To mention the scale of a map, which is more natural and formal, "Four and one half feet to an inch" or "Four and half feet to an inch" ?
In writing, I would use "four and one half feet.
In speech, I would say "four and one half feet if I want to emphasize the number - e.g. I am telling someone the conversion for the first time.
If I am referring to the conversion or speaking quickly, I might say "four and a half feet.
[spoken] He gave me a map of the city that was four and one half feet to the inch..... Can you believe that? How am I supposed to carry a map with a scale of four and a half feet to the inch! The map was huge! ....Four and one half feet to the inch.
Caveat: I am an engineer in the U.S. My demographic has a reputation for being very precise with numbers, so it may be the case that others use "four and one half a little less frequently than me. The point is that either is acceptable, and the choice between them is a matter of style.
EDIT: In response to comments.
Fractions in ratios are a little awkward, but not totally unheard of. For instance, in describing road grades or streambed slopes, they pop up. The OP asked about scale ratios in maps, and I agree that that is a peculiar scale to use, but mostly because it makes for huge maps. Maybe in an architectural drawing?
User3169 suggests I point out that I switched the OP's feet to an inch to feet to the inch. Using to the is much more common, at least in the U.S.
"Four and one half" is grammatical, but it is much less common than "four and a half". ("Four and half" is not grammatical).
My intuition also says that "Four and one half" is American, and I would not expect to find it in British English.
Looking at GloWbE (the corpus of global web-based English) bears out my expectations. "and one half" occurs 376 times in the corpus, with over 100 being in US sources, 59 British, and 50 Canadian.
"And a half" occurs 39482 times (more than 100 times as often), and GB sources slightly outnumber US sources (8563, 8120 respectively).