5.486 Найдите произведение: a) 8/9 ⋅ 3/4; б) 11/45 ⋅ 9/22; в) 51/29 ⋅ 58/85; г) 1/4 ⋅ 4/5 ⋅ 5/6.

Ответ: а) 2/3; б) 11/110; в) 6/5; г) 1/6

1. a) \[\frac{8}{9} \cdot \frac{3}{4} = \frac{8 \cdot 3}{9 \cdot 4} = \frac{2 \cdot 1}{3 \cdot 1} = \frac{2}{3}\]
2. б) \[\frac{11}{45} \cdot \frac{9}{22} = \frac{11 \cdot 9}{45 \cdot 22} = \frac{1 \cdot 1}{5 \cdot 2} = \frac{1}{10}\]
3. в) \[\frac{51}{29} \cdot \frac{58}{85} = \frac{51 \cdot 58}{29 \cdot 85} = \frac{3 \cdot 2}{1 \cdot 5} = \frac{6}{5}\]
4. г) \[\frac{1}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} = \frac{1 \cdot 4 \cdot 5}{4 \cdot 5 \cdot 6} = \frac{1 \cdot 1 \cdot 1}{1 \cdot 1 \cdot 6} = \frac{1}{6}\]

Ответ: а) 2/3; б) 1/10; в) 6/5; г) 1/6