Ok let's just say that the f-number (1.8, 2, 4, ... 22, 32) represent a fractional number that represents the ratio between the focal length and the opening diameter, which in turn determines what the amount of light being let through the lens is. While the f-number is itself actually not a fraction or a ratio, it is indicative of what the actual ratio is.
In other words, this ratio is expressed as a fraction, whose denominator is printed on the lens aperture ring. Thus, while larger fractions represent closer ratios, which represent larger diameters, the actual f-numbers are usually only expressed the denominator of that fraction, meaning that larger f-numbers mean smaller holes.
And on a different note, I'm not sure if anyone has explained this part yet so here it goes: The reason the f-number has to be determined by a ratio instead of simply by the diameter of the opening is because when you use a lens with a longer focal length (and thus are zooming in to a smaller section of the scene), you are also recieving less light from that scene. So when you are viewing a smaller area, there are basically less light "rays" coming at you. For example, a 5mm diameter will let through a lot less light on a 500mm lens than on a 35mm, but the fraction of light initially coming through the lens that the diameter lets through is the same. Thus, a ratio is used to represent the actual amount of light that a particular f-stop lets in, which is a factor of both the focal length and aperture diameter.