For example, to multiply 28 by 11, one constructs a table of multiples of 28 like the following: The several entries in the first column that together sum to 11 (i.e., 8, 2, and 1) are checked off.
The product is then found by adding up the multiples corresponding to these entries; thus, 224 56 28 = 308, the desired product.
The entire process is analogous to the process of solving the algebraic equation for the problem (circle (Rhind papyrus, problem 50): 1/9 of the diameter is discarded, and the result is squared.
He multiplies one-third the height times 28, finding the volume to be 56; here 28 is computed from 2 × 2 2 × 4 4 × 4.The process is repeated again for the remainder obtained by subtracting 56 from the previous remainder of 84, or 28, which also happens to exactly equal the entry at 1 and which is then checked off.The entries that have been checked off are added up, yielding the quotient: 8 2 1 = 11.These problems reflect well the functions the scribes would perform, for they deal with how to distribute beer and bread as wages, for example, and how to measure the areas of fields as well as the volumes of pyramids and other solids.The Egyptians, like the Romans after them, expressed numbers according to a decimal scheme, using separate symbols for 1, 10, 100, 1,000, and so on; each symbol appeared in the expression for a number as many times as the value it represented occurred in the number itself. This rather cumbersome notation was used within the hieroglyphic writing found in stone inscriptions and other formal texts, but in the papyrus documents the scribes employed a more convenient abbreviated script, called In such a system, addition and subtraction amount to counting how many symbols of each kind there are in the numerical expressions and then rewriting with the resulting number of symbols.