Simplificação de frações $$\frac{15}{9}$$

Dividir numerador e denominador pelo mesmo número $$\frac{15\left(\div3\right)}{9\left(\div3\right)}=\frac{5}{3}$$

Adição números racionais $$\frac{4}{5}+\frac{3}{2}$$

Reduzir ao mesmo denominador; Somar numeradores manter denominador $$\frac{4\left(\times2\right)}{5\left(\times2\right)}+\frac{3\left(\times5\right)}{2\left(\times5\right)}=\frac{8}{10}+\frac{15}{10}=\frac{23}{10}$$

Adição de números racionais $$-\frac{3}{4}-\frac{4}{5}$$

Reduzir ao mesmo denominador; Somar/subtrair (de acordo com as regras) numeradores, manter denominador $$-\frac{3\left(\times5\right)}{4\left(\times5\right)}-\frac{4\left(\times4\right)}{5\left(\times4\right)}=-\frac{15}{20}-\frac{16}{20}=-\frac{31}{20}$$

Multiplicação de números racionais $$-\frac{4}{3}\times\left(-\frac{5}{2}\right)$$

Multiplicar numeradores e denominadores; Aplicar as regras da multiplicação e divisão para definir o sinal. $$-\frac{4}{3}\times\left(-\frac{5}{2}\right)=\ +\ \frac{4\times5}{3\times2}=\frac{20\div2}{6\div2}=\frac{10}{3}$$

Divisão de números racionais $$\frac{8}{5}\div\left(-\frac{4}{3}\right)$$

Aplicar as regras dos sinais para a multiplicação e divisão Multiplicar pelo inverso $$\frac{8}{5}\div\left(-\frac{4}{3}\right)=\ -\frac{8}{5}\times\frac{3}{4}=-\frac{24\div4}{20\div4}=-\frac{6}{5}$$

Multiplicação de frações $$\frac{2}{3}\times\frac{3}{4}$$

Multiplicar numeradores e denominadores; $$\frac{2}{3}\times\frac{3}{4}=\frac{2\times3}{3\times4}=\frac{6}{12}=\frac{1}{2}$$

Subtração de frações $$\frac{5}{6}-\frac{1}{3}$$

Reduzir ao mesmo denominador; Subtrair numeradores, manter denominador $$\frac{5\left(\times2\right)}{6\left(\times2\right)}-\frac{1\left(\times2\right)}{3\left(\times2\right)}=\frac{10}{12}-\frac{2}{12}=\frac{8}{12}=\frac{2}{3}$$

Expressões numéricas calcule, apresentando o resultado numa fração irredutível $$-\frac{4}{5}-\left(-\frac{3}{2}+\frac{2}{5}\right)\div\left(-\frac{11}{10}\right)$$

$$-\frac{4}{5}-\left(-\frac{3\left(\times5\right)}{2\left(\times5\right)}+\frac{2\left(\times2\right)}{5\left(\times2\right)}\right)\div\left(-\frac{11}{10}\right)$$ $$=-\frac{4}{5}-\left(-\frac{15}{10}+\frac{4}{10}\right)\div\left(-\frac{11}{10}\right)$$ $$=-\frac{4}{5}-\left(-\frac{11}{10}\right)\div\left(-\frac{11}{10}\right)$$ $$=-\frac{4}{5}-\left(-\frac{11}{10}\right)\times\left(-\frac{10}{11}\right)=-\frac{4}{5}-1$$ $$=-\frac{4}{5}-\frac{5}{5}=-\frac{9}{5}$$

Expressões numéricas calcule, apresentando o resultado numa fração irredutível: $$-\left[\left(-\frac{3}{2}\right)\times\left(-\frac{2}{5}\right)\right]\div\left(-\frac{8}{10}\right)$$

$$-\left(\frac{3\times2}{2\times5}\right)\div\left(-\frac{8}{10}\right)=\frac{3}{5}\div\frac{8}{10}$$ $$=\frac{3}{5}\times\frac{10}{8}=\frac{30}{40}=\frac{3}{4}$$

Operações Racionais para 8º Ano Flashcards

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