How to do +, -, *, / with number in a base b?

Is there a way to perform these operations in a particular base b but 10? I can convert it back to base 10 and perform the operation, however, I think it's kinda odd by doing this way.

Thanks,
Chan

If what you are interested in are paper-and-pencil methods, then the same algorithms that one uses in base 10 work in base $b$, provided you remember to perform all operations in base $b$. (Of course, it may be that the proliferation of calculators has atrophied some people's ability to do it even in base $10$...)

For example, if you want to add $573641$ and $561373$ in base $9$ (I just made them up), then we add can add them right to left, with carries; note that in base $9$, $7+4 = 12$, $6+3=10$, etc. So we get: $$\begin{array}{r} 573641\\\ \underline{+\ 561373}\\\ 1245124 \end{array}$$ Similar with subtraction, multiplication, and long division.