9. \( 1 \frac{3}{8}+4 \frac{4}{9}= \)

To solve \( 1 \frac{3}{8}+4 \frac{4}{9} \), first convert the mixed numbers into improper fractions. For \( 1 \frac{3}{8} \): \( 1 \cdot 8 + 3 = 8 + 3 = 11 \), so \( 1 \frac{3}{8} = \frac{11}{8} \). For \( 4 \frac{4}{9} \): \( 4 \cdot 9 + 4 = 36 + 4 = 40 \), so \( 4 \frac{4}{9} = \frac{40}{9} \). Now, add the two fractions \( \frac{11}{8} + \frac{40}{9} \) by finding a common denominator, which is 72. Convert \( \frac{11}{8} \) to \( \frac{99}{72} \) and \( \frac{40}{9} \) to \( \frac{320}{72} \). Now, add \( \frac{99}{72} + \frac{320}{72} = \frac{419}{72} \). Therefore, the final answer is \( 5 \frac{59}{72} \).