In ancient Egypt, fractions were represented as the sum of inverses to natural numbers. Processing fractions in this representation is computationally complicated. Because of this complexity, traditionally, Egyptian fractions used to be considered an early inefficient approach. In our previous papers, we showed, however, that the Egyptian fractions actually provide an optimal solution to problems important for ancient Egypt -- such as the more efficient distribution of food between workers. In these papers, we assumed, for simplicity, that we know the exact amount of food needed for each worker -- and that this value must be maintained with absolute accuracy. In this paper, we show that the corresponding food distribution can become even more efficient if we make the setting more realistic by allowing "almost exact" (approximate) representations.