5/9+4/9×3 1/6×(4/19+1 5/38- 75/76)​

Найдем значение выражения:

5/9 + 4/9 × 3 целых 1/6 × (4/19 +1 целая 5/38 - 75/76) по действиям:

1) 4/19 +1 целая 5/38 = ( 4 * 2) / ( 19 * 2) + 1 целая 5/38 = 8/38 + 1 целая 5/38 = 1 целая 13/38;

2) 1 целая 13/38 - 75/76 = 1 целая (13 * 2)/( 38 * 2) - 75/76 = 1 целая 26/76 - 75/76 = 102/76 - 75/76 = 27/76;

3) 4/9 × 3 целых 1/6 = 4/9 × (3 * 6 +1) = 4/9 × 19/6 = ( 4 * 19)/ ( 9 * 6) = (2 * 19)/ (9 * 3) = 38/27;

4) 38/27 × 27/76 = ( 38 * 27) /( 27 * 76) = (1 * 1)/ ( 1 * 2) = 1/2;

5) 5/9 + 1/2 = 10/18 + 9/18 = 19/18 = 1 целая 1/18.

ответ: 1 целая 1/18.