Arithmetic Operations

$\displaystyle ab+ac=a(b+c)$	$\displaystyle \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$	$\displaystyle \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$
$\displaystyle \frac{\Big(\frac{a}{b}\Big)}{\Big(\frac{c}{d}\Big)}=\bigg(\frac{a}{b}\bigg)\bigg(\frac{d}{c}\bigg)=\frac{ad}{bc}$	$\displaystyle \frac{\Big(\frac{a}{b}\Big)}{c}=\frac{a}{bc}$	$\displaystyle \frac{a}{\Big(\frac{b}{c}\Big)}=\frac{ac}{b}$
$\displaystyle a\bigg(\frac{b}{c}\bigg)=\frac{ab}{c}$	$\displaystyle \frac{a-b}{c-d}=\frac{b-a}{d-c}$	$\displaystyle \frac{ab+ac}{a}=b+c$