For example, since $$s\rightarrow u+\overline{v_e}+e^{-}$$, then sticking a $\overline{u}$ next to the quarks ($s$ and $u$) we get $$s\overline{u}\rightarrow u\overline{u}+\overline{v_e}+e^{-}$$, which becomes $$K^{-}\rightarrow \pi^0+\overline{v_e}+e^{-}$$ -- a valid decay equation.
So I was wondering: If you take a quark equation (like the $s$ decay one above) and add some other quark to each quark in that equation (like how we added $\overline{u}$ above), do we always get a valid equation (e.g. the $K^{-}$ decay above).
Thanks