Number Systems and Operations

Types of Numbers

• Natural Numbers: Positive integers, starting from 1 (e.g., 1, 2, 3,...).
• Whole Numbers: Non-negative integers, including 0 (e.g., 0, 1, 2, 3,...).
• Integers: Positive and negative whole numbers, including 0 (e.g.,..., -3, -2, -1, 0, 1, 2, 3,...).
• Rational Numbers: Fractions, can be expressed as a/b, where a and b are integers (e.g., 3/4, 22/7).
• Irrational Numbers: Cannot be expressed as a simple fraction, have non-repeating decimal representations (e.g., π, e).
• Real Numbers: Include all rational and irrational numbers, can be represented on the number line.
• Complex Numbers: Include real and imaginary parts, can be expressed as a + bi, where a and b are real numbers and i is the imaginary unit (e.g., 3 + 4i).

Number Operations

• Addition: Combining two or more numbers to get a total or a sum.
• Subtraction: Finding the difference between two numbers.
• Multiplication: Repeating a number a certain number of times to get a product.
• Division: Splitting a number into equal parts or groups.
• Order of Operations: A set of rules to follow when performing multiple operations, often remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

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 numbers, following the rules of multiplication and addition (e.g., 2(3 + 4) = 2 × 3 + 2 × 4).
• Identity Property: A number remains the same when added to or multiplied by a certain value (e.g., 0 is the additive identity, and 1 is the multiplicative identity).