Question

como resolver 4,22...+ 4,122...

Answer 1

Primeiro devemos descobrir a fração geratriz dessas dízimas:

Primeiro 4,222...
$\\x=4,222...\\10x=42,222...\\10x-x=42,222-4,222\\9x=38\\\\\boxed{x= \frac{38}{9}}$

Agora 4,1222...
$x=4,1222...\\10x=41,222...\\100x=422,222...\\\\100x-10x=412,222-41,222\\90x=371\\\\\boxed{x=\frac{371}{90}}$

Agora somamos as frações:
$\frac{38}{9} + \frac{371}{90} = \frac{(38\cdot10)+371}{90}=\\\\ \frac{380+371}{90}=\ \textgreater \ \boxed{\boxed{ \frac{751}{90}}}$