“What is the order of operations?” PEMDAS, BODMAS

What is the Order of Operations?

It’s basically a system we made up. There isn’t anything wrong with it. But it is just a system for everyone to do things in a standard order. If the system was different, we would simply notate things differently and still be able to do mathematics.

Since there is a standard system, when you see a problem, it’s understood that it should be solved in a certain manner.

BODMAS/PEMDAS

Honestly, I had never seen “BODMAS” before today. But it seems like a valid way to think about the order of operations.

In school I learned PEMDAS. For reference, I was in fifth grade in California in the 1990s.

  1. Parentheses
  2. Exponents
  3. Multiplication & Division
  4. Addition & Subtraction

There are six letters, but I only wrote four numbers with two items on numbers 3 & 4.

The reason for that is that you can think about multiplication and division as essentially being variations of the same operation. Five multiplied by three is the same as five divided by 1/3, etc. And you can either subtract or add a negative number to get the same effect.

Compared to BODMAS

Brackets, Of, Division, Multiplication, Addition, Subtraction

  1. Brackets
  2. Of
  3. Division & Multiplication
  4. Addition & Subtraction

Again, I combined items for #3 and #4, same items.

That acronym includes the word “of” which does come up sometimes. Where it says ‘brackets’, that’s pretty much the same thing as ‘parentheses’ in PEMDAS. There can be a few variations.

Types of Parentheses/Brackets

( )

[ ]

{ }

For either brackets or parentheses, I would pay more attention to their location. You do the inner sets of parentheses first.

And the notation can become easier to follow if you use more than one type of parentheses/brackets.

An Example,

3-3×6+2

Do the multiplication first and then the addition/subtraction.

3 – 18 + 2

Once you only have addition/subtraction, the order does not matter too much.

Personally, I would add the 3 and the 2 first in my head and then subtract 18. It can be done other orders.

5- 18 = -13

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