Frazioni

4/9-((3-2/3)*1/3-(5/6-1/2)/(11/4-8/4-1/4))

4/9-((7/3*1/3)-(5/6-3/6)/(1/2))

4/9-(7/9-1/3*2)

4/9-(7/9-2/3)

4/9-1/9 = 3/9

3/9 = 1/3

============================================================

$\small 0,\overline4-\left[(3-0,\overline6)×\dfrac{1}{3}-(0,8\overline3-0,5) : \left(\dfrac{11}{4}-2-0,25\right)\right] =$

$\small =\dfrac{4-0}{9}-\left[\left(3-\dfrac{6-0}{9}\right)×\dfrac{1}{3}-\left(\dfrac{83-8}{90}-\dfrac{\cancel5^1}{\cancel{10}_2}\right) : \left(\dfrac{11}{4}-2-\dfrac{\cancel{25}^1}{\cancel{100}_4}\right)\right] =$

$\small =\dfrac{4}{9}-\left[\left(3-\dfrac{\cancel6^2}{\cancel9_3}\right)×\dfrac{1}{3}-\left(\dfrac{\cancel{75}^5}{\cancel{90}_6}-\dfrac{1}{2}\right) : \left(\dfrac{11}{4}-2-\dfrac{1}{4}\right)\right] =$

$\small =\dfrac{4}{9}-\left[\left(3-\dfrac{2}{3}\right)×\dfrac{1}{3}-\left(\dfrac{5}{6}-\dfrac{1}{2}\right) : \left(\dfrac{11-8-1}{4}\right)\right] =$

$\small =\dfrac{4}{9}-\left[\left(\dfrac{9-2}{3}\right)×\dfrac{1}{3}-\left(\dfrac{5-3}{6}\right) : \dfrac{\cancel2^1}{\cancel4_2}\right] =$

$\small =\dfrac{4}{9}-\left[\dfrac{7}{3}×\dfrac{1}{3}-\dfrac{\cancel2^1}{\cancel6_3} : \dfrac{1}{2}\right] =$

$\small =\dfrac{4}{9}-\left[\dfrac{7}{9}-\dfrac{1}{3}·2\right] =$

$\small =\dfrac{4}{9}-\left[\dfrac{7}{9}-\dfrac{2}{3}\right] =$

$\small =\dfrac{4}{9}-\left[\dfrac{7-6}{9}\right] =$

$\small =\dfrac{4}{9}-\dfrac{1}{9} =$

$\small =\dfrac{\cancel3^1}{\cancel9_3} = \dfrac{1}{3} $