Converting to gear inches is what confuses things. It's just extraneous when comparing gears, where gear ratios are all that's needed.

(52/11 -52/12) = (52/11)/(52/12) - 1 = (12/11) - 1 = 1.0909 - 1 = .091 = 9.1%
52/12

When you think about it, only the rear cogs matter for the percentage increase when all else is the same so you can write it down at the start:

(12-11)/11 = 1/11 = .091