3 4/5 +2 4/7

To add the mixed numbers \(3 \frac{4}{5}\) and \(2 \frac{4}{7}\), follow these steps:

1. Convert each mixed number into an improper fraction.

   For \(3 \frac{4}{5}\): \[ 3 \frac{4}{5} = \frac{(3 \times 5) + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]

   For \(2 \frac{4}{7}\): \[ 2 \frac{4}{7} = \frac{(2 \times 7) + 4}{7} = \frac{14 + 4}{7} = \frac{18}{7} \]

2. Now, add the improper fractions. To do this, find a common denominator. The least common multiple of 5 and 7 is 35.

3. Convert each fraction to have the common denominator of 35: \[ \frac{19}{5} = \frac{19 \times 7}{5 \times 7} = \frac{133}{35} \] \[ \frac{18}{7} = \frac{18 \times 5}{7 \times 5} = \frac{90}{35} \]

4. Now add the two fractions: \[ \frac{133}{35} + \frac{90}{35} = \frac{133 + 90}{35} = \frac{223}{35} \]

5. Convert back to a mixed number: \[ \frac{223}{35} = 6 \frac{13}{35} \]

Therefore, \(3 \frac{4}{5} + 2 \frac{4}{7} = 6 \frac{13}{35}\).