78. Вычислите: a) 0,46 ⋅ 3/23; б) 5,53 : 7/9; в) 5/8 - 0,73; г) 0,289 : 17/18; д) 17,17 : 1 5/12; е) 343,4 : 14 3/7.

Решение:

1. a) \( 0,46 \cdot \frac{3}{23} = \frac{46}{100} \cdot \frac{3}{23} = \frac{2 \cdot 23}{100} \cdot \frac{3}{23} = \frac{2 \cdot 3}{100} = \frac{6}{100} = 0,06 \)
2. б) \( 5,53 : \frac{7}{9} = \frac{553}{100} : \frac{7}{9} = \frac{553}{100} \cdot \frac{9}{7} = \frac{79 \cdot 7}{100} \cdot \frac{9}{7} = \frac{79 \cdot 9}{100} = \frac{711}{100} = 7,11 \)
3. в) \( \frac{5}{8} - 0,73 = \frac{5}{8} - \frac{73}{100} = \frac{5 \cdot 25}{8 \cdot 25} - \frac{73 \cdot 2}{100 \cdot 2} = \frac{125}{200} - \frac{146}{200} = \frac{125 - 146}{200} = \frac{-21}{200} = -0,105 \)
4. г) \( 0,289 : \frac{17}{18} = \frac{289}{1000} : \frac{17}{18} = \frac{289}{1000} \cdot \frac{18}{17} = \frac{17 \cdot 17}{1000} \cdot \frac{18}{17} = \frac{17 \cdot 18}{1000} = \frac{306}{1000} = 0,306 \)
5. д) \( 17,17 : 1 \frac{5}{12} = 17,17 : \frac{17}{12} = \frac{1717}{100} : \frac{17}{12} = \frac{1717}{100} \cdot \frac{12}{17} = \frac{101 \cdot 17}{100} \cdot \frac{12}{17} = \frac{101 \cdot 12}{100} = \frac{1212}{100} = 12,12 \)
6. е) \( 343,4 : 14 \frac{3}{7} = 343,4 : \frac{101}{7} = \frac{3434}{10} : \frac{101}{7} = \frac{3434}{10} \cdot \frac{7}{101} = \frac{34 \cdot 101}{10} \cdot \frac{7}{101} = \frac{34 \cdot 7}{10} = \frac{238}{10} = 23,8 \)

Ответ: а) 0,06; б) 7,11; в) -0,105; г) 0,306; д) 12,12; е) 23,8.