109. Найдите значение выражения: a) (3 3/11 * 1 2/3 - 2 3/8) : 16/39 * 1 1/7; б) (9/16 + 4 2/3) : 9/56

Решение:

1. \( 3 \frac{3}{11} \cdot 1 \frac{2}{3} - 2 \frac{3}{8} = \frac{36}{11} \cdot \frac{5}{3} - \frac{19}{8} = \frac{12 \cdot 5}{11} - \frac{19}{8} = \frac{60}{11} - \frac{19}{8} = \frac{480 - 209}{88} = \frac{271}{88} \)
2. \( \frac{271}{88} : \frac{16}{39} \cdot 1 \frac{1}{7} = \frac{271}{88} \cdot \frac{39}{16} \cdot \frac{8}{7} = \frac{271 \cdot 39 \cdot 8}{88 \cdot 16 \cdot 7} = \frac{271 \cdot 39}{11 \cdot 16 \cdot 7} = \frac{10569}{1232} \)
3. \( \frac{9}{16} + 4 \frac{2}{3} = \frac{9}{16} + \frac{14}{3} = \frac{27 + 224}{48} = \frac{251}{48} \)
4. \( \frac{251}{48} : \frac{9}{56} = \frac{251}{48} \cdot \frac{56}{9} = \frac{251 \cdot 56}{48 \cdot 9} = \frac{251 \cdot 7}{6 \cdot 9} = \frac{1757}{54} \)

Ответ: а) 10569/1232; б) 1757/54.