Order of Operations

In mathematics, and particularly in Algebra, the order of operations is crucial. If not followed properly, you can end up with an entirely different answer than the one you should have. In order to do it properly, it helps to have a pneumonic. This pneumonic will give you a fool-proof method every time.

Please Excuse My Dear Aunt Sally. This pneumonic (PEMDAS) also stands for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. The reasoning is that you would break down the algebraic equation in that order. If an operation is missing in an equation, then skip over it. Otherwise, begin with the Parentheses and simplify the equation down to the answer or the simplest form.

Parentheses. In the case of 2(x + x²), the first thing to do is get rid of the parentheses by multiplying all of the way across. The result would be 2x + 2x². Now you would proceed with the rest of the equation. If you had a dual-sided equation, such as 16 = 2(x + 2x), then remember the rule: Whatever you do to one side, you must do to the other. After multiplying out, 16 = 2x + 4x, you would be ready to divide BOTH sides by "x." This would leave 16/x = 6. We then multiply BOTH sides "x" to get rid of the "x" in the denominator. We have 16 = 6x and divide both sides by 6. x = 16/6, or simplified, x = 8/3.

Exponents. This is fairly simple. Exponents can be simplified if a number or an entire equation is raised to a power and cannot be simplified if they are simply attached to a variable. 4² would be simplified to 16, and (2 + 8)² would be simplified first to 2² + 8², which equals 4 + 64, which equals 68.

Multiplication, Division, Addition and Subtraction. Remember, these are not just the operations, but the order of operations. In the case of x = 4 + 5(8) - 6, then multiplication would be done first. x = 4 + 40 - 6. Followed through, this is, x = 44 - 6 or 38. If however, you did NOT do the order of operations and just added, multiplied and subtracted across from left to right, you would come up with the incorrect answer. x = 4 + 5(8) - 6, so that would be x = 9(8) - 6, which is x = 72 - 6. x would then equal 66 instead of 38, which is the correct answer.

Obviously the order of operations is crucial to proper algebraic equations. Follow the order of operations correctly and you will get the answer right every time!

Sources:

http://www.purplemath.com/modules/orderops.htm