Real Numbers

These lessons, with videos, examples and solutions, explain what real numbers are and some of their properties.

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The Real Number System
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The following diagram shows real numbers are made up of rational numbers, integers, whole numbers, and irrational numbers. Scroll down the page for more examples and solutions on real numbers and their properties.

Real Numbers

Introduction to Real Numbers
When analyzing data, graphing equations and performing computations, we are most often working with real numbers. Real numbers are the set of all numbers that can be expressed as a decimal or that are on the number line. Real numbers have certain properties and different classifications, including natural, whole, integers, rational and irrational.

This video goes over the basics of the real number system that is mainly used in Algebra. The video covers rational numbers, and irrational numbers.

Properties of Real Numbers
When analyzing data or solving problems with real numbers, it can be helpful to understand the properties of real numbers. These properties of real numbers, including the Associative, Commutative, Multiplicative and Additive Identity, Multiplicative and Additive Inverse, and Distributive Properties, can be used not only in proofs, but in understanding how to manipulate and solve equations.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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