The math copro socket usually has it's own clock crystal in those old motherboards so you can set the speed independently of the CPU simply by swapping the crystal for a faster or slower one as your needs dictate and yes, you can mismatch the speed of the math copro against the CPU and it will still work. The CPU will just have to wait to get the results back if the copro is slower.

I had 286 16MHz and installed a Intel 287 10MHz - it worked just fine @16MHz. Also 387@33MHz run just fine @40MHz too and it didn't even got hot - just slightly warm to the touch. Some motherboards have a setting to run Copro in sync with CPU clock or not - on 386 platform only Intel 387 can be used this way. Other brands don't use the pins for async mode so it's always runs at CPU clock.

Ok that is good to know, I found several 8 and 10 mhz ones, maybe I'll just pick a 10 to be safe (pretty sure the cpu is 8 but if it doesn't matter too much then I have some wiggle room).

I suppose I am taking a gamble just buying it loose off the internet, and I would be better off buying a boxed, sealed chip but the only one I've found like that is $40. I realize this is probably a fraction of its original value, but I was not looking to spend that much. What should I expect to pay, within reason?