  Greeks used an Egyptian system of fractions. With the exception of 2/3, all fractions are proper parts which modern readers will see as unit fractions: 1/n. For example, 2/5 is 1/3 1/15 (that is, the sum of 1/3 and 1/15). Additionally, Greeks used systems of measure, as we do, with units of measure being divided up into more refined units of measure. 1 foot is 16 finger-widths (inches). Hence, one can always eliminate fractions by going, as we do, to a more refined measure (1, 1/2, 1/4 feet or 1 foot 12 inches). This feature of measure may be reflected in Plato's observation (Rep. vii) that in arithmetic, one can always eliminate parts of units. 