My grandson Ian sent me a text which I will quote,”I’m amazed at how many people don’t know PEMDAS.” My answer was, “I’m one of them. What is it?” His answer was, “You know math and you don’t know?” He even blamed me for teaching it to him. It’s a nmenomic to remember the order you supposedly should use to evaluate a mathematical expression, like one of those puzzles you find given on Facebook. The order states: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction – PEMDAS.
Now with a graduate degree in math, I take issue with learning that. Why? Because, not only might it be wrong in certain cases, but it might not permit you to use other techniques to simplify your calculations. Moreover, as a former IBM programmer, one of the things one learns is that ambiguity is not acceptable. It causes bugs. In most cases, PEMDAS is ambiguous. Programmers make sure by using parentheses appropriately grouping variables or constants to remove the ambiguity. Whenever I encounter one of those so-called math puzzles with a string of arithmetic expressions, I always answer “undefined”
In mathematics past grade school, (offense intended) you learn what you can and can’t do. You don’t have to memorize this mnemonic. In fact you shouldn’t even consider it. The idea is to simplify an expression so you can calculate it or use it easily. Relying on PEMDAS is destined to be a mistake. For instance, suppose, the expression inside the parentheses is impossible to calculate, do you give up? Not necessarily. There are other ways to simplify an expression by using other techniques that you learn when you learn math. Giving a demonstration is difficult with a normal set of typface characters so I won’t. If you really want to see an example, you can email me at alanwallach@gmail.com.
However, there is one math mnemonic which is essential and I have never forgotten it. I learned it from Mr. Kenton, my math II teacher in high school. The mnemonic of the famous Indian chief SOHCAHTOA. That is not ambiguous. It’s the trigonometric functions of the angles of a right triangle. Sine= Opposite/Hypotenuse, Cosine= Adjacent/Hyponenuse, Tangent= Opposite/Adjacent. Enough said.