Question

Determine a fração irredutível que representa o resultado da expressão: 
- (0,202020...+ 0,33333...- 1,6262...) ÷ 0,515151…

Answer 1

$0,202020\dots=\dfrac{20}{99}$

$0,333\dots=\dfrac{3}{9}=\dfrac{1}{3}$

$1,6262\dots=1\frac{62}{99}=\dfrac{99+62}{99}=\dfrac{161}{99}$

$0,5151\dots=\dfrac{51}{99}=\dfrac{17}{33}$

$-(0,2020\dots+0,333\dots-1,6262\dots)\div0,5151\dots$

$-\left(\dfrac{20}{99}+\dfrac{1}{3}-\dfrac{161}{99}\right)\div\dfrac{17}{33}$

$-\left(-\dfrac{108}{99}\right)\div\dfrac{17}{33}$

$\dfrac{108}{99}\div\dfrac{17}{33}=\dfrac{108}{99}\cdot\dfrac{33}{17}=\dfrac{108}{51}$

Answer 2

Ireedutivel 36/17=(108/51)/3