Question

0,3888...+1,4555...​

Answer 1

$x=0,3888\times10\\10x=3,888... \times10\\100x=38,888...$

$-\underline{\begin{cases}100x=38,\cancel{888...} \\10x=3,\cancel{888...} \end{cases}}$

$90x=35\\x=\dfrac{35\div5}{90\div5}=\dfrac{7}{18}$

$y=1,4555...\times10\\10y=14,555... \times10\\100y=145,555$

$-\underline{\begin{cases}100y=145,555... \\10y=14,555... \end{cases}}$

$90y=131\\y=\dfrac{131}{90}$

$\mathsf{0,3888...+1,4555... =\dfrac{7}{18}+\dfrac{131}{90}}$

$\mathsf{\dfrac{35+131}{90}=\dfrac{166\div2}{90\div2}=\dfrac{83}{45}}$