To find the sum of \( 2 \frac{1}{5} \) and \( 1 \frac{3}{5} \), we can first convert the mixed numbers into improper fractions.
-
Convert \( 2 \frac{1}{5} \): \[ 2 \frac{1}{5} = 2 \times 5 + 1 = 10 + 1 = 11 \quad \text{(over 5)} = \frac{11}{5} \]
-
Convert \( 1 \frac{3}{5} \): \[ 1 \frac{3}{5} = 1 \times 5 + 3 = 5 + 3 = 8 \quad \text{(over 5)} = \frac{8}{5} \]
Now, add the two improper fractions: \[ \frac{11}{5} + \frac{8}{5} = \frac{11 + 8}{5} = \frac{19}{5} \]
Next, convert \( \frac{19}{5} \) back to a mixed number: \[ 19 \div 5 = 3 \quad \text{(with a remainder of } 4\text{)} \]
So, \( \frac{19}{5} \) can be written as: \[ 3 \frac{4}{5} \]
Therefore, the sum of \( 2 \frac{1}{5} \) and \( 1 \frac{3}{5} \) is: \[ \boxed{3 \frac{4}{5}} \]