Frazioni

Trasformiamo tutti i  decimali in frazioni:

0,09 (con 09 periodico) =  9/99 = 1/11;

0,18(con 18 periodico) = 18/99 = 2/11;

0,15 (con 15 periodico) = 15/99 = 5/33;

0,18 = 18/100 = 9/50;

0,2(con 2 periodico) = 2/9;

(1/11 + 2/11 - 3/11) * 5/33 + 9/50 * 2/9 =

= 0 * 5/33 + 2/50 = 

= 0 + 1/25 = 1/25.

@andreag   ciao.

(9/99 + 18/99 - 3/11)·(15/99) + 18/100·(2/9)=

=0·(15/99) + 1/25= 1/25

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$\small \left(0,\overline{09}+0\overline{18} - \dfrac{3}{11}\right)×0,\overline{15} + 0,18×0,\overline2 =$

$\small =\left(\dfrac{9-0}{99} + \dfrac{18-0}{99} - \dfrac{3}{11}\right)×\dfrac{15-0}{99} + \dfrac{\cancel{18}^9}{\cancel{100}_{50}}×\dfrac{2-0}{9} =$

$\small =\left(\dfrac{\cancel9^1}{\cancel{99}_{11}} + \dfrac{\cancel{18}^2}{\cancel{99}_{11}} - \dfrac{3}{11}\right)×\dfrac{\cancel{15}^5}{\cancel{99}_{33}} + \dfrac{\cancel9^1}{\cancel{50}_{25}}×\dfrac{\cancel2^1}{\cancel9_1} =$

$\small =\left(\dfrac{1}{11} + \dfrac{2}{11} - \dfrac{3}{11}\right)×\dfrac{5}{33} + \dfrac{1}{25}×\dfrac{1}{1} =$

$\small = \dfrac{0}{11}×\dfrac{5}{33} + \dfrac{1}{25}=$

$\small = 0×\dfrac{5}{33} + \dfrac{1}{25}=$

$\small = 0 + \dfrac{1}{25}= \dfrac{1}{25}$