Types of Numbers

Types of Numbers

• Natural Numbers: Positive integers, also known as counting numbers (1, 2, 3, ...)
• Whole Numbers: Non-negative integers, including 0 (0, 1, 2, 3, ...)
• Integers: All whole numbers and their negative counterparts (...,-3, -2, -1, 0, 1, 2, 3, ...)
• Rational Numbers: Numbers that can be expressed as a ratio of two integers (e.g. 3/4, 22/7)
• Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers (e.g. π, e)
• Real Numbers: All rational and irrational numbers
• Complex Numbers: Numbers that include an imaginary component (e.g. 3 + 4i)

Number Operations

• Addition: Combining two or more numbers to get a total or a sum (e.g. 2 + 3 = 5)
• Subtraction: Finding the difference between two numbers (e.g. 5 - 3 = 2)
• Multiplication: Repeated addition of a number (e.g. 2 × 3 = 6)
• Division: Splitting a number into equal parts or groups (e.g. 6 ÷ 2 = 3)

Number Properties

• Commutative Property: The order of numbers does not change the result of an operation (e.g. 2 + 3 = 3 + 2)
• Associative Property: The order in which numbers are grouped does not change the result of an operation (e.g. (2 + 3) + 4 = 2 + (3 + 4))
• Distributive Property: A number can be distributed to multiple addends (e.g. 2 × (3 + 4) = 2 × 3 + 2 × 4)

Types of Numbers

• Natural Numbers are positive integers, starting from 1, also referred to as counting numbers.
• Whole Numbers include 0 and all positive integers, making them non-negative integers.
• Integers encompass all whole numbers and their negative counterparts, including 0.
• Rational Numbers can be expressed as a ratio of two integers, such as 3/4 or 22/7.
• Irrational Numbers cannot be expressed as a ratio of two integers, examples include π and e.
• Real Numbers consist of all rational and irrational numbers.
• Complex Numbers have an imaginary component, such as 3 + 4i.

Number Operations

• Addition involves combining two or more numbers to get a total or a sum, for instance, 2 + 3 = 5.
• Subtraction finds the difference between two numbers, such as 5 - 3 = 2.
• Multiplication is repeated addition of a number, for example, 2 × 3 = 6.
• Division splits a number into equal parts or groups, such as 6 ÷ 2 = 3.

Number Properties

• The Commutative Property states that the order of numbers does not change the result of an operation, shown in 2 + 3 = 3 + 2.
• The Associative Property highlights that the order in which numbers are grouped does not change the result of an operation, demonstrated in (2 + 3) + 4 = 2 + (3 + 4).
• The Distributive Property enables a number to be distributed to multiple addends, seen in 2 × (3 + 4) = 2 × 3 + 2 × 4.