Introduction to Numbers

Mathematical object used to count, label, and measure.

In this unit, we will delve into the world of numbers. Numbers are the fundamental building blocks of mathematics, and understanding them is crucial for mastering more complex mathematical concepts. We will explore different types of numbers and learn how to perform basic operations with them.

Classification of Numbers

Numbers can be classified into several types, each with its own properties and uses. Here are the main types of numbers we will be discussing:

• Natural Numbers: These are the counting numbers that we use in everyday life. They start from 1 and go on indefinitely (1, 2, 3, 4, 5, ...).

• Whole Numbers: These are similar to natural numbers, but they also include 0. So, the set of whole numbers starts from 0 and goes on indefinitely (0, 1, 2, 3, 4, 5, ...).

• Integers: These include all natural numbers, their negatives, and zero (-3, -2, -1, 0, 1, 2, 3, ...).

• Rational Numbers: These are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. This includes all integers, as they can be expressed as a fraction with 1 as the denominator.

• Irrational Numbers: These are numbers that cannot be expressed as a fraction. They are non-repeating, non-terminating decimals. An example is the number pi (π).

Understanding Prime and Composite Numbers

• Prime Numbers: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, and 13.

• Composite Numbers: A composite number is a natural number that has positive divisors other than 1 and itself. In other words, it can be formed by multiplying two smaller natural numbers. Examples include 4, 6, 8, 9, 10, and 12.

Introduction to Factors and Multiples

• Factors: A factor of a number is an integer that divides the number without leaving a remainder. For example, the factors of 6 are 1, 2, 3, and 6.

• Multiples: A multiple of a number is the product of that number and an integer. For example, the multiples of 5 are 5, 10, 15, 20, and so on.

Basic Operations with Different Types of Numbers

We will also cover how to perform basic operations (addition, subtraction, multiplication, and division) with different types of numbers. This includes understanding how to add, subtract, multiply, and divide integers, rational numbers, and irrational numbers.

By the end of this unit, you should have a solid understanding of the different types of numbers and how to work with them. This knowledge will be crucial as we move on to more complex mathematical concepts in the following units.