461. Найдите значение выражения: 1) (2 13/48 + 2 5/12) : (3 3/4 - 9 3/12); 2) (8 : 2 10/19 - 1 13/15 * 6/19) : (3 1/12 - 25/36).

Решение:

1. \( (2 \frac{13}{48} + 2 \frac{5}{12}) : (3 \frac{3}{4} - 9 \frac{3}{12}) = (\frac{109}{48} + \frac{29}{12}) : (\frac{15}{4} - \frac{111}{12}) = (\frac{109}{48} + \frac{116}{48}) : (\frac{45}{12} - \frac{111}{12}) = \frac{225}{48} : \frac{-66}{12} = \frac{225}{48} \times \frac{12}{-66} = \frac{225}{4} \times \frac{1}{-66} = \frac{225}{-264} = -\frac{75}{88} \)
2. \( (8 : 2 \frac{10}{19} - 1 \frac{13}{15} \times \frac{6}{19}) : (3 \frac{1}{12} - \frac{25}{36}) = (8 : \frac{48}{19} - \frac{28}{15} \times \frac{6}{19}) : (\frac{37}{12} - \frac{25}{36}) = (8 \times \frac{19}{48} - \frac{168}{285}) : (\frac{111}{36} - \frac{25}{36}) = (\frac{19}{6} - \frac{56}{95}) : \frac{86}{36} = (\frac{1805 - 336}{570}) : \frac{43}{18} = \frac{1469}{570} \times \frac{18}{43} = \frac{1469 \times 18}{570 \times 43} = \frac{1469 \times 1}{31.66 \times 43} \approx \frac{1469}{1360.78} \approx 1.08 \)

Ответ: 1) \(-\frac{75}{88}\); 2) \(\approx 1.08\).