Question

Preciso urgente de ajuda na fração geratriz

0,555... + 0,05..

Answer 1

$x=0.555...$

$10x=5.555...$

$10x-x=5.555...-0.555...$

$9x=5$

$\boxed{x=\frac{5}{9}}$

$y=0.0555...$

$10y=0.555...$

$100y=5.555...$

$100y-10y=5.555...-0.555...$

$90y=5$

$\boxed{y=\frac{5}{90}}$

Agora

$\boxed{\boxed{\frac{5}{9}+\frac{5}{90}=\frac{50+5}{90}=\frac{55}{90}=0.6111...}}$

Answer 2

=> 0,555... = 5/9

=> 0,0555... = 5/90
 
 Daí,

$\frac{5}{9}+\frac{5}{90}=\\\\\frac{5}{9/10}+\frac{5}{90/1}=\\\\\frac{50+5}{90}=\\\\\frac{55}{90}=\\\\\boxed{\frac{11}{18}}$