Вычислите: 1) 1/4 : 1/4 ⋅ 2/7; 2) 1/6 ⋅ 3/7 : 5/14; 3) 1/3 ⋅ 7/8 : 9/14; 4) 6/7 : 5/7 ⋅ 4/9.

Ответ:

1) 1/4 : 1/4 ⋅ 2/7 = 1/4 * 4/1 * 2/7 = 1/1 * 2/7 = 2/7

2) 1/6 ⋅ 3/7 : 5/14 = 1/6 * 3/7 * 14/5 = (1 * 3 * 14) / (6 * 7 * 5) = 42/210 = 1/5

3) 1/3 ⋅ 7/8 : 9/14 = 1/3 * 7/8 * 14/9 = (1 * 7 * 14) / (3 * 8 * 9) = 98/216 = 49/108

4) 6/7 : 5/7 ⋅ 4/9 = 6/7 * 7/5 * 4/9 = (6 * 7 * 4) / (7 * 5 * 9) = 168/315 = 8/15

Ответ: 1) 2/7; 2) 1/5; 3) 49/108; 4) 8/15