Final answer:
The fraction with the fewest mitochondria would be the microsomal fraction obtained through differential centrifugation of homogenated and fractionated rat liver cells.
Step-by-step explanation:
The fraction that would have the fewest mitochondria in a homogenated and fractionated rat liver cell using differential centrifugation is the microsomal fraction.
Differential centrifugation separates cell components based on their mass. The microsomal fraction is obtained by centrifuging the homogenate at a higher speed compared to other fractions, such as the nuclear fraction and the mitochondrial fraction. Since mitochondria are relatively heavy organelles, they will sediment and collect in the mitochondrial fraction, while the microsomal fraction will have the fewest mitochondria.
It is important to note that further biochemical analysis should be performed to confirm the presence of specific organelles in each fraction.