[Arithmetic 6] Extending the concept of fractions

I. THE CONCEPT OF FRACTIONS

    Fractions are written in the form $\dfrac{a}{b}$ where $a$, $b$ are integers and $b$ is not zero ($a$, $b$ $\in$ $\mathbb{Z}$, $b \ne 0$), $a$ is the numerator, $b$ is the denominator of the fractions.
Example:
    Fractions: $\dfrac{1}{2}$, $\dfrac{-3}{4}$, $\dfrac{7}{-6}$, $\dfrac{-11}{-12}$, etc.

    Not fractions: $\dfrac{1}{0}$, $\dfrac{1.2}{5}$, $- 9$, etc.

* Comment: Integer $a$ can be written as $\dfrac{a}{1}$.

II. BASIC PROPERTIES OF FRACTIONS

1) $\dfrac{a}{b} = \dfrac{{a.\color{red}m}}{{b.\color{red}m}}$ where $m$ $\in$ $\mathbb{Z}$ and $m \ne 0$

2) $\dfrac{a}{b} = \dfrac{{a : \color{red}n}}{{b : \color{red}n}}$ where $n$ $\in$ CD($a$, $b$)