[Arithmetic 6] Reducing a fraction

I. HOW TO REDUCE A FRACTION

Rule: In order to reduce a fraction, divide the numerator and denominator by their divisor (other than 1 and $-$1).
        $\dfrac{a}{b} = \dfrac{{a : n}}{{b : n}}$ where $n$ $\in$ CD($a$, $b$)
Note:
_ Fractions in lowest terms (or fractions which can not be reduced further) are fractions such that their numerator and denominator have only 1 and $-$1 as common divisors.

        $\dfrac{a}{b}$ is $a$ fraction in lowest terms $\Leftrightarrow$ CD($a$, $b$) = $\left\{ { \pm 1} \right\}$

_ When reducing a fraction, we often reduce it to the fraction in lowest terms and has positive denominator.

II. EXAMPLES

Example: Reduce the following fractions:

$\dfrac{{6}}{{8}} = \dfrac{3}{4}$ (divide both the numerator and denominator by 2)

$\dfrac{{ - 5}}{{10}} = \dfrac{{ - 1}}{2}$ (divide both the numerator and denominator by 5)

$\dfrac{{18}}{{ - 33}} = \dfrac{{ - 6}}{{11}}$ (divide both the numerator and denominator by $-$3)

$\dfrac{{ - 36}}{{ - 12}} = \dfrac{3}{1} = 3$ (divide both the numerator and denominator by $-$12)