fractional_arithmetic.md

Fractional Arithmetic (Project)

We propose that students develop, in the theory developed so far, the usual arithmetical laws for fractions of the form \( \frac{x}{y} \) where \(x,y\) are numbers and $y \neq 0$. One can choose whether to treat \( \frac{x}{y} \) as an abbreviation for x \* (1/y) or to define it accordingy. One could denote fractions by x // y in the .ftl style, or one could switch to the LaTeX style and use \frac{x}{y}. (Note that a single slash / has already been used for the inverse and lead to ambiguities when encountering 1 / x.)

After fixing notation, state and prove lemmas like \( \frac{a}{b} * \frac{c}{d} = \frac{a*c}{b*d} \), \( \frac{a}{b} + \frac{c}{d} = \dots \), \( \frac{\frac{a}{b}}{\frac{c}{d}} = \dots \), etc.