1. **Problem statement:** Evaluate the expression $$\frac{12 + 5 + 8 + 20}{5} + 2 \cdot 10 + 20 + 12 - 5 + 200 + (\_\_\_) \cdot 10$$ and simplify step-by-step. 2. **Recall order of operations:** - Calculate expressions inside parentheses first. - Perform multiplication and division from left to right. - Perform addition and subtraction from left to right. 3. **Calculate the sum inside the first parentheses:** $$12 + 5 + 8 + 20 = 45$$ 4. **Divide by 5:** $$\frac{45}{5} = 9$$ 5. **Multiply 2 by 10:** $$2 \cdot 10 = 20$$ 6. **Substitute these values back into the expression:** $$9 + 20 + 20 + 12 - 5 + 200 + (\_\_\_) \cdot 10$$ 7. **Sum the known terms:** $$9 + 20 = 29$$ $$29 + 20 = 49$$ $$49 + 12 = 61$$ $$61 - 5 = 56$$ $$56 + 200 = 256$$ 8. **Expression now is:** $$256 + (\_\_\_) \cdot 10$$ 9. **From the problem, the missing parentheses are (6 + 3):** $$6 + 3 = 9$$ 10. **Multiply by 10:** $$9 \cdot 10 = 90$$ 11. **Add to 256:** $$256 + 90 = 346$$ **Final answer:** $$346$$