Rational Numbers

Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to 0.

Key Concepts

• Definition: A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q is not equal to 0.
• Examples: Examples of rational numbers include 1/2, 3/4, 5, -7, etc.
• Non-examples: Non-examples of rational numbers include irrational numbers such as √2, π, etc.
• Properties: Rational numbers can be added, subtracted, multiplied, and divided.

Operations with Rational Numbers

When performing operations with rational numbers, it is important to follow the rules for addition, subtraction, multiplication, and division of fractions. Here are the key operations:

• Addition: To add two rational numbers, find a common denominator and then add the numerators.
• Subtraction: To subtract two rational numbers, find a common denominator and then subtract the numerators.
• Multiplication: To multiply two rational numbers, simply multiply the numerators and denominators separately.
• Division: To divide two rational numbers, multiply the first number by the reciprocal of the second number.

Equivalent Rational Numbers

Rational numbers can be equivalent if they represent the same value. This occurs when two fractions have the same value, but are written in different forms. To determine if two rational numbers are equivalent, simplify each fraction and compare the results.

Study Tips

When studying rational numbers, it's important to practice operations with fractions, understand the concept of equivalent fractions, and be comfortable with converting between fractions and decimals.

Summary

Rational numbers are an essential part of mathematics and are used in many real-world applications. Understanding how to work with rational numbers is crucial for success in various mathematical topics.