The Big Four (Operations, that is)

I think we all know what the Big Four are...Deloitte, PricewaterhouseCoopers, Ernst & Young, and KPMG. Just kidding!

The Big Four that I am referring to are addition, subtraction, multiplication, and division.

We know that there are two pairs of inverse operations; addition can be undone by subtraction and multiplication can be undone by division.

However, both addition and multiplication also contain commutative properties:

With the commutative property of addition, you can change the order of the numbers in an addition problem without changing the result:

6 + 5 = 11                5 + 6 = 11

With the commutative property of multiplication, you can change the order of the numbers in a multiplication problem without changing the result:

6 * 5 = 30               5 * 6 = 30

Note that subtraction and division do NOT have commutative properties:

6 - 5 = 1                 5 - 6 = - 1
6 / 5 = 1.2              5 / 6 = 0.8333

However, when you throw parentheses into the mix, the result that you achieve can vary, especially in a problem with mixed operations. This is not the case in the following instances:

With the associative property of addition, if every operation is addition, numbers can be grouped in any order and any pair can be added first. Moving parentheses does not change the answer.

1 + (2 + 3) = 1 + 5 = 6                 (1+2) + 3 = 3 + 3 = 6

In the associative property of multiplication, if every operation is multiplication, numbers can be grouped in any order and any pair can be added first. Moving parentheses does not change the answer.

1 * (2 * 3) = 1 * 6 = 6                  (1 * 2) * 3 = 2 * 3 = 6


And, of course, always keep in mind that addition can be undone by subtraction and multiplication can be undone by division. Think of what I just mentioned as the ying and yang of math, or as debits and credits for you accountants out there.