"A fraction of" does not literally mean a fraction of in the mathematical sense. Its commonly accepted use in English is much more refined.

Well, 5/2 is also a fraction... What would you think of the headline if the fraction they refered to was 5/2?

If you ignore the meaning assigned to it in everyday English and concentrate on the mathematical sense, it leads to absurdities as practically all physical objects can be described in terms of fractions as they include improper fractions, irrational and complex numbers in the nominator or denominator etc.

"A fraction of the price" means "significantly less". When someone promises to sell you a new Macbook for a fraction of the price but it turns out the price difference is 5 cents, from your point of view they're correct but you have every right to feel cheated.

It’s not a rational fraction, but I think it’s still a fraction. And now I’m wondering about 1/i, inverse quaternions (I barely get those even normally), and if 1/M ≠ M^(-1).

(Nice puns, BTW).

Of course these exist and that's why we have the process of rationalization.[0]

https://en.wikipedia.org/wiki/Rationalisation_(mathematics)

A rational number (with a terminating decimal representation or a repeating, non-terminating decimal representation) can always be expressed in fractional p/q form.

I don't think the additional "rational" qualifier is needed for fractions.

Looks like all three replies to this share the same misunderstanding of my intent, so I assume my use of “it’s” was unhelpfully vague.

1/pi is not rational and therefore not “a rational fraction”, but think 1/pi is “a fraction”.

Your comment brought me to the realization that the relationship doesn't hold both ways. A rational number can always be written as a fraction but a fraction is not always rational. Never considered this before today :)

A rational number is one that can be written as a fraction (of two integers).

What's a rational fraction? Integer parts as opposed to e.g. 1.5/2.3?

1/i = (1/i) * (i/i) = i/(i*i) = i/(-1) = -i