Origins of the prevalence of halving and two-thirds operations in Egyptian arithmetic

Determine why halving and taking two-thirds were among the common operations used by scribes in ancient Egyptian arithmetic.

Background

The paper identifies doubling, halving, decupling, and taking two-thirds as common operations in ancient Egyptian multiplication and division. Although a decimal number system may explain the natural occurrence of decupling, the paper observes that the historical reasons for the prevalence of the other operations are not established.

The question is relevant to the paper's proposal that the physical affordances of a knotted rope may have helped motivate or support these arithmetic procedures.