Find the sum. Simplify the answer. \( 5 \frac{2}{5}+2 \frac{1}{10} \)

To find the sum \( 5 \frac{2}{5}+2 \frac{1}{10} \), let's convert both mixed numbers to improper fractions. First, convert \( 5 \frac{2}{5} \): \[ 5 \frac{2}{5} = 5 \times 5 + 2 = 25 + 2 = \frac{27}{5} \] Next, convert \( 2 \frac{1}{10} \): \[ 2 \frac{1}{10} = 2 \times 10 + 1 = 20 + 1 = \frac{21}{10} \] Now, to add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. Convert \( \frac{27}{5} \) to a denominator of 10: \[ \frac{27}{5} = \frac{27 \times 2}{5 \times 2} = \frac{54}{10} \] Now we can add: \[ \frac{54}{10} + \frac{21}{10} = \frac{54 + 21}{10} = \frac{75}{10} \] To simplify \( \frac{75}{10} \): \[ \frac{75 \div 5}{10 \div 5} = \frac{15}{2} \] Now convert \( \frac{15}{2} \) back to a mixed number: \[ \frac{15}{2} = 7 \frac{1}{2} \] So the simplified sum is \( 7 \frac{1}{2} \).