Fractional masses of stream components may be viewed as probabilities in multinomial distributions, consequently, the problem of mass balancing multi-node flowsheets is formulated utilizing the maximum entropy approach. Full observation (measurement) of stream fractional components and full or partial observation of stream fractional mass sprits are assumed. The cases of estimating ＇normalized/single observation＇ and ＇scaled/single observation＇ stream fractional components data sets are investigated. The results obtained are extended to handle stream components with multiple-observations and multiple-observations data sets, where weighting factors are introduced to reflect the scatter in the data observed. Furthermore, the obtained results are modified to handle weighted observed stream components. In the ensuing optimization problems, it is demonstrated that some of the Lagrangian (constant) multipliers depend on the rest of the Lagrangian multipliers. As a result, a subspace of the Lagrangian multipliers space and a set of independent stream fractional mass sprits are used to search for the optimum estimates of stream fractional components and stream fractional mass splits. A brief critique comparison between the maximum entropy approach and the least squares approach is carried out where the advantages and disadvantages of each technique are pointed out. Naturally each technique has strengths and weaknesses. Actual data are used in the critical evaluation.