2 5/6+4 8/9

To add the mixed numbers \(2 \frac{5}{6}\) and \(4 \frac{8}{9}\), follow these steps:

1. Convert each mixed number into an improper fraction.

   • For \(2 \frac{5}{6}\): \[ 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \]

   • For \(4 \frac{8}{9}\): \[ 4 \frac{8}{9} = \frac{4 \times 9 + 8}{9} = \frac{36 + 8}{9} = \frac{44}{9} \]

2. Add the two improper fractions: \[ \frac{17}{6} + \frac{44}{9} \]

   To add these fractions, find a common denominator. The least common multiple of 6 and 9 is 18.

3. Convert each fraction to have a denominator of 18:

   • For \(\frac{17}{6}\): \[ \frac{17}{6} = \frac{17 \times 3}{6 \times 3} = \frac{51}{18} \]

   • For \(\frac{44}{9}\): \[ \frac{44}{9} = \frac{44 \times 2}{9 \times 2} = \frac{88}{18} \]

4. Now add the fractions: \[ \frac{51}{18} + \frac{88}{18} = \frac{51 + 88}{18} = \frac{139}{18} \]

5. Convert the improper fraction back to a mixed number: \[ 139 \div 18 = 7 \quad \text{(remainder 13)} \] So, \(\frac{139}{18} = 7 \frac{13}{18}\).

Thus, the sum of \(2 \frac{5}{6} + 4 \frac{8}{9}\) is: \[ \boxed{7 \frac{13}{18}} \]