Question

Escreva na forma de fração a divisão dos decimais abaixo:
a) 0,333..../0,444...
b) 1,222.../ 1,111...

Answer 1

resolução!

A = 0,333.. / 0,444...

A = 3/9 ÷ 4/9

A = 1/3 ÷ 4/9

A = 1/3 * 9/4

A = 9/12

A = 3/4

B = 1,2222... / 1,111...

B = 12 - 1/9 ÷ 11 - 1/9

B = 11/9 ÷ 10/9

B = 11/9 * 9/10

B = 99/90

B = 11/10

Answer 2

a)

$\mathsf{x=0,333...\times10}\\\mathsf{10x=3,333...}$

$\begin{cases}\mathsf{10x=3,333...}\\\mathsf{x=0,333...}\end{cases}$

$\mathsf{9x=3\to~x=\dfrac{3\div3}{9\div3}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{x=\dfrac{1}{3}}}}}}$

$\mathsf{x=0,444...\times10}\\\mathsf{10x=4,444...}$

$\begin{cases}\mathsf{10x=4,444...}\\\mathsf{x=0,444...}\end{cases}$

$\mathsf{9x=4}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{x=\dfrac{4}{9}}}}}}$

$\mathsf{\dfrac{0,333... }{0,444...}=\dfrac{\frac{3}{9}}{\frac{4}{9}}=\dfrac{3}{4}}$