Question

Sejam X = 0,1666… e Y = 0,333… . Encontre a fração que representa o produto de X por Y
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Answer 1

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$\sf x=0,1666...\cdot 10\\\sf 10x=1,666\cdot 10\\\sf 100x=16,666...\\-\underline{\begin{cases}\sf100x=16,\diagup\!\!\!6\diagup\!\!\!6\diagup\!\!\!6...\\\sf10x=1,\diagup\!\!\!6\diagup\!\!\!6\diagup\!\!\!6...\end{cases}}\\\sf 90x=15\\\sf x=\dfrac{15\div15}{90\div 15}\\\sf x=\dfrac{1}{6}$

$\sf y=0,333...\cdot 10\\\sf 10y=3,333...\\-\underline{\begin{cases}\sf 10y=3,\diagup\!\!\!3\diagup\!\!\!3\diagup\!\!\!3...\\\sf y=0,\diagup\!\!\!3\diagup\!\!\!3\diagup\!\!\!3...\end{cases}}\\\sf 9y=3\\\sf y=\dfrac{3\div3}{9\div3}\\\sf y=\dfrac{1}{3}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf x\cdot y=\dfrac{1}{6}\cdot\dfrac{1}{3}=\dfrac{1}{18}\checkmark }}}}$