In prokaryotic cells such as bacteria, cell division is a much simpler process.  Since these cells only have one chromosome, there isn't the problem of separating multiple chromosomes to ensure that each daughter cell contains one chromosome of each type.  In both binary fission and mitosis, DNA replication precedes division. In fission, the duplicated circular chromosomes (there are now two identical chromosomes) each attach to the bacterial cell membrane.  As the cell membrane grows, the distance between the two identical chromosomes increases.  A septum then forms between the two chromosomes, partitioning the one cell into two cells.   Look at the diagram of binary fission in your text.