"He's probably spending a major fraction of his time trying to avoid getting caught." D. Rumsfeld
I was thinking this should be "the major fraction" based on thinking that the major fraction should be greater than half, but checking other usages, it seems common to use it to mean "one of the larger subsets of the whole" without necessarily being more than half. So I'd change my answer to "good English".
I think the point is that Rumsfeld confused the word "fraction" with "portion". However, I don't think that's an uncommon mistake.