Operações com frações
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| $\displaystyle \frac{a}{b}\pm \frac{c}{d}=\frac{ad\pm cb}{bd} \land b, d \ne 0$ || $\displaystyle \frac{2}{3}-\frac{4}{5}=\frac{2\times 5-4 \times 3}{3 \times 5}=-\frac{2}{15}$ || $\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd} \land b, d \ne 0$ || $\displaystyle \frac{2}{3}\times \frac{4}{5}=\frac{2\times 4}{3 \times 5}=\frac{8}{15}$ | | $\displaystyle \frac{a}{b}\pm \frac{c}{d}=\frac{ad\pm cb}{bd} \land b, d \ne 0$ || $\displaystyle \frac{2}{3}-\frac{4}{5}=\frac{2\times 5-4 \times 3}{3 \times 5}=-\frac{2}{15}$ || $\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd} \land b, d \ne 0$ || $\displaystyle \frac{2}{3}\times \frac{4}{5}=\frac{2\times 4}{3 \times 5}=\frac{8}{15}$ | ||
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| − | | $\displaystyle \frac{\;\frac{a}{b}\;}{\frac{c}{d}}=\frac{ad}{bc} \land | + | | $\displaystyle \frac{\;\frac{a}{b}\;}{\frac{c}{d}}=\frac{ad}{bc} \land b, c, d \ne 0$ || $\displaystyle \frac{\frac{3}{5}}{\;\frac{7}{8}\;}= \frac{3 \times 8}{5 \times 7}=\frac{24}{35}$ || $\displaystyle \frac{ab+ac}{a} = b+c \land a\neq 0$ || $\displaystyle \frac{6+3}{3} = \frac{3 \times (2+1)}{3}=2+1=3$ |
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| $\displaystyle\frac{ab+c}{a} \neq b+c$ || $\displaystyle \frac{3 \times 2+1}{3}\ne | | $\displaystyle\frac{ab+c}{a} \neq b+c$ || $\displaystyle \frac{3 \times 2+1}{3}\ne | ||
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\frac{5}{4}+\frac{3}{4}$ | \frac{5}{4}+\frac{3}{4}$ | ||
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| − | |$\displaystyle \frac{a}{b+c} \neq \frac ab + \frac ac$ | + | |$\displaystyle \frac{a}{b+c} \neq \frac ab + \frac ac$ || $\displaystyle \frac{4}{8}=\frac{4}{3+5} \neq |
\frac{4}{3} + \frac{4}{5}=\frac{32}{15}$ || $\displaystyle \frac{a+c}{b+d}\neq\frac ab+\frac cd$ || $\displaystyle \frac{8}{10}=\frac{3+5}{4+6} \neq | \frac{4}{3} + \frac{4}{5}=\frac{32}{15}$ || $\displaystyle \frac{a+c}{b+d}\neq\frac ab+\frac cd$ || $\displaystyle \frac{8}{10}=\frac{3+5}{4+6} \neq | ||
\frac{3}{4}+\frac{5}{6}=\frac{38}{24}$ | \frac{3}{4}+\frac{5}{6}=\frac{38}{24}$ | ||
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[[Exercícios-1|Exercícios]] | [[Exercícios-1|Exercícios]] | ||
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| + | [[Matemática Elementar#Números e conjuntos|Voltar]] [[Potências|Seguinte]] | ||
Latest revision as of 18:10, 28 January 2013
[edit] Operações com frações
| Propriedades | Exemplos | Propriedades | Exemplos | |
|---|---|---|---|---|
| $\displaystyle \frac{a}{b}\pm \frac{c}{d}=\frac{ad\pm cb}{bd} \land b, d \ne 0$ | $\displaystyle \frac{2}{3}-\frac{4}{5}=\frac{2\times 5-4 \times 3}{3 \times 5}=-\frac{2}{15}$ | $\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd} \land b, d \ne 0$ | $\displaystyle \frac{2}{3}\times \frac{4}{5}=\frac{2\times 4}{3 \times 5}=\frac{8}{15}$ | |
| $\displaystyle \frac{\;\frac{a}{b}\;}{\frac{c}{d}}=\frac{ad}{bc} \land b, c, d \ne 0$ | $\displaystyle \frac{\frac{3}{5}}{\;\frac{7}{8}\;}= \frac{3 \times 8}{5 \times 7}=\frac{24}{35}$ | $\displaystyle \frac{ab+ac}{a} = b+c \land a\neq 0$ | $\displaystyle \frac{6+3}{3} = \frac{3 \times (2+1)}{3}=2+1=3$ | |
| $\displaystyle\frac{ab+c}{a} \neq b+c$ | $\displaystyle \frac{3 \times 2+1}{3}\ne 2+1$ | $\displaystyle \frac{b+c}a=\frac ba+\frac ca$ | $\displaystyle \frac{5+3}{4}= \frac{5}{4}+\frac{3}{4}$ | |
| $\displaystyle \frac{a}{b+c} \neq \frac ab + \frac ac$ | $\displaystyle \frac{4}{8}=\frac{4}{3+5} \neq \frac{4}{3} + \frac{4}{5}=\frac{32}{15}$ | $\displaystyle \frac{a+c}{b+d}\neq\frac ab+\frac cd$ | $\displaystyle \frac{8}{10}=\frac{3+5}{4+6} \neq \frac{3}{4}+\frac{5}{6}=\frac{38}{24}$ |
