There's one pattern in it:
Letters used: T, A, N, G, E, R, I, M
alphabetically sorted: A, E, G, I, M, N, R, T
The letters together with their fractions:
A=
1/200, E=
2/7, G=
3/2, I=
3/8, M=
5/6, N=
5/8, R=
8/4, T=
8/5
So towards the end of the alphabet, the numerators are either constant or increasing, but never decreasing. Not sure if that's enough of a rule for building fractions for the unused letters, because I can't see a rule for the denominators. And the 1/200 for the letter A is kind of irritating. Now where's my anorak?