Fractions in the Suan Shu Shu (China, Beginning of the 2nd Century BCE)

The Su{`a}n Sh{`u} Sh{=u} contains 301 instances of regular expressions for fractions. They can be “mono-dimensional” (formed with one integer name only) for unit fractions, “bidimensional” (with two integer names) for both unit and non-unit fractions, or lexicalized only for 1/3, 1/2 and 2/3. The present paper gives a complete description of the diversity of these forms. Bidimensional expressions are predicative phrases: the name n f{=e}n of a unit fraction 1/n acts as subject and the numerator’s name as predicate; according to the syntactic context, the morpheme zh{=i} can be used as an optional marker of this predicative relation.