Espressione

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$\small 0,3·0,\overline7 : 2,\overline2 +7,\overline{72}·0,22-0,805=$

$\small =\dfrac{3}{10}·\dfrac{7-0}{9} : \dfrac{22-2}{9} +\dfrac{772-7}{99}·\dfrac{22}{100}-\dfrac{805}{1000}=$

$\small =\dfrac{3}{10}·\dfrac{7}{9} : \dfrac{20}{9} +\dfrac{765}{99}·\dfrac{\cancel{22}^{11}}{\cancel{100}_{50}}-\dfrac{\cancel{805}^{161}}{\cancel{1000}_{200}}=$

$\small =\dfrac{3}{10}·\dfrac{7}{9}·\dfrac{9}{20} +\dfrac{85}{11}·\dfrac{11}{50}-\dfrac{161}{200}=$

$\small =\dfrac{3}{10}·\dfrac{7}{\cancel9_1}·\dfrac{\cancel9^1}{20} +\dfrac{\cancel{85}^{17}}{\cancel{11}_1}·\dfrac{\cancel{11}^1}{\cancel{50}_{10}}-\dfrac{161}{200}=$

$\small =\dfrac{3}{10}·7·\dfrac{1}{20} +17·\dfrac{1}{10}-\dfrac{161}{200}=$

$\small = \dfrac{21}{200} +\dfrac{17}{10}-\dfrac{161}{200}=$

$\small = \dfrac{21+340-161}{200}=$

$\small = \dfrac{\cancel{200}^1}{\cancel{200}_1}= 1$