1. **State the problem:** We need to find the sum of 35 and 45, i.e., calculate $35 + 45$. 2. **Formula used:** Addition of two numbers is given by $$a + b = c$$ where $a$ and $b$ are the numbers to add, and $c$ is the result. 3. **Calculate the sum:** $$35 + 45 = 80$$ 4. **Explanation:** Adding 35 and 45 means combining their values. Since 35 plus 40 is 75, and adding the remaining 5 gives 80, the total sum is 80. 5. **Final answer:** $$35 + 45 = 80$$