Whole Numbers: Properties and Operations

Whole Numbers

Definition

• A whole number is a positive integer, including 0, without fractions or decimals.

Properties

• Closure: The result of adding or multiplying two whole numbers is always a whole number.
• Commutative Property: The order of whole numbers being added or multiplied does not change the result.
• Associative Property: The order in which whole numbers are added or multiplied does not change the result.
• Distributive Property: The multiplication of a whole number over the addition of two whole numbers is equal to the sum of the multiplications.

Operations

• Addition: The result of combining two or more whole numbers.
• Subtraction: Finding the difference between two whole numbers.
• Multiplication: Repeated addition of a whole number.
• Division: Repeated subtraction of a whole number.

Exponents

Definition

• An exponent is a small number that indicates the power to which a base number should be raised.

Rules of Exponents

• Product of Powers: a^m × a^n = a^(m+n)
• Power of a Product: (ab)^m = a^m × b^m
• Power of a Power: (a^m)^n = a^(mn)
• Zero Exponent: a^0 = 1 (except for 0^0, which is undefined)
• Negative Exponent: a^(-m) = 1/a^m

Applications

• Simplifying Expressions: Using the rules of exponents to simplify expressions with exponents.
• Solving Equations: Using exponents to solve equations involving exponential functions.

Note: These notes provide a concise overview of whole numbers and exponents. For a more comprehensive understanding, it is recommended to practice problems and explore additional resources.

Whole Numbers

• A whole number is a positive integer, including 0, without fractions or decimals.
• Closure property: The result of adding or multiplying two whole numbers is always a whole number.
• Commutative property: The order of whole numbers being added or multiplied does not change the result.
• Associative property: The order in which whole numbers are added or multiplied does not change the result.
• Distributive property: Multiplication of a whole number over the addition of two whole numbers is equal to the sum of the multiplications.

Operations on Whole Numbers

• Addition: Combining two or more whole numbers.
• Subtraction: Finding the difference between two whole numbers.
• Multiplication: Repeated addition of a whole number.
• Division: Repeated subtraction of a whole number.

Exponents

• An exponent is a small number that indicates the power to which a base number should be raised.
• Product of powers: a^m × a^n = a^(m+n).
• Power of a product: (ab)^m = a^m × b^m.
• Power of a power: (a^m)^n = a^(mn).
• Zero exponent: a^0 = 1 (except for 0^0, which is undefined).
• Negative exponent: a^(-m) = 1/a^m.

Applications of Exponents

• Simplifying expressions: Using the rules of exponents to simplify expressions with exponents.
• Solving equations: Using exponents to solve equations involving exponential functions.

Learn about the definition and properties of whole numbers, including closure, commutative, associative, and distributive properties.