Question

Se x= 0,333... e y= 0,666... então quanto vale x+y?

Answer 1

$\large\boxed{\begin{array}{l}\rm x=0,333\dotsc\cdot10\\\rm 10x=3,333\dotsc\\\rm 10x=3+0,333\dotsc\\\rm 10x=3+x\\\rm 10x-x=3\\\rm 9x=3\\\rm x=\dfrac{3\div3}{9\div3}=\dfrac{1}{3}\\\\\rm y=0,666\dotsc\cdot 10\\\rm 10y=6,666\dotsc\\\rm 10y=6+0,666\dotsc\\\rm 10y=6+y\\\rm 10y-y=6\\\rm 9y=6\\\rm y=\dfrac{6\div3}{9\div3}=\dfrac{2}{3}\\\\\rm x+y=\dfrac{1}{3}+\dfrac{2}{3}\\\\\rm x+y=\dfrac{3}{3}=1\end{array}}$