Question

determine o valor da soma:
a) 1, 333...+ 0, 1666...=
b) 0, 333... × 7 sobre 2 × 8 sobre 3=

Answer 1

a) Calculando a fração geratriz de $1,333...$ e $0,1666...$ 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:

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