Aiutatemi! 3 Espressioni con numeri decimali

[(16-1)/9-1] : 4/9

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$\dfrac{25}{24}-\dfrac{7}{8}+0,\overline6-0,9·0,\overline5=$

$= \dfrac{25}{24}-\dfrac{7}{8}+\dfrac{6-0}{9}-\dfrac{9}{10}·\dfrac{5-0}{9}=$

$= \dfrac{25}{24}-\dfrac{7}{8}+\dfrac{\cancel6^2}{\cancel9_3}-\dfrac{9}{10}·\dfrac{5}{9}=$

$= \dfrac{25}{24}-\dfrac{7}{8}+\dfrac{2}{3}-\dfrac{\cancel9^1}{\cancel{10}_2}·\dfrac{\cancel5^1}{\cancel9_1}=$

$= \dfrac{25}{24}-\dfrac{7}{8}+\dfrac{2}{3}-\dfrac{1}{2}·\dfrac{1}{1}=$

$= \dfrac{25}{24}-\dfrac{7}{8}+\dfrac{2}{3}-\dfrac{1}{2}=$

$= \dfrac{25-21+16-12}{24}=$

$= \dfrac{\cancel8^1}{\cancel{24}_3}=$

$=\dfrac{1}{3}$

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$\dfrac{5}{16}·0,2\overline6+(0,5-0,2-0,15)·0,\overline4=$

$=\dfrac{5}{16}·\dfrac{26-2}{90}+\left(\dfrac{5}{10}-\dfrac{2}{10}-\dfrac{15}{100}\right)·\dfrac{4-0}{9}=$

$=\dfrac{5}{16}·\dfrac{\cancel{24}^4}{\cancel{90}_{15}}+\left(\dfrac{\cancel5^1}{\cancel{10}_2}-\dfrac{\cancel2^1}{\cancel{10}_5}-\dfrac{\cancel{15}^3}{\cancel{100}_{20}}\right)·\dfrac{4}{9}=$

$=\dfrac{\cancel5^1}{\cancel{16}_4}·\dfrac{\cancel4^1}{\cancel{15}_3}+\left(\dfrac{1}{2}-\dfrac{1}{5}-\dfrac{3}{20}\right)·\dfrac{4}{9}=$

$=\dfrac{1}{4}·\dfrac{1}{3}+\left(\dfrac{10-4-3}{20}\right)·\dfrac{4}{9}=$

$=\dfrac{1}{12}+\dfrac{\cancel3^1}{\cancel{20}_5}·\dfrac{\cancel4^1}{\cancel9_3}=$

$=\dfrac{1}{12}+\dfrac{1}{5}·\dfrac{1}{3}=$

$=\dfrac{1}{12}+\dfrac{1}{15}=$

$=\dfrac{5+4}{60}=$

$=\dfrac{9}{60}=$

$=\dfrac{\cancel9^3}{\cancel{60}_{20}}=$

$=\dfrac{3}{20}$

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$(1,\overline6-1) : 0,\overline4=$

$= \left(\dfrac{16-1}{9}-1\right) : \dfrac{4-0}{9}=$

$= \left(\dfrac{15}{9}-1\right) : \dfrac{4}{9}=$

$= \left(\dfrac{\cancel{15}^5}{\cancel9_3}-1\right) · \dfrac{9}{4}=$

$= \left(\dfrac{5}{3}-1\right) · \dfrac{9}{4}=$

$= \left(\dfrac{5-3}{3}\right) · \dfrac{9}{4}=$

$= \dfrac{\cancel2^1}{\cancel3_1} · \dfrac{\cancel9^3}{\cancel4_2}=$

$= \dfrac{1}{1}·\dfrac{3}{2}=$

$= \dfrac{3}{2}$