The phrase "although the fraction of" is correct and usable in written English.
It can be used when introducing a contrast or exception related to a portion or percentage of something.
Example: "Although the fraction of students passing the exam has increased, there are still many who struggle with the material."
Alternatives: "even though the percentage of" or "despite the portion of".
Although the fraction of patients is given exogenously, in Appendix A. we endogenize the patients' hospital choice.
Although the fraction of Tickets mailed on the IMM was very high in each month of the rollout, it did decline in successive months.
Although the fraction of low educated people decreased between 1996 and 2008 (about 17 percentage points), Spain remained well behind other countries (Portugal, Italy and Greece).
Unknown crystal phase was precipitated in the glass ceramic added with LiI, although the fraction of the Li7P3S11 crystal with high conductivity decreased.
Although the fraction of injuries from SESDs is less than that reported for nonsafety devices, it remains a "preventable fraction" and is a sizable target for further advances.
For each eruption, modal bubble size does not vary significantly with distance from the vent, although the fraction of complex ash particles capable of recording the larger bubbles decreases with distance (Figure 9).
On the other hand, KI quenches PLP-GSAM fluorescence, although only the fraction of coenzyme molecules present as the enolimine tautomer is significantly accessible to the solvent, clearly indicating an asymmetric structure of the active sites.
Although the fractions of cells undergoing megakaryocytic pathway (∼10%) and monocyte-macrophage differentiation (∼6%) were small, the difference is statistically significant compared to the control group.
Although the fractions of the unfolded states are small at equilibrium, <0.1%, the dramatic increase in the concentration, ∼200-fold, would be magnified by the order of the likely nucleation reaction, i.e., squared for second-order, cubed for third-order, etc., suggesting that amorphous aggregation of the U state may also play a role in toxicity (Figure 7).
The functional analysis showed a vast diversity of the biological processes in the network interfaces, although, the fractions of shared edges between the cellular networks are low.
Further, although the fractions of occluded PAS vary among the subunits, the active sites of subunits B and C are accessible more frequently than those of subunits A and D. Similar results were obtained in all three CG-BD runs.
