} : \frac{22}{45} = \frac{3}{11} \cdot \frac{45}{22} = \frac{3 \cdot 45}{11 \cdot 22} = \frac{135}{242} \]
5. д) \[ \frac{12}{7} : \frac{14}{27} = \frac{12}{7} \cdot \frac{27}{14} = \frac{12 \cdot 27}{7 \cdot 14} = \frac{324}{98} = \frac{162}{49} = 3 \frac{15}{49} \]
6. е) \[ \frac{18}{39} : \frac{13}{36} = \frac{18}{39} \cdot \frac{36}{13} = \frac{18 \cdot 36}{39 \cdot 13} = \frac{648}{507} = \frac{216}{169} = 1 \frac{47}{169} \]
7. ж) \[ \frac{24}{17} : \frac{51}{40} = \frac{24}{17} \cdot \frac{40}{51} = \frac{24 \cdot 40}{17 \cdot 51} = \frac{960}{867} = \frac{320}{289} = 1 \frac{31}{289} \]
8. з) \[ \frac{32}{33} : \frac{55}{48} = \frac{32}{33} \cdot \frac{48}{55} = \frac{32 \cdot 48}{33 \cdot 55} = \frac{1536}{1815} = \frac{512}{605} \]
9. и) \[ \frac{16}{81} : \frac{45}{57} : \frac{19}{4} = \frac{16}{81} \cdot \frac{57}{45} \cdot \frac{4}{19} = \frac{16 \cdot 57 \cdot 4}{81 \cdot 45 \cdot 19} = \frac{3648}{69465} = \frac{1216}{23155} \]
10. к) \[ \frac{72}{49} : \frac{5}{88} : \frac{77}{25} = \frac{72}{49} \cdot \frac{88}{5} \cdot \frac{25}{77} = \frac{72 \cdot 88 \cdot 25}{49 \cdot 5 \cdot 77} = \frac{158400}{18865} = \frac{31680}{3773} \]
11. л) \[ \frac{18}{95} : \frac{35}{3} : \frac{19}{42} = \frac{18}{95} \cdot \frac{3}{35} \cdot \frac{42}{19} = \frac{18 \cdot 3 \cdot 42}{95 \cdot 35 \cdot 19} = \frac{2268}{62775} = \frac{756}{20925} \]
12. м) \[ \frac{20}{23} : \frac{73}{48} : \frac{46}{73} = \frac{20}{23} \cdot \frac{48}{73} \cdot \frac{73}{46} = \frac{20 \cdot 48 \cdot 73}{23 \cdot 73 \cdot 46} = \frac{70080}{77254} = \frac{35040}{38627} \]
13. н) \[ \left( \frac{4}{5} \right)^2 = \frac{4^2}{5^2} = \frac{16}{25} \]
14. о) \[ \left( \frac{2}{3} \right)^3 = \frac{2^3}{3^3} = \frac{8}{27} \]
15. п) \[ \left( \frac{7}{8} \right)^2 = \frac{7^2}{8^2} = \frac{49}{64} \]
16. р) \[ \left( \frac{5}{4} \right)^3 = \frac{5^3}{4^3} = \frac{125}{64} = 1 \frac{61}{64} \]

Ответ: Решения представлены выше.