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HomeHomework HelpmathematicsProperties of Real Numbers

Properties of Real Numbers

The properties of real numbers describe the rules and relationships governing arithmetic operations such as addition, subtraction, multiplication, and division, including identities, inverses, and the commutative, associative, and distributive properties.

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Mathematics
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Overview

Understanding the properties of real numbers is essential for mastering basic mathematics. Real numbers include both rational and irrational numbers, and they follow specific properties that simplify calculations. Key properties such as the Commutative, Associative, and Distributive properties help ...

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Key Terms

Real Numbers
All numbers on the number line, including rational and irrational numbers.

Example: 3, -1.5, √2

Rational Numbers
Numbers that can be expressed as a fraction of two integers.

Example: 1/2, 0.75, -3

Irrational Numbers
Numbers that cannot be expressed as a simple fraction.

Example: π, √2

Commutative Property
The order of numbers does not affect the sum or product.

Example: a + b = b + a

Associative Property
The grouping of numbers does not affect the sum or product.

Example: (a + b) + c = a + (b + c)

Distributive Property
a(b + c) = ab + ac, distributing a across the sum.

Example: 2(3 + 4) = 2*3 + 2*4

Related Topics

Rational and Irrational Numbers
Explore the differences and properties of rational and irrational numbers.
intermediate
Algebraic Expressions
Learn how to manipulate and simplify algebraic expressions using real numbers.
intermediate
Equations and Inequalities
Understand how to solve equations and inequalities involving real numbers.
advanced

Key Concepts

Commutative PropertyAssociative PropertyDistributive PropertyIdentity Property