Espressiono

0,(6) = 2/3  ;  0,(5) = 5/9

25/24-7/8+2/3-0,9*5/9

(25-21)/24+2/3-1/2

1/6+2/3-1/2 

(1+4-3)/6 = 2/6 = 1/3

0,1(6) = 1/6 ; 0,(1) = 1/9

(5+4*1/6)*9

45+6 = 51

25/24 - 7/8 + 6/9 - 9/10 * 5/9=

= 25/24 - 7/8 + 2/3 - 1/2 =

mcm = 2^3 * 3 = 24;

= 25/24 - 21/24 + 16/24 - 12/24 =

= (25 - 21 + 16 -12) /24 = 8/24; dividendo per 8:

= 1/3.

(4/9 : 2/9 + 5/10) : 325/100;

[3,25 = 325 / 100 =325 : 5 / (100 : 5) = 13/4].

(4/9 * 9/2 + 1/2) : 13 / 4 =

= (2 + 1/2) * 4/13 =

= (4/2 + 1/2) * 4/13 =

= 5/2 * 4/13 = 10/13.

 (5 + 4 * (16 - 1)/90 ) : 1/9=

(5 + 4 *15/90) : 1/9 =

= (5 + 4 * 1/6) : 1/9 =

= (5 + 2/3) * 9/1 =

= (15/3 + 2/3) * 9/1 =

= 17/3 * 9 = 17 * 3 = 51.

@giustot  ciao

141A)

$\frac{25}{24} - \frac{7}{8} + 0,(6) - 0,9×0,(5) =$

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

$=\frac{25}{24} - \frac{7}{8} + \frac{6}{9} - \frac{9}{10}×\frac{5}{9} =$

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

$=\frac{25}{24} - \frac{7}{8} + \frac{2}{3} - \frac{1}{2}=$ $(mcm= 24)$:

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

$= \frac{8}{24}=$

$= \frac{1}{3}$.

141B)

$(5 + 4×0,1(6)) : 0,(1) =$

$= (5 + 4×\frac{16-1}{90}): \frac{1-0}{9} =$

$= (5 + 4×\frac{15}{90}): \frac{1}{9} =$

$= (5 + 4×\frac{1}{6})×9 =$

$= (5 + 2×\frac{1}{3})×9 =$

$= (5 + \frac{2}{3})×9 =$

$= (\frac{15+2}{3})×9 =$

$= \frac{17}{3}×9 =$

$= \frac{17}{1}×3 =$

$= 51$.

@giustot

Consiglio: determina, preventivamente, per i numeri decimali che trovi nelle espressioni  le loro frazioni generatrici e poi fare tutte le operazioni con sole frazioni