Operações com frações

Revision as of 13:16, 16 November 2012

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

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-===Exercícios Propostos===
+[[Exercícios-1|Exercícios]]
-Utilizando os símbolos $=$ ou $\neq$, e impondo as condições necessárias, preencha os espaços de forma a que a afirmação resultante seja verdadeira.
-Justifique a sua resposta.
-(a) $\displaystyle \frac{ab+ac}{a} \ \dots \ b+ac$.
-(b) $\displaystyle \frac{a-b}{b-a} \ \dots \ -1 \ \land \ \dots \ $.
-(c) $\displaystyle -(a+b) \ \dots \ -a+b$.
-(d) $\displaystyle (a-b)-c \ \dots \ a-(b-c)$.
-(e) $\displaystyle -\frac{\;a\;}{b} \ \dots \ \frac{\;-a\;}{b} \ \land \ \dots $.
-(f) $\displaystyle \frac{\;\frac{a}{b}\;}{c} \ \dots \ \displaystyle\frac{\;a\;}{bc} \ \land \ \dots \ $