Раскройте скобки: 1) 14 * (1/2m+3/7n) 2) 1/6 * (12/17b-18/23c) 3) 8 * (1/4p-5/24q+7/12t) 4) 1 3/4 * (4a+16/21b-2 2/3)

Обозначим числа в примере неизвестными a, b, c и d. a * (b + c + d) = a * b + a * c + a * d. Примеры решаем за алгоритмом.

1) 14 * (1/2 * m + 3/7 * n) = 14/1 * 1/2 * m + 14/1 * 3/7 * n = ((14 * 1) / (1 * 2)) * m + ((14 * 3) / (1 * 7)) * n = 14/2 * m + 42/7 * n = 7 * m + 6 * n;

2) 1/6 * (12/17 * b - 18/23 * c) = 1/6 * 12/17 * b - 1/6 * 18/23 * c = ((1 * 12) / (6 * 17)) * b - ((1 * 18) / (6/23)) * c = 12/102 * b - 18/138 * c = 2/17 * b - 3/23 * c;

3) 8 * (1/4 * p - 5/24 * q + 7/12 * t) = 8/1 * 1/4 * p - 8/1 * 5/24 * q + 8/1 * 7/12 * t = ((8 * 1) / (1 * 4)) * p - ((8 * 5) / (1 * 24)) * q + ((8 * 7) / (1 * 12)) * t = 8/4 * p - 40/24 * q + 56/12 * t = 2 * p - 5/3 * q + 14/3 * t = 2 * p - 1 2/3 * q + 4 2/3 * t;

4) 1 3/4 * (4 * a + 16/21 * b - 2 2/3) = 7/4 * 4/1 * a + 7/4 * 16/21 * b - 7/4 * 8/3 = ((7 * 4) / (4 * 1)) * a + ((7 * 16) / (4 * 21)) * b - ((7 * 8) / (4 * 3)) = 28/4 * a + 112/84 * b - 56/12 = 7 * a + 4/3 * b - 14/3 = 7 * a + 1 1/3 * b - 4 2/3.

Ответ: 7 * m + 6 * n; 2/17 * b - 3/23 * c; 2 * p - 1 2/3 * q + 4 2/3 * t; 7 * a + 1 1/3 * b - 4 2/3.