Numbers are a fundamental concept in mathematics. They are used to quantify, count, measure, and perform calculations. In this lesson, we will explore different types of numbers, their properties, and their uses in mathematical operations.

## Types of Numbers

There are different types of numbers in mathematics. Here are the most common ones:

Natural Numbers – Natural numbers are positive integers that are used to count objects. They are denoted by the symbol “N” and include numbers like 1, 2, 3, 4, 5, and so on.

Whole Numbers – Whole numbers are the same as natural numbers, except they also include zero. They are denoted by the symbol “W” and include numbers like 0, 1, 2, 3, 4, 5, and so on.

Integers – Integers are numbers that include both positive and negative numbers, as well as zero. They are denoted by the symbol “Z” and include numbers like -3, -2, -1, 0, 1, 2, 3, and so on.

Rational Numbers – Rational numbers are numbers that can be expressed as a ratio of two integers. They include fractions, decimals, and percentages. Rational numbers are denoted by the symbol “Q.”

Irrational Numbers – Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They include numbers like pi (π) and the square root of 2 (√2). Irrational numbers are denoted by the symbol “I.”

## Properties of Numbers

Numbers have different properties that allow us to perform calculations and manipulate them in various ways. Here are some of the most important properties of numbers:

Commutative Property – The commutative property states that the order in which we add or multiply numbers does not affect the result. For example, 2 + 3 = 3 + 2 and 2 × 3 = 3 × 2.

Associative Property – The associative property states that the grouping of numbers when we add or multiply them does not affect the result. For example, (2 + 3) + 4 = 2 + (3 + 4) and (2 × 3) × 4 = 2 × (3 × 4).

Distributive Property – The distributive property states that when we multiply a number by a sum, we can distribute the multiplication over each term in the sum. For example, 2 × (3 + 4) = 2 × 3 + 2 × 4.

Identity Property – The identity property states that when we add or multiply a number by 1, the result is that same number. For example, 3 + 1 = 3 and 3 × 1 = 3.

## Uses of Numbers

Numbers are used in various mathematical operations like addition, subtraction, multiplication, division, and more. They are also used in geometry, trigonometry, algebra, and calculus. Numbers are important in science, finance, and many other fields.

Numbers are an essential part of mathematics. Understanding the different types of numbers, their properties, and their uses can help you perform calculations and solve problems more efficiently.

Remember to always use the correct type of number in your calculations and to apply the correct properties of numbers to manipulate them.