Plurality of fraction that has an assigned mathematical symbol

Question

I am aware of the general rule that the plurality of a fraction matches the plurality of the thing it modifies, as in “a fraction of investors are informed.”

Does this change when I assign a mathematical symbol to the fraction, as in “a fraction x of investors are informed”? “Are” still seems like the best choice there, but I’m not sure. Now, what about a construction like “the fraction x of informed investors is greater than a threshold X”? “Is” seems like the better choice there. If that’s correct, what’s the reasoning behind the apparent exception?

Answer 1

By naming the fraction, you've given it a singular identity as a quantity. To me, that justifies the singular verb.

In your middle example, “a fraction x of investors are informed”, attaching a variable name to the fraction seems odd. You could avoid the question with "X is the fraction of investors who are informed", with a singular verb "is" for X and a plural verb "are..." for investors.

Answer 2

"A fraction of investors" means "Some investors", so it's plural because the sentence is about investors.

In your second example, the fraction itself is the singular subject of the sentence because you're comparing it as a number with another number.

A simpler version:

Five people are coming to lunch. (it's about some people)

Five people is more than four people. (it's about the number of people)