# Whole Numbers

Natural numbers are the counting numbers {1, 2, 3, …} (the non-negative integers)

A whole number is a number that is not a fraction or a decimal. The whole numbers include all the natural numbers and Zero.

Integers are the natural numbers and their negatives {… −3, −2, −1, 0, 1, 2, 3, …}.

positive number is a number that is bigger than zero.  In business, positive numbers were used to represent assets.

negative number is a real number that is less than zero. Such numbers are often used to represent a value that is a deficit.

Negative numbers have many applications in business and personal finance. Example: How can we have less than nothing? When we’re in debt.

Two numbers that have the same magnitude but are opposite in signs are called Opposite Numbers. Example: +5 and -5 are Opposite Numbers

The absolute value (or modulus) |a| of an integer a is the numerical value of a without regard to its sign.  Example:  |-5| = 5

Now we will consider the four basic operations with whole numbers: addition, subtraction, multiplication, and division.

## The number system

The number system is the system of representing numbers.

Natural Numbers (N).  [The numbers that occurs commonly in nature]. They are the numbers {1, 2, 3, 4, 5, …}

Whole Numbers (W). This is the set of natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.

Integers (Z). This is the set of all whole numbers plus all the negatives (or opposites) of the natural numbers, i.e., {… , -2, -1, 0, 1, 2, …}

Rational numbers (Q). This is the set of all the fractions, where the top and bottom numbers are integers; e.g., ¼, ½, ¾,… [Note: The denominator cannot be zero].

Real numbers (R). This set includes all numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5, 2.5, etc. It also includes all the irrational numbers such as π, e, √2,  etc. Every real number corresponds to a point on the number line.

When you count backwards from zero, you go into negative numbers. Negative numbers are used to represent the magnitude of a loss or deficiency, example: “ a bank records deposits as positive numbers and withdrawals as negative numbers”.

The Irrational Numbers are real numbers that cannot be written as a simple fraction. Irrational numbers have decimal expansions that neither terminate nor become periodic.  Examples  (π = 3.1415926535897932384626433832795…),  e, also known as Euler’s number  (e=2.718281828459045235360…),  the Square Root of 2, written as √2,  (√2 = 1.41421356237…), etc.

Real Number Voc

Extending vocabulary using the Frayer Model.

Frayer Template

Create a graphic organizer (Frayer Model) for the following vocabulary words:  integer number, absolute value, opposite, rational number.

(keep a copy in your notebook)

Your ability to understand math problems can be improved with math journal writing. Be sure to include all the relevant information.   Remember- Show your work and answers in Your Math Journal   !