Question

Calcule as frações geratriz (mandem o cálculo completo pvf)

A) 6,333... B)1,222....

C)3,222.... D)4,888888....

E)3,222222.... F)2,666666.....

Answer 1

$\large\boxed{\begin{array}{l}\rm A)~\sf x=6,333\dotsc\cdot10\\\sf 10x=63,333\dotsc\\\sf 10x=57+6,333\dotsc\\\sf 10x=57+x\\\sf 10x-x=57\\\sf 9x=57\\\sf x=\dfrac{57\div3}{9\div3}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{19}{3}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm B)~\sf x=1,222\dotsc\cdot10\\\sf 10x=12,222\dotsc\\\sf 10x=11+1,222\dotsc\\\sf 10x=11+x\\\sf 10x-x=11\\\sf 9x=11\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{11}{9}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm C)~\sf x=3,222\dotsc\cdot10\\\sf 10x=32,222\dotsc\\\sf 10x=29+3,222\dotsc\\\sf 10x=29+x\\\sf 10x-x=29\\\sf 9x=29\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{29}{9}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm D)~\sf x=4,888\dotsc\cdot10\\\sf 10x=48,888\dotsc\\\sf 10x=44+4,888\dotsc\\\sf 10x=44+x\\\sf 10x-x=44\\\sf 9x=44\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{44}{9}}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\rm E)~\sf x=3,222222\dotsc\cdot10\\\sf 10x=32,222\dotsc\\\sf 10x=29+3,222\dotsc\\\sf 10x=29+x\\\sf 10x-x=29\\\sf 9x=29\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{29}{9}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm F)~\sf x=2,666\dotsc\cdot10\\\sf 10x=26,666\\\sf 10x=24+2,666\dotsc\\\sf 10x=24+x\\\sf 10x-x=24\\\sf 9x=24\\\sf x=\dfrac{24\div3}{9\div3}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{8}{3}}}}}\end{array}}$