Вопрос:

289 Найди значение выражения: a) 3/11 : 22/45; б) 12/7 : 14/27; в) 18/39 : 13/36; г) 24/17 : 51/40; д) 18/81 : 16/57;\(\ne\)) 72/49 : 5/88; ж) 18/95 : 35/42; 3) 20/23 : 73/46

Ответ:

a) \( \frac{3}{11} : \frac{22}{45} = \frac{3}{11} \cdot \frac{45}{22} = \frac{3 \cdot 45}{11 \cdot 22} = \frac{135}{242} \)д) \( \frac{18}{81} : \frac{16}{57} = \frac{18}{81} \cdot \frac{57}{16} = \frac{2 \cdot 9}{9 \cdot 9} \cdot \frac{3 \cdot 19}{2 \cdot 8} = \frac{2}{9} \cdot \frac{57}{16} = \frac{1}{9} \cdot \frac{57}{8} = \frac{1 \cdot 57}{9 \cdot 8} = \frac{57}{72} = \frac{19 \cdot 3}{24 \cdot 3} = \frac{19}{24} \)
б) \( \frac{12}{7} : \frac{14}{27} = \frac{12}{7} \cdot \frac{27}{14} = \frac{6 \cdot 2}{7} \cdot \frac{27}{2 \cdot 7} = \frac{6}{7} \cdot \frac{27}{7} = \frac{6 \cdot 27}{7 \cdot 7} = \frac{162}{49} \)e) \( \frac{72}{49} : \frac{5}{88} = \frac{72}{49} \cdot \frac{88}{5} = \frac{72 \cdot 88}{49 \cdot 5} = \frac{6336}{245} \)
в) \( \frac{18}{39} : \frac{13}{36} = \frac{18}{39} \cdot \frac{36}{13} = \frac{18 \cdot 36}{39 \cdot 13} = \frac{654}{507} = \frac{218 \cdot 3}{169 \cdot 3} = \frac{218}{169} \)ж) \( \frac{18}{95} : \frac{35}{42} = \frac{18}{95} \cdot \frac{42}{35} = \frac{18 \cdot 42}{95 \cdot 35} = \frac{756}{3325} \)
г) \( \frac{24}{17} : \frac{51}{40} = \frac{24}{17} \cdot \frac{40}{51} = \frac{24 \cdot 40}{17 \cdot 51} = \frac{960}{867} = \frac{320 \cdot 3}{289 \cdot 3} = \frac{320}{289} \)3) \( \frac{20}{23} : \frac{73}{46} = \frac{20}{23} \cdot \frac{46}{73} = \frac{20 \cdot 46}{23 \cdot 73} = \frac{20 \cdot 2 \cdot 23}{23 \cdot 73} = \frac{40}{73} \)