Let $\tilde{s}_n$ and $\tilde{p}_n$ be estimators of the quantities $s$ and $p$, respectively ($\mathbb{E}[\tilde{s}_n]=s$ and $\mathbb{E}[\tilde{p}_n]=p$). Imagine we have obtained asymptotic bounds for the errors of these estimators (e.g., using Chebyshev inequality or Chernoff bounds): $$|\tilde{s}_n-s|\leq\mathcal{O}_p(a_n),$$ $$|\tilde{p}_n-p|\leq\mathcal{O}_p(b_n).$$
For example, see page 2.
How can we use the bounds of the errors of the estimators to bound the error of operations of the estimators: e.g., $\frac{\tilde{s}_n}{\tilde{p}_n}$ in estimating $\frac{s}{p}$ or $\tilde{s}_n\, \tilde{p}_n$ in estimating $s\, p$?