The order of operations

Facebook and linkedin are littered with seemingly simple puzzles


For some reason these tend to draw masses of comments and create pretty sizable arguments.  This is largely as many people are not aware (or overlook) the concept of the order of operations.

Whilst the video on the order of operations explains it quite well I will break it down below:

What is the order of operations?

Well it’s purely a set of rules to follow when calculating an equation.

Rather than simply reading from left to right as you would with this article, mathematical equations should be read (and deciphered) using these principles.  The principles state the order by which to complete an equation.

In brief you give priority and start by doing things enclosed in brackets (or parenthesis for the US kids) basically this stuff (   ).

Next you complete any what are called indices or exponents; so stuff like to the “power of”, roots, squares etc.  This will make sense in the examples below, but anything really in superscript we call at face value treat as an exponent.

Then it gets a bit tricky, because most of the laws state multiplication prior to division, well not 100% accurate; basically consider those two functions at the same time.  It’s not that the multiplication needs to be done prior to the divisions- this is inaccurate.  It should be multiplication and division or if you want division and multiplication.

Then addition and subtraction, again like the multiplication and division argument, the rule does not state addition prior to subtraction.  These again should be considered as being equal, so you can say subtraction and addition or vice versa- the end point is the same

Commonly acronyms are used to encapsulate these rules, and for many make them easier to remember.


  • Brackets
  • Indices
  • Multiplication
  • Division
  • Addition
  • Subtraction

PEMDAS- same stuff- but more adopted in the US

  • Parenthesis
  • Exponents
  • Multiplication
  • Division
  • Subtraction

Whilst both of these have Multiplication coming before Division and Addition coming before Subtraction, remember that doesn’t matter- it’s just to make the acronym sound cool rather than adding functionality.


Limitations of the order of operations

I’m not going to say it’s totally faultless, as arguably if an equation is considered as a question; the method by the the question is framed may require a result different than that provided through the use of the rules.

I’ll go through some of these when I get a sec, but feel free to add in the comments below.

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