Catalyzes the ATP-dependent phosphorylation of fructose-l-phosphate to fructose-l,6-bisphosphate. ATP + beta-D-fructose 1-phosphate = ADP + beta-D-fructose 1,6-bisphosphate + H(+) Part of the fruBKA (fru) operon, which is induced in the presence of fructose via the FruR (Cra) regulatory protein (PubMed:33476373). Transcription is repressed by FruR in the absence of fructose (PubMed:33649152). CRP activates expression of the fru operon in the absence of glucose (PubMed:33649152). The two regulators can work independently to control the expression of the operon depending on carbon source availability (PubMed:33649152). Does not affect growth on glucose. Mutant shows a severe growth defect on fructose. Belongs to the carbohydrate kinase PfkB family.