Symbiogenesis is an evolutionary theory that says that prokaryotes eventually evolved into eukaryotes (having multiple organelles and better structure) by forming symbiotic relationships with other bacteria that have been absorbed, or have entered the cell in an initially parasitic way.
My question is that when the individual bacteria have become organelles, what happens when the cell reproduces? The bacteria were individual entities with their own reproduction mechanisms before they became organelles. Do they still divide in their own way inside a cell (and are subsequently present in both halves of the cell when it is dividing itself), or does their division somehow get incorporated into the cell's own DNA?
I'm not sure about all organelles but mitochondria and chloroplasts are commonly used examples of independent devision in eukaryotic cells. They have independent DNA that forms separate mitotic spindles during division. Similar mechanisms likely existed for other organelles originally but the genetic material may have eventually been combined with the nuclear DNA for simplicity. This is a very simplified explanation but I think addresses the basic question.