Answer:
[tex]-\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]-\frac{1}{2} +(\frac{3}{4}\times \frac{4}{9} )\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=-\frac{1}{2}+\frac{3}{4}\times \frac{4}{9}\\\\\frac{3}{4}\times \frac{4}{9}=\frac{1}{3}\\\\\frac{3}{4}\times \frac{4}{9}=\frac{1}{3}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}2,\:3:\quad 6\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{1}{2}=\frac{1\times \:3}{2\times \:3}=\frac{3}{6}\\\\\frac{1}{3}=\frac{1\times \:2}{3\times \:2}=\frac{2}{6}\\\\=-\frac{3}{6}+\frac{2}{6}\\[/tex]
[tex]=-\frac{3}{6}+\frac{2}{6}\\\\=\frac{-3+2}{6}\\\\=\frac{-1}{6}\\\\=-\frac{1}{6}[/tex]
