Fibrous cellulose triacetate prepared from purified cotton under various temperatures was dissolved in the solution of 70%, monochloroacetic acid and it was fractionated using water as a precipitant. Eight fractions were obtained through the stepwise precipitation. Degree of polymerization and molecular weight of each fraction were measured viscometrically. Integral and differential molecular weight distribution curve were drawn for each sample prepared under various temperatures and were carefully observed. On this experimental study, following conclusions were obtained: Fractional precipitation can be carried out for fibrous cellulose triacetate in the solution of 70% monochloroacetic acid using water as a precipitant. The differences on the shapes of molecular weight distribution curve were occured on account of the various acetylation temperatures. At the relatively higher acetylation temperatures, the cellulose was randomly degraded and the portion of low degree of polymerization was increased. Commercial acetate, therefore, may not be prepared at above 40$^{circ}C$ according to the molecular weight distribution curve regardless of higher viscosity and average degree of polymerization. It was concluded that the optimum acetylation temperature for commercial acetate was approximately 30$^{circ}C$.