Espressione

(3/8+(7/4*3/14*8/9+2/3))-(3/10+1/15-1/6)

(3/8+(3/8*8/9+2/3)-(9+2-5)/30

3/8+1/2+2/3-1/5

3/8+1-1/5

11/8-1/5

(55-8)/40 

47/40 

1,17500...

174)

$\small \left[0,375+\left(1,75 : 4,\overline6·0,\overline8+0,\overline6\right)\right]-\left(0,3+0,0\overline6-0,1\overline6\right)=$

$\small =\left[\dfrac{\cancel{375}^3}{\cancel{1000}_8}+\left(\dfrac{\cancel{175}^7}{\cancel{100}_4} : \dfrac{46-4}{9}·\dfrac{8-0}{9}+\dfrac{6-0}{9}\right)\right]-\left(\dfrac{3}{10}+\dfrac{6-0}{90}-\dfrac{16-1}{90}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{7}{4} : \dfrac{\cancel{42}^{14}}{\cancel9_3}·\dfrac{8}{9}+\dfrac{\cancel6^2}{\cancel9_3}\right)\right]-\left(\dfrac{3}{10}+\dfrac{\cancel6^1}{\cancel{90}_{15}}-\dfrac{\cancel{15}^1}{\cancel{90}_6}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{7}{4} : \dfrac{14}{3}·\dfrac{8}{9}+\dfrac{2}{3}\right)\right]-\left(\dfrac{3}{10}+\dfrac{1}{15}-\dfrac{1}{6}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{\cancel7^1}{\cancel4_1}·\dfrac{\cancel3^1}{\cancel{14}_2}·\dfrac{\cancel8^2}{\cancel9_3}+\dfrac{2}{3}\right)\right]-\left(\dfrac{9+2-5}{30}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{1}{1}·\dfrac{1}{2}·\dfrac{2}{3}+\dfrac{2}{3}\right)\right]-\dfrac{\cancel6^1}{\cancel{30}_5}=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{\cancel2^1}{\cancel6_3}+\dfrac{2}{3}\right)\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3}{8}+\dfrac{\cancel3^1}{\cancel3_1}\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3}{8}+1\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3+8}{8}\right]-\dfrac{1}{5}=$

$\small = \dfrac{11}{8}-\dfrac{1}{5}=$

$\small = \dfrac{55-8}{40}= \dfrac{47}{40}$

$\small (= 1,175).$

0,375 = 375 /1000 ; si semplifica per 5^3 = 125;

0,375 = 3/8;

1,75 = 175/100; si semplifica per 25; 

1,75 = 7/4;

4,6(con 6 periodico) = (46 - 4)/9 = 42/9 = 14/3; si  semplifica per 3;

0,8 (con 6 periodico) = (8-0)/9 = 8/9;

0,6 (con 6 periodico) = (6 - 0)/9 = 6/9 = 2/3;

0,3 = 3/10;

0,06(con 6 periodico) = (6 - 0)/90 = = 6/90 = 2/30;  si  semplifica per 3;

0,16 (con 6 periodico) = (16 - 1) /90 = 15/90 = 1/6; (si  semplifica per 15);

[3/8 +(7/4 : 14/3 x 8/9 + 2/3)] - (3/10 + 2/30  - 1/6) =

= [3/8 +(7/4 * 3/14 x 8/9 + 2/3)] - (9/30 + 2/30 - 5/30) =

= [3/8 + 1/3  + 2/3 ] - 6/30 =

= [9/24 + 8/24 + 16/24] - 1/5 =

= 33/24 - 1/5 =

= 11/8 - 1/5 =

= 55/40 - 8/40 = 47/40; facendo la divisione:

47 : 40 = 1,175.

Ciao @modena78