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Properties of Real Numbers

Rule

Properties of Real Numbers

Real numbers have certain properties when it comes to operations, identities, and equalities.

Rule

Operations

When performing operations on real numbers five different properties can be used.

Name Property
Distributive Property
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication

These properties can be used when solving equations or simplifying expressions to easier find the correct solution.

Rule

Identities

Real numbers have two important identities (equations that always hold true).

Additive Identity
Multiplicative Identity
Rule

Equalities

The equalities for real numbers indicates that different operations can be performed on equations and still yield the same equation.

Name Property
Addition Property of Equality If then
Subtraction Property of Equality  If then
Multiplication Property of Equality If then
Division Property of Equality If then

Finally, there are two special equalities; Symmetric Property of Equality and Transitive Property of Equality.

Rule

Symmetric Property of Equality

Real numbers can be written in different ways. For example and The Symmetric Property of Equality then implies that the order does not matter.

Rule

Transitive Property of Equality

Given three real numbers, and the transitive property of equality refers to:

If  and then
Rule

Closure Properties

Real numbers are said to be closed under addition and multiplication. That is, adding or multiplying two real numbers results in a real number.