3 6/10+5, 9

To add the mixed numbers \(3 \frac{6}{10}\) and \(5 \frac{9}{10}\), follow these steps:

1. Convert the mixed numbers to improper fractions.

   • For \(3 \frac{6}{10}\): \[ 3 \frac{6}{10} = \frac{3 \times 10 + 6}{10} = \frac{30 + 6}{10} = \frac{36}{10} \]

   • For \(5 \frac{9}{10}\): \[ 5 \frac{9}{10} = \frac{5 \times 10 + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10} \]

2. Now, add the two improper fractions: \[ \frac{36}{10} + \frac{59}{10} = \frac{36 + 59}{10} = \frac{95}{10} \]

3. Simplify \(\frac{95}{10}\): \[ \frac{95}{10} = \frac{95 \div 5}{10 \div 5} = \frac{19}{2} \]

4. Convert \(\frac{19}{2}\) back to a mixed number: \[ 19 \div 2 = 9 \text{ remainder } 1 \Rightarrow 9 \frac{1}{2} \]

Thus, the final answer is: \[ 3 \frac{6}{10} + 5 \frac{9}{10} = 9 \frac{1}{2} \]