Starting from what I know (the difference between ribbons), I decided to go from the bottom and work my way up. I then noticed a pattern (each sum was three more of the previous one), and decided to keep my pattern of the three numbers but not have to do any major mental work and instead add three to the previous sum until I got to 38.
32^3/5 = 8
64^2/3 = 16
81^1/4 = 3
49^1/2 = 7
125^2/3 = 25
now just put them in order from the smallest value to the largest
Let the smaller one is x so the larger is x+1
x(x+1)=1332
x^2+x=1332
x^2 +x -1332 =0
(x - 36)(x + 37) =0
so x = 36 or x = -37
therefor the larger integer is either 37 or -36
Least 3/5, 0.65, 0.75, 7/8 greatest