Number Systems and Operations

Study Notes

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).

Description

Learn about different types of numbers, including natural, whole, integers, rational, irrational, real and complex numbers. Understand number operations such as addition, subtraction, multiplication, and division, as well as number properties like commutative, associative and distributive properties.