[tex]\huge{\boxed{\frac{1}{2}}}[/tex]To divide by a fraction, you multiply by its reciprocal, which you find by flipping the numerator and the denominator. [tex]\frac{1}{3} \div \frac{6}{9} = \frac{1}{3} * \frac{9}{6}[/tex]Multiply the numerators and the denominators separately. [tex]\frac{1}{3} * \frac{9}{6} = \frac{1*9}{3*6} = \frac{9}{18}[/tex]Simplify by dividing both sides of the equation by [tex]9[/tex]. [tex]\frac{9 \div 9}{18 \div 9} = \boxed{\frac{1}{2}}[/tex]