$7($Optional$,10$ points bonus$)$

Find number systems for which the following operations are correct. Determine possible bases of the

numbers for each operations $($there might be more than one possible base$)$:

$1234+5432=6666$

$\frac{302}{20}=12\mathrm{.}1$

$\frac{41}{3}=13$

$6*9=42$