<P> "The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende, published at Leyden in 1585, together with a French translation, La Disme, by the Flemish mathematician Simon Stevin (1548--1620), then settled in the Northern Netherlands . It is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Persian astronomer Al - Kāshī used both decimal and sexagesimal fractions with great ease in his Key to arithmetic (Samarkand, early fifteenth century)." </P> <P> While the Persian mathematician Jamshīd al - Kāshī claimed to have discovered decimal fractions himself in the 15th century, J. Lennart Berggren notes that he was mistaken, as decimal fractions were first used five centuries before him by the Baghdadi mathematician Abu'l - Hasan al - Uqlidisi as early as the 10th century . </P> <P> In primary schools, fractions have been demonstrated through Cuisenaire rods, Fraction Bars, fraction strips, fraction circles, paper (for folding or cutting), pattern blocks, pie - shaped pieces, plastic rectangles, grid paper, dot paper, geoboards, counters and computer software . </P> <P> Several states in the United States have adopted learning trajectories from the Common Core State Standards Initiative's guidelines for mathematics education . Aside from sequencing the learning of fractions and operations with fractions, the document provides the following definition of a fraction: "A number expressible in the form a b (\ displaystyle (\ tfrac (a) (b))) where a (\ displaystyle a) is a whole number and b (\ displaystyle b) is a positive whole number . (The word fraction in the standards always refers to a non-negative number .)" The document itself also refers to negative fractions . </P>

What is the sum of these mixed numbers