How do you simplify -3 1/9 - (-1 1/3)

[tex]\mathrm{Apply\:rule}:\quad \:a-\left(-b\right)=a+b\\-\frac{28}{9}-\left(-\frac{4}{3}\right)=-\frac{28}{9}+\frac{4}{3}\\=-\frac{28}{9}+\frac{4}{3}[/tex]

[tex]=-\frac{28}{9}+\frac{12}{9}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\\=\frac{-28+12}{9}\\\mathrm{Add\:the\:numbers:}\:-28+12=-16\\=\frac{-16}{9}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{16}{9}[/tex]

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions:}[/tex]

[tex]\frac{16}{9}=1\frac{7}{9}\\\frac{16}{9}=1 \\9\overline{|\smallspace16}\:\:\:\:\\\begin{matrix}\:\:\:\:\:\:\emptyspace1\:\:\:\:\:\:\:\:\:\:\:\:\\ 9\overline{|\smallspace16}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace9}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\\\\\\\frac{16}{9}=1\frac{7}{9}\\=-1\frac{7}{9}\\answer: \\=-1\frac{7}{9}[/tex]