Respostas

2013-07-29T18:31:06-03:00
A) Calculando a fração geratriz de 1,333...0,1666... de temos:

10x=13,33...\\x=1,333...

\Longrightarrow 9x=12

x=\dfrac{12}{9}=\dfrac{4}{3}

100y=16,666...\\10y=1,666...

\Longrightarrow 90y=15

y=\dfrac{15}{90}=\dfrac{1}{6}

Então:

1,333...+0,1666...=\dfrac{4}{3}+\dfrac{1}{6}

1,333...+0,1666...=\dfrac{9}{6}=\dfrac{3}{2}

b) Calculando a fração geratriz de 0,333..., temos:

10x=3,33...\\x=0,333...

\Longrightarrow 9x=3

x=\dfrac{3}{9}=\dfrac{1}{3}

Agora efetuando o cálculo:

\dfrac{1}{3}\times\dfrac{7}{2}\times\dfrac{8}{3}=\dfrac{28}{9}