Help with calculating how conversion works with pen?

Say i have 75% fire res and 80% chaos res and 50% ele to chaos damage taken (Devine Flesh).
Now assume a monster hits me for 1000 pure fire dmg with 10% fire pen and 15% chaos pen.
What is the order of operations and what pen actually applies to what? If both pen apply is it addative or multiplicative?
And what ecaxtly is the difference between pen and res reduction? are they the same or is there a reason they are seperate?
Thanks to all who helps.

damage taken as comes before the mitigation -> your incoming damage will be split to chaos and fire part and then mitigated by resists

penetration and -res work the same (and stack, -res going first) as long as the monster does not have overcapped resists.

unlike -res, penetration does not care about resists above the cap, it subtracts from the cap

You might find the wiki's section on Receiving Damage helpful.