[Risolto] Rapporti tra numeri rapporti tra grandezze

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$\dfrac{1+\frac{1}{3}-\frac{3}{2}×\frac{1}{2}+\frac{1}{5} : \frac{2}{15}}{\left(\frac{1}{2}+\frac{3}{4}×\frac{3}{8} : \frac{3}{16}\right) : \frac{2}{5}} =$

$= \dfrac{1+\frac{1}{3}-\frac{3}{4}+\frac{1}{\cancel5_1} × \frac{\cancel{15}^3}{2}}{\left(\frac{1}{2}+\frac{\cancel9^3}{\cancel{32}_2} × \frac{\cancel{16}^1}{\cancel3_1}\right) × \frac{5}{2}} =$

$= \dfrac{1+\frac{1}{3}-\frac{3}{4}+\frac{3}{2}}{\left(\frac{1}{2}+\frac{3}{2}\right) × \frac{5}{2}} =$

$= \dfrac{\frac{12+4-9+18}{12}}{\frac{4}{2} × \frac{5}{2}} =$

$= \dfrac{\frac{25}{12}}{\frac{\cancel4^2}{\cancel2_1} × \frac{5}{2}} =$

$= \dfrac{\frac{25}{12}}{\frac{\cancel2^1}{1} × \frac{5}{\cancel2_1}} =$

$= \dfrac{\frac{25}{12}}{5}=$

$= \dfrac{\cancel{25}^5}{12}×\dfrac{1}{\cancel5_1}=$

$= \dfrac{5}{12}$

4/3-3/4+3/2 = (16-9+18)/12 = 25/12

(1/2+9/32*16/3)*5/2 ) = (1/2+3/2)*5/2 = 10/2 = 5 

(25/12) / 5 = 5/12