Espressione-risultato 7/55

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$\small \left(5-\dfrac{1}{5}\right) : \left\{\left[\dfrac{1}{4}+\dfrac{27}{28}×\left(\dfrac{22}{45}-\dfrac{1}{10}\right)\right]^2 : \left(\dfrac{1}{4}\right)^3-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \left(\dfrac{25-1}{5}\right) : \left\{\left[\dfrac{1}{4}+\dfrac{27}{28}×\left(\dfrac{44-9}{90}\right)\right]^2 : \dfrac{1}{64}-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\left[\dfrac{1}{4}+\dfrac{\cancel{27}^3}{\cancel{28}_4}×\dfrac{\cancel{35}^5}{\cancel{90}_{10}}\right]^2 × 64-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\left[\dfrac{1}{4}+\dfrac{3}{4}×\dfrac{\cancel5^1}{\cancel{10}_2}\right]^2 × 64-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\left[\dfrac{1}{4}+\dfrac{3}{4}×\dfrac{1}{2}\right]^2 × 64-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\left[\dfrac{1}{4}+\dfrac{3}{8}\right]^2 × 64-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\left[\dfrac{2+3}{8}\right]^2 × 64-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\left[\dfrac{5}{8}\right]^2 × 64-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\dfrac{25}{\cancel{64}_1} × \cancel{64}^1-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{25-\dfrac{31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \left\{\dfrac{75-31}{3}\right\}-\dfrac{1}{5}=$

$\small = \dfrac{24}{5} : \dfrac{44}{3}-\dfrac{1}{5}=$

$\small = \dfrac{\cancel{24}^6}{5} × \dfrac{3}{\cancel{44}_{11}}-\dfrac{1}{5}=$

$\small = \dfrac{6}{5} × \dfrac{3}{11}-\dfrac{1}{5}=$

$\small = \dfrac{18}{55}-\dfrac{1}{5}=$

$\small = \dfrac{18-11}{55}=$

$\small = \dfrac{7}{55}$

24/5 : ((1/4+27/28*(220-45)/450)^2 : 1/64 -31/5)-1/5

24/5 : ((1/4+27/28*175/450)^2*64-31/3)-1/5

24/5 : ((1/4+3/8)^2*64-31/3)-1/5

24/5 : (25/64*64-31/3)-1/5

24/5 * 3/44 -1/5

18/55-1/5 

7/55