1. **State the problem:** Simplify the expression $36 - 8 / 4 + 1$. 2. **Recall the order of operations:** Division and multiplication are performed before addition and subtraction. 3. **Perform the division first:** $$8 / 4 = 2$$ 4. **Rewrite the expression:** $$36 - 2 + 1$$ 5. **Perform subtraction and addition from left to right:** $$36 - 2 = 34$$ $$34 + 1 = 35$$ 6. **Final answer:** $$35$$