а) 4 1/12 - 1 5/6х = 2 17/24
1 5/6х = 4 1/12 - 2 17/24
1 5/6х = 4 2/24 - 2 17/24
1 5/6х = 3 26/24 - 2 17/24
11/6х = 1 9/24
х = 1 9/24 : 11/6
х = 33/24 * 6/11
х = 3/4
Проверка: 4 1/12 - 11/6 * 3/4 = 49/12 - 33/24 = 98/24 - 33/24 = 65/24 = 2 17/24
б) 3 1/3 : (3/7х - 13/15) = 1 9/16
3/7х - 13/15 = 3 1/3 : 1 9/16
3/7х - 13/15 = 10/3 : 25/16
3/7х - 13/15 = 10/3 * 16/25
3/7х - 13/15 = 32/15
3/7х = 32/15 + 13/15
3/7х = 45/15
х = 45/15 : 3/7
х = 3 * 7/3
х = 7
Проверка: 3 1/3 : (3/7 * 7 - 13/15) = 10/3 : (3 - 13/15) = 10/3 : 2 2/15 = 10/3 : 32/15 = 10/3 * 15/32 = 50/32 = 1 18/32 = 1 9/16
Задача. <-----4 2/3 км/ч-----< село >------4 2/3 : 1 1/6 (км/ч) ------->
1) 4 2/3 : 1 1/6 = 14/3 : 7/6 = 14/3 * 6/7 = 4 (км/ч) - скорость второго пешехода
2) 4 2/3 + 4 = 8 2/3 (км/ч) - скорость удаления
3) 26 : 8 2/3 = 26 : 26/3 = 26 * 3/26 = 3 (ч) - через три часа расстояние между ними будет 26 км.
а) 9 5/6 : 6 5/9 = 59/6 : 59/9 = 59/6 * 9/59 = 9/6 = 1 3/6 = 1 1/2
б) 3 1/3 : 10 = 10/3 * 1/10 = 1/3
в) 3,75 : (3/8 : 1 3/7) = 14 2/7
1) 3/8 : 1 3/7 = 3/8 : 10/7 = 3/8 * 7/10 = 21/80
2) 375/100 : 21/80 = 375/100 * 80/21 = 125/5 * 4/7 = 500/35 = 14 10/35 = 14 2/7