Operations to Order

You've probably heard the acronym PEMDAS at some point in your academic career. If you haven't taken a math class since the bare minimum to graduate your last level of schooling, you've probably forgotten what it means because who even fucking uses MATH in REAL LIFE, JEEZ. (Everyone btw, you philistine.)

PEMDAS is supposed to be a mnemonic to help you remember order of operations. (If you don't know what a mnemonic is, get out bookmark dictionary.com or something.) When you see an equation, you're supposed to evaluate it in a certain order. PEMDAS is an acronym for that order:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

Why is there a rule for this? Because if we didn't agree on the rules before we started talking about something, nobody would know what the fuck they were doing. Imagine trying to play monopoly with five different sets of house rules and everyone constantly arguing over shit the other players were doing. Eventually somebody robs the bank, the board gets flipped, and the Waterworks are on fire.

To avoid that, you lay out your agreed-upon house rules BEFORE you start playing. Math's the same way. We lay out our rules, and then we work based on them. So, PEMDAS is our rule for turn-order. Here's how it works.

PARENTHESES - first, evaluate whatever is in parentheses, starting with the innermost ones and moving to the outermost if you have multiple sets of parentheses. An operation inside parentheses is commonly referred to as a quantity. (x+2)² is read as x plus 2 quantity squared.

Example:

EXPONENTS - next, whatever exponents are involved.

Example:

or, if there are no parentheses to be done first:

MULTIPLICATION/DIVISION - these are basically the same operation, remember? But if you're not going to the trouble of re-writing all your division as fractions (and why aren't you? It's so much easier that way), multiply first and then divide.

Example:

ADDITION/SUBTRACTION - also basically the same operation and it doesn't even require much rewriting. This comes last, after everything else has been figured out. See above examples for further examples.

Let's do an example that brings everything together.

DON'T TRIP, YOU GUYS. THIS IS GONNA LOOK REALLY FUCKING COMPLICATED.



What.

What did I tell you last time? Start at the top and just keep working until you get something you know how to solve. Math is all about breaking problems down and working in steps.

So let's start with the parentheses and go down through PEMDAS from there.


Click the image for a step-by-step walkthrough
[NOTE: I wrote (7-3)³ here but calculated (7-3)⁴. It's been changed in the equations, but the .jpg still says 3 until I get around to changing it.]

Knowing how to apply PEMDAS is vital as a basis for fucking everything else you will ever do in math.

YOU'RE WELCOME.