I've been pondering gear ratios lately in an effort to tweak gears without having to go to the trouble of finding say a rare 7 tooth sprocket, and being able to effectively ratio the tooth to something as low as say 5, by increasing the teeth on the chainring. Is their such a ratio?

What I'm looking for is a ratio that correponds the number of additional teeth on the back cog to the X variable of that number on the front chain ring.(i;e 3 cog teeth = 5 chainring teeth)

(Bare in mind these are for fixed-gear)Using the junior velo gear chart(http://www.juniorvelo.com/?p=4090) I found that 42/10 equals 111.5 gear inches almost equaling 54/13 at 110.2. gear inches. Does that mean that 42/10 is the same mechanical advantage of 54/13? I found that where in this latter equation 3 back cog teeth = 1/4 ratio, in others the cog teeth it's 1/6. Does anyone know if this is correct? I can't seem to find anything directly pertaining to swapping gears like this

Thanks in advance,
Tinkerer