Divide. Write the answer in simplest form. \( 1 \frac{4}{9} \div 2 \frac{5}{6} \) Aelect the correct choice below and, if necessary, fill in the answer box to complete your choice. B. The quotient is undefined. B. \( \frac{5}{6}=\square \) (Type a whole number or a simplified fraction.)

To divide the mixed numbers \( 1 \frac{4}{9} \) and \( 2 \frac{5}{6} \), we first convert them into improper fractions. 1. Convert \( 1 \frac{4}{9} \): \[ 1 \frac{4}{9} = 1 + \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{13}{9} \] 2. Convert \( 2 \frac{5}{6} \): \[ 2 \frac{5}{6} = 2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6} \] Now we can perform the division: \[ \frac{13}{9} \div \frac{17}{6} \] To divide by a fraction, we multiply by its reciprocal: \[ \frac{13}{9} \times \frac{6}{17} \] Now we multiply the fractions: \[ \frac{13 \times 6}{9 \times 17} = \frac{78}{153} \] Next, we simplify \( \frac{78}{153} \). We find the greatest common divisor (GCD) of 78 and 153. The prime factorization of 78 is: \[ 78 = 2 \times 3 \times 13 \] The prime factorization of 153 is: \[ 153 = 3 \times 3 \times 17 = 3^2 \times 17 \] The GCD is \( 3 \). Now we divide both the numerator and the denominator by their GCD: \[ \frac{78 \div 3}{153 \div 3} = \frac{26}{51} \] Next, we check if \( \frac{26}{51} \) can be simplified further. The prime factorization of 26 is \( 2 \times 13 \) and for 51 is \( 3 \times 17 \). Since they have no common factors, \( \frac{26}{51} \) is in simplest form. Thus, the final answer is: \[ \frac{26}{51} \] So, the answer is: \[ \frac{26}{51} = \square \]