Respostas

  • Usuário do Brainly
2013-06-26T01:55:01-03:00

Observe que:

 

\text{A}=\dfrac{2}{3}-1,\overline{4}

 

\text{A}=\dfrac{2}{3}-1+\dfrac{4}{9}=\dfrac{2}{3}-\dfrac{13}{9}=\dfrac{6-13}{9}=\dfrac{-7}{9}

 

Analogamente, temos:

 

\text{B}=0,7-0,\overline{7}

 

\text{B}=\dfrac{7}{10}-\dfrac{7}{9}

 

\text{B}=\dfrac{63-70}{9}=\dfrac{-7}{90}

 

Desse modo, temos, \dfrac{\text{A}}{\text{B}}=\dfrac{\frac{-7}{9}}{\frac{-7}{90}}=\dfrac{-7}{9}\cdot\dfrac{90}{-7}=\dfrac{90}{9}=10