How the order of operations determines how you evaluate an algebraic expression?

Answer 1

Well, if I understand what you're asking, the order of operations is simple and helpful. For example, if you have this equation (with "a" being the variable): 3a - 4 * (18-14) = 20

then you first do parentheses (P in PEMDAS). So, the answer to 18-14 would be 4. Then, since there are no exponents (E), you multiply (M) 4 * 4, which equals 16. Next, since the remaining part of the equation is 3a - 16 = 20, you add (A) 16 to the other side to balance out the equation. Now, all is left is 3a = 36. Now, you just divide (the remaining part of the equation does NOT follow the rule. It goes out of order for some reason). The answer to a is 12. The equation does follow the rules of the order of operations. At the point 3a-16=20, you cannot combine any more terms in the order of addition or subtraction because their aren't any like terms to combine. In algebra, you are solving for the unknown variable, in this case (a). In order to solve for (a), you have to isolate the variable. You do this by balancing out the equation and adding 16 to both sides of the equation, therefore being left with 3a=36. Then you divide by three to further isolate the variable. When left with unlike terms, in essence, you do the order of operations in reverse.