When $$10\frac{5}{6}$$ is divided by 91, we get a fraction $$\frac{a}{b}$$, where $$a$$ and $$b$$ are natural numbers with no common factors other than 1. Then $$(b - a)$$ is equal to

First $$10\frac{5}{6} = \frac{65}{6}$$, so dividing by 91 gives $$\frac{65}{6} \times \frac{1}{91} = \frac{65}{546}$$. Since $$65 = 5 \times 13$$ and $$546 = 2 \times 3 \times 7 \times 13$$, cancelling 13 leaves $$\frac{5}{42}$$ in lowest terms. So $$a = 5$$, $$b = 42$$ and $$b - a = 37$$.