Simplify $182+3\cdot 7-64\div 2+27\div 3$.
I see that this problem involves different operations: addition, subtraction, multiplication, and division. To simplify it, I need to follow the order of operations, which is parentheses, exponents, multiplication and division, and then addition and subtraction. I can remember this by using the acronym PEMDAS. I don't see any parentheses or exponents in the problem, so I can skip those steps. Next, I look for multiplication and division. I see that there are three terms that involve multiplication or division: 3\cdot 7, 64\div 2, and 27\div 3. I can simplify each of these terms by performing the arithmetic. 3\cdot 7 is 21, 64\div 2 is 32, and 27\div 3 is 9. I can replace these terms with their simplified values in the problem. This gives me $182+21-32+9$. Now, I only have addition and subtraction left. I can perform these operations from left to right. 182+21 is 203, 203-32 is 171, and 171+9 is 180. Therefore, the simplified value of the expression is 180. 