National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Rational Numbers
Math Forum response addressing how many elements are in the set of rational numbers. Responses investigate the countability of sets, and how sets with an infinite number of elements can be counted and compared to other "infinite sets."
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Rational / Irrational Numbers
Math Forum response providing methods to prove that between any two numbers there exist a rational and an irrational number.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Counting Rationals and Integer
Math Forum response providing a proof that there are as many rational numbers as integers.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Definitions of Rational, Irrational
Math Forum definition and explanation of rational and irrational numbers, the definitions of mathematics is also addressed.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Irrational Pi
Math Forum response to the question of why pi is not rational if it is a ratio of circumference to diameter.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: About Rational Numbers
Math Forum response giving a rather thorough overview of rational and irrational numbers, with a brief look at the history of these and other number sets.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Square Roots and Irrational Numbers
Math Forum response to whether square roots of all non-perfect squares are irrational. Contains a proof showing that such cases are, indeed, irrational.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Irrational Numbers; Rational Square Roots
Dr. Math responds to how one can tell whether a number is rational or irrational. A proof is discussed in the response.
University of Toronto (Canada)
University of Toronto: Rational Numbers
This site from the University of Toronto provides a look at rational numbers and properties of the rational number system.
Other
The Prime Glossary: Rational Numbers
This site gives a definition of what a rational number is. Gives examples and formulas. Very helpful.
Other
Interactive Real Analysis: Natural Numbers, Integers, Rationals
A rigorous definition of natural numbers, integers, and rationals numbers, using advanced mathematics language. Contains links to proofs.
Sophia Learning
Sophia: Multiplying Rationals: Lesson 2
This lesson demonstrates how to multiply rational numbers using algebraic notation. It is 2 of 6 in the series titled "Multiplying Rationals."
Sophia Learning
Sophia: Representing Rational Numbers Using Variables: Lesson 2
This lesson demonstrates how to represent rational numbers using variables. It is 2 of 9 in the series titled "Representing Rational Numbers Using Variables."
Sophia Learning
Sophia: Simplifying Rational Expressions: Lesson 2
This lesson demonstrates how to simplify rational expressions. It is 2 of 6 in the series titled "Simplifying Rational Expressions."
Sophia Learning
Sophia: Simplifying Rational Expressions: Lesson 6
This lesson demonstrates how to simplify rational expressions. It is 6 of 6 in the series titled "Simplifying Rational Expressions."
ClassFlow
Class Flow: Squares and Square Roots
[Free Registration/Login Required] Students complete multi-step computations using order of operations in situations involving combinations of rational numbers including whole number exponents and square roots of square numbers.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Why Repeating Decimals Are Rational?
Math Forum response to why all repeating decimals are rational numbers, including examples and concise explanations.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Zero as Denominator
Math Forum response which explains why zero can not be the denominator of any rational number.
Purple Math
Purplemath: Number Types
This site explores the different types of numbers: natural numbers, whole numbers, integers, and rational and irrational numbers. Content includes some practice questions.
Tech Target
Rational Number: A Whatis Definition
A very good and in-depth explanation of what a rational number is.
Math Open Reference
Math Open Reference: Irrational Number
Learn about irrational numbers with this easy reference guide. Provides a detailed definition and examples that enhance further explanation. Provides links to related topics.
University of Utah
University of Utah: The Number System
This site from The University of Utah provides a definition of commonly used numbers including rational numbers, natural numbers, integers, real and complex numbers and more.
Wikimedia
Wikipedia: Rational Numbers
Learn the definition of rational numbers. You can also look at some examples and properties, plus learn about Egyptian fractions. Links are provided for additional information.