**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, …}.

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

A **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.

## Place value

__WN01 __Place_Value** **

__IN10 Basic Operations with Whole Numbers 1__

__IN11 __Basic_Operations with Whole Numbers 2

__WN02 __Round

*WN34 Distributive Property*

*WN35 Word Problems Test*

*WN36 Money Word Problems*

*WN37 Square Root of N*

*WN48 Place Value (Unit)*

*WN49 Place Value (Unit)*

*WN50 Place Value (Write your Number)*

### BS01 Quiz Basic Skills

*Real Numbers (Help)*

*Place Value (Help)*

**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.

Extending vocabulary using the Frayer Model.

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 !