1. **State the problem:** We are asked to round the numbers 5.14 and 4.57 to the nearest whole number and then add the results. 2. **Round each number:** - 5.14 rounded to the nearest whole number is $5$ because $0.14 < 0.5$. - 4.57 rounded to the nearest whole number is $5$ because $0.57 \geq 0.5$. 3. **Add the rounded numbers:** $$5 + 5 = 10$$ 4. **Final answer:** The sum of the rounded numbers is $10$.