Question

Sendo x= 4,333... e y= 3,444..., calcule o valor de :

Vejam a imagem abaixo
Ajudem por fvvv

Answer 1

Vamos começar achando a fração geratriz das dizimas:

$x~=~4,333...~=~4+0,333...\\\\x~=~4,333...~=~4+\frac{3}{9}\\\\x~=~4,333...~=~\frac{9~.~4~+~1~.~3}{9}\\\\\boxed{x~=~4,333...~=~\frac{39}{9}}\\\\\\\\y~=~3,444...~=~3+0,444...\\\\y~=~3,444...~=~3+\frac{4}{9}\\\\y~=~3,444...~=~\frac{9~.~3~+~1~.~4}{9}\\\\\boxed{y~=~3,444...~=~\frac{31}{9}}$

Agora resolvendo as expressões:

$e)\\\\\frac{\frac{39}{9}.\frac{31}{9}}{\frac{39}{9}+\frac{31}{9}}~=~\frac{\frac{39}{9}.\frac{31}{9}}{\frac{70}{9}}~=~\frac{39}{9}~.~\frac{31}{9}~.~\frac{9}{70}~=~\frac{39~.~31}{9~.~70}~=~\frac{1209}{630}~=~\boxed{\frac{403}{210}}\\\\\\\\f)\\\\\frac{\frac{39}{9}~:~\frac{31}{9}}{\frac{39}{9}+\frac{31}{9}}~=~\frac{\frac{39}{9}~.~\frac{9}{31}}{\frac{70}{9}}~=~\frac{\frac{39}{31}}{\frac{70}{9}}~=~\frac{39}{31}~.~\frac{9}{70}~=~\boxed{\frac{351}{2170}}$

$g)\\\\\frac{\frac{39}{9}~.~\frac{31}{9}}{\frac{39}{9}~:~\frac{31}{9}}~=~\frac{\frac{39}{9}~.~\frac{31}{9}}{\frac{39}{9}~.~\frac{9}{31}}~=~\frac{\frac{39~.~31}{81}}{\frac{39}{31}}~=~\frac{39~.~31}{81}~.~\frac{31}{39}~=~\frac{31^2}{81}~=~\boxed{\frac{961}{81}}$