8/27 + m = 17/27
m = 17/27 - 8/27
m = 9/27
m = 1/3

n + 1/8 = 3/8
n = 3/8 - 1/8
n = 2/8
n = 1/4

1/3 + n = 5/12
n = 5/12 - 1/3
n = 5/12 - 4/12
n = 1/12

m + 1/4 = 2/3
m = 2/3 - 1/4
m = 8/12 - 3/12
m = 5/12

n + 1/25 = 2/5
n = 2/5 - 1/25
n = 10/25 - 1/25
n = 9/25

2/13 + m = 3/5
m = 3/5 - 2/13
m = 39/65 - 10/65
m = 29/65

Проверим результаты:

1/3 + 1/3 = 2/3 = 8/27 + 1/3 = 9/271/4 + 1/4 = 2/8 = 2/8 = 1/8 + 3/81/12 + 1/4 = 3/12 = 5/12 = 1/3 + 1/125/12 + 1/4 = 3/4 = 2/3 = 8/12 + 1/49/25 + 1/25 = 10/25 = 2/5 = 1/5 + 1/2529/65 + 2/13 = 3/5 = 6/13 = 2/13 + 3/5

Таким образом, все уравнения решены верно.