When performing operations on real numbers five different properties can be used.
|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.
Real numbers have two important identities (equations that always hold true).
The equalities for real numbers indicates that different operations can be performed on equations and still yield the same equation.
|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.
Real numbers can be written in different ways. For example and The Symmetric Property of Equality then implies that the order does not matter.
Given three real numbers, and the transitive property of equality refers to:
Real numbers are said to be closed under addition and multiplication. That is, adding or multiplying two real numbers results in a real number.