Fundamentals of Compensation Quantitative Methods

BASIC MATHEMATICAL OPERATIONS

First, we'll begin with a review of the four basic mathematical operations: addition, subtraction, multiplication, and division. These sections are meant to serve as a refresher for those who haven't taken a math class since high school! More advanced concepts and techniques will follow.

Addition

Addition is a process that combines values.

The simplest mathematical computation is addition. Addition combines numbers to make a total called the sum. This operation is usually indicated by the "+" sign.

Of all computations, addition, together with its inverse, subtraction, is the source of most computation errors.

For years, the IRS has listed addition and subtraction mistakes as the lead

Addition can have the following properties:

Commutative: When two numbers are added, the sum is the same regardless of the order of the numbers being added.

Example: 1 + 2 = 2 + 1 = 3

Associative: When more than two numbers are added, the sum is the same regardless of the order of the numbers being added.

Example: 1 + 2 + 3 = 1 + 3 + 2 = 2 + 1 + 3 = 2 + 3 + 1 = 3 + 1 + 2 = 3 + 2 + 1 = 6

Additive identity: The sum of any number and zero is the number.

Example: 2 + 0 = 2

Distributive property: The sum of two numbers times a third number is the sum of the first number times the third number and the second number times the third number.

Example: (2 + 3)4 = (2 x 4) + (3 x 4) = 20

Order of operation

The operations of multiplication and division are performed FIRST in most mathematical and statistical equations unless parentheses indicate a sub-operation to be performed first or exponents or square roots need to be calculated (after any sub-operations in parentheses). In general, the order of operations uses the following rules:

1. First do all operations that fall inside parentheses.
2. Then complete any work with exponents or square roots.
3. Then do operations of multiplication and division (working from left to right).
4. Finally do operations of addition and subtraction (working from left to right).

Example of the order of operations

6 x 2² + 3 x (5 + 1) =
6 x 2² + 3 x 6
6 x 4 + 3 x 6 =
24 + 18 = 42