1. **State the problem:** Calculate the sum of 4 and 7. 2. **Formula used:** Addition of two numbers is given by $a + b$ where $a$ and $b$ are numbers. 3. **Apply the formula:** Here, $a=4$ and $b=7$, so we calculate: $$4 + 7$$ 4. **Perform the addition:** Adding 4 and 7 gives: $$11$$ 5. **Conclusion:** The sum of 4 and 7 is 11.