What is the quotient of \( \frac{5}{6} \div 1 \frac{1}{2} \) ? Write your answer in fraction form and simplify the answer, if possible. (1 point)

To solve \( \frac{5}{6} \div 1 \frac{1}{2} \), first convert the mixed number \( 1 \frac{1}{2} \) into an improper fraction. This gives us: \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}. \] Now, we rewrite the division as multiplying by the reciprocal: \[ \frac{5}{6} \div \frac{3}{2} = \frac{5}{6} \times \frac{2}{3}. \] Now multiply the fractions: \[ \frac{5 \times 2}{6 \times 3} = \frac{10}{18}. \] Next, simplify \( \frac{10}{18} \) by dividing both the numerator and denominator by their greatest common divisor, which is 2: \[ \frac{10 \div 2}{18 \div 2} = \frac{5}{9}. \] The final answer is \[ \frac{5}{9}. \]