Modern Analysis
The original mathematical texts never explain where the procedures and formulas came from. This holds true for the EMLR as well. Scholars have attempted to deduce what techniques the ancient Egyptians may have used to construct both the unit fraction tables of the EMLR and the 2 /n tables known from the Rhind Mathematical Papyrus and the Lahun Mathematical Papyri. Both types of tables were used to aid in computations dealing with fractions, and for the conversion of measuring units.
It has been noted that there are groups of unit fraction decompositions in the EMLR which are very similar. For instance lines 5 and 6 easily combine into the equation 1/3 + 1/6 = 1/2. It is easy to derive lines 11, 13, 24, 20, 21, 19, 23, 22, 25 and 26 by dividing this equation by 3, 4, 5, 6, 7, 8, 10, 15, 16 and 32 respectively.
Some of the problems would lend themselves to a solution via an algorithm which involves multiplying both the numerator and the denominator by the same term and then further reducing the resulting equation:
This method leads to a solution for the fraction 1/8 as appears in the EMLR when using N=25 (using modern mathematical notation):
Read more about this topic: Egyptian Mathematical Leather Roll
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