Consider the given expression,
[tex]3\frac{1}{3}-(\frac{-4}{5}+\frac{2}{3})[/tex]
First of all, convert the mixed fraction into standard form,
[tex]\begin{gathered} =\frac{3(3)+1}{3}-(\frac{-4}{5}+\frac{2}{3}) \\ =\frac{9+1}{3}-(\frac{-4}{5}+\frac{2}{3}) \\ =\frac{10}{3}-(\frac{-4}{5}+\frac{2}{3}) \end{gathered}[/tex]
Now, resolve the parenthesis,
[tex]\begin{gathered} =\frac{10}{3}-(\frac{-4(3)+2(5)}{5\cdot3}) \\ =\frac{10}{3}-(\frac{-12+10}{15}) \\ =\frac{10}{3}-(\frac{-2}{15}) \\ =\frac{10}{3}+\frac{2}{15} \end{gathered}[/tex]
Now, simplify the last fraction,
[tex]\begin{gathered} =\frac{10}{3}+\frac{2}{15} \\ =\frac{10(5)+2(1)}{15} \\ =\frac{50+2}{15} \\ =\frac{52}{15} \end{gathered}[/tex]
Thus, the simplified fraction of the given expression is 52/15.
