Operações com frações

Propriedades	Exemplos	Propriedades	Exemplos
$\displaystyle \frac{a}{b}\pm \frac{c}{d}=\frac{ad\pm cb}{bd} \land b, d \ne 0$	$\displaystyle \frac{2}{3}-\frac{4}{5}=\frac{2\times 5-4 \times 3}{3 \times 5}=-\frac{2}{15}$	$\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd} \land b, d \ne 0$	$\displaystyle \frac{2}{3}\times \frac{4}{5}=\frac{2\times 4}{3 \times 5}=\frac{8}{15}$
$\displaystyle \frac{\;\frac{a}{b}\;}{\frac{c}{d}}=\frac{ad}{bc} \land b, c, d \ne 0$	$\displaystyle \frac{\frac{3}{5}}{\;\frac{7}{8}\;}= \frac{3 \times 8}{5 \times 7}=\frac{24}{35}$	$\displaystyle \frac{ab+ac}{a} = b+c \land a\neq 0$	$\displaystyle \frac{6+3}{3} = \frac{3 \times (2+1)}{3}=2+1=3$
$\displaystyle\frac{ab+c}{a} \neq b+c$	$\displaystyle \frac{3 \times 2+1}{3}\ne 2+1$	$\displaystyle \frac{b+c}a=\frac ba+\frac ca$	$\displaystyle \frac{5+3}{4}= \frac{5}{4}+\frac{3}{4}$
$\displaystyle \frac{a}{b+c} \neq \frac ab + \frac ac$	$\displaystyle \frac{4}{8}=\frac{4}{3+5} \neq \frac{4}{3} + \frac{4}{5}=\frac{32}{15}$	$\displaystyle \frac{a+c}{b+d}\neq\frac ab+\frac cd$	$\displaystyle \frac{8}{10}=\frac{3+5}{4+6} \neq \frac{3}{4}+\frac{5}{6}=\frac{38}{24}$