Rational Numbers Properties and Definition

Rational Numbers

Definition

• A rational number is a number that can be expressed as the quotient or fraction of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
• It can also be defined as a finite decimal or a ratio of two integers.

Properties

• Closure: The set of rational numbers is closed under addition, subtraction, multiplication, and division (except by zero).
• Commutativity: The order of rational numbers does not change the result of addition and multiplication.
• Associativity: The order in which rational numbers are added or multiplied does not change the result.
• Distributivity: Multiplication of rational numbers distributes over addition.

Addition

• To add two rational numbers, follow these steps:
  1. Convert both numbers to have the same denominator (if necessary).
  2. Add the numerators.
  3. Keep the same denominator.

Multiplication

• To multiply two rational numbers, follow these steps:
  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Simplify the resulting fraction (if possible).

Subtraction

• To subtract one rational number from another, follow these steps:
  1. Convert both numbers to have the same denominator (if necessary).
  2. Subtract the numerators.
  3. Keep the same denominator.

Rational Numbers

Definition

• A rational number is a number that can be expressed as the quotient or fraction of two integers (p/q), where p and q are integers and q ≠ 0.
• It can also be defined as a finite decimal or a ratio of two integers.

Properties

Arithmetic Operations

• The set of rational numbers is closed under addition, subtraction, multiplication, and division (except by zero).
• The order of rational numbers does not change the result of addition and multiplication (commutativity).
• The order in which rational numbers are added or multiplied does not change the result (associativity).
• Multiplication of rational numbers distributes over addition (distributivity).

Operations with Rational Numbers

Addition

• Convert both numbers to have the same denominator (if necessary).
• Add the numerators.
• Keep the same denominator.

Multiplication

• Multiply the numerators.
• Multiply the denominators.
• Simplify the resulting fraction (if possible).

Subtraction

• Convert both numbers to have the same denominator (if necessary).
• Subtract the numerators.
• Keep the same denominator.

Learn about the definition and properties of rational numbers, including closure and commutativity.