Add. Write your answer as a mixed number in simplest form. \( 5 \frac{5}{6}+4 \frac{1}{9} \)

To add \( 5 \frac{5}{6} + 4 \frac{1}{9} \), we first convert the mixed numbers to improper fractions. For \( 5 \frac{5}{6} \): \[ 5 \cdot 6 + 5 = 30 + 5 = 35 \] So, \( 5 \frac{5}{6} = \frac{35}{6} \). For \( 4 \frac{1}{9} \): \[ 4 \cdot 9 + 1 = 36 + 1 = 37 \] So, \( 4 \frac{1}{9} = \frac{37}{9} \). Next, we need a common denominator to add the two fractions. The least common multiple of 6 and 9 is 18. Now we convert both fractions: \[ \frac{35}{6} = \frac{35 \cdot 3}{6 \cdot 3} = \frac{105}{18} \] \[ \frac{37}{9} = \frac{37 \cdot 2}{9 \cdot 2} = \frac{74}{18} \] Now, we can add them: \[ \frac{105}{18} + \frac{74}{18} = \frac{105 + 74}{18} = \frac{179}{18} \] To convert \( \frac{179}{18} \) back to a mixed number, we divide: 179 divided by 18 is 9 with a remainder of 17. Therefore, \( \frac{179}{18} = 9 \frac{17}{18} \). So, \( 5 \frac{5}{6} + 4 \frac{1}{9} = 9 \frac{17}{18} \).