You'll still need to do the addition, and then you'd need to eyeball 15 3/4 as a number between 1 and 2, do the division, and then eyeball the result into a fraction.

I think I've only seen decimal marked slide rules, you could certainly have a fraction marked rule, but it wouldn't be that helpful, because 15 3/4 is not easy to turn into

10 * (1 + 1/2 + 3/4 * 1/5 )

And then you're not at a power of two fraction anymore either. Some other tool would be better; probably a pocket calculator that's taken advantage of half a century of computational advances and can manage fractions.