Question

Calculati:
a)0,1(6)-[(0,25-1 $\frac{1}{2}$)-(0,(3)-2$\frac{1}{3} )]$

Answer 1

    
[tex]\displaystyle 0,1(6)-[(0,25-1 \frac{1}{2} )-(0,(3)-2 \frac{1}{3} )] = \\ \\ = \frac{16-1}{90}-[( \frac{1}{4} -\frac{3}{2} )-( \frac{1}{3}-\frac{7}{3} )] = \\ \\ = \frac{15}{90}-[( \frac{1}{4} -\frac{6}{4} )-( \frac{1}{3}-\frac{7}{3} )] = \\ \\ = \frac{1}{6}-[( -\frac{5}{4} )-( -\frac{6}{3} )] = \\ \\ =\frac{1}{6}-[-\frac{5}{4} +2 ] = \frac{1}{6}-[-\frac{5}{4} + \frac{8}{4} ] = \frac{1}{6}-\frac{3}{4} =\frac{2}{12}-\frac{9}{12} =\boxed{-\frac{7}{12}}[/tex]