The reason your math teacher made you (most likely) remember PEMDAS, or “Please Excuse My Dear Aunt Sally,” is because without it we wouldn’t be able to properly read mathematics. For example, you can read the sentence, “The quick brown fox jumps over the lazy dog,” and picture what it is trying to convey. There’s a dog, he or she is lazy, maybe laying down. A fox, which is the color brown, jumps over the dog and is doing this at a fast speed. Everyone reads this sentence and understands it in the exact same way. We know which adjectives describe which nouns and what the verb is referring to. We know the fox jumped, not the dog. We know that the word “brown” describes the color of the fox. We learned the rules of English in order to be able to read, write, and communicate so that everyone knows exactly what we are trying to say. The order of operations is the equivalent of this, but for mathematics.
Without the order of operations, everyone would do calculations however he or she wanted and everyone could get different answers. If I say to you, “First add two and eight, then divide your sum by five,” I could write it out as: (2+8)÷5 or (2+8)/5. If you follow the order of operations properly, you will get the solution I was referring to. If you don’t, you don’t understand what I’m trying to say. I also use the knowledge of the order of operations to write those expressions. I couldn’t write 2+8÷5 because the answer you would get, following the correct procedures according to the order of operations, would not be the one I was referring to. The order of operations allows everyone to be able to communicate mathematics correctly, without further explanation or confusion.
PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction and that’s the order you’re supposed to do the mathematics (sort of). You’d think math teachers would love PEMDAS, and I’m sure you thought they did, but most math teachers have a huge problem with it. It makes their students think that multiplication comes before division and addition before subtraction when in fact multiplication and division are essentially the same operation, as is addition and subtraction. With two small examples, let me explain. 2-1 (two minus one) is mathematically equivalent to 2+(-1) (two plus negative one). 4×2 (four times two) is mathematically equivalent to 4÷½ (four divided by one half). If we have a longer expression for which we will use PEMDAS to simplify, like 4÷½-2+4×2, and we don’t use PEMDAS correctly, then when I rewrite the expression but keep it mathematically equivalent, like 4×2+(-2)+4÷½, you’d get a different solution even though both expressions are mathematically equivalent and give you the same solution if you follow the order of operations correctly.
Ok, that was a lot of boring math stuff and I apologize, so here’s an awesome graphic design I found on shirt.woot! to lighten up this post a little. Enjoy!
You can use the order of operations to read this expression!