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Looking for videos, worksheets, and activities to help Algebra students learn about the Properties Of Real Numbers: commutative, associative, distributive, identity, inverse, closure, and density properties.

11 - Introductory Algebra - Properties Of Real Numbers

Lecture on the properties of real numbers

Commutative Property of Addition

a + b = b + a

Commutative Property of Multiplication

a • b = b • a

Associative Property of Addition

a + ( b + c ) = ( a + b ) + c

Associative Property of Multiplication

a • ( b • c ) = ( a • b ) • c

Distributive Property

a • ( b + c ) = a • b + a • c

Additive Identity Property

a + 0 = a

Multiplicative Identity Property

a • 1 = a

Additive Inverse Property

a + ( -a ) = 0

Multiplicative Inverse Property

a • 1/a = 1, where a ≠ 0

Closure Property of Real Numbers

When you add real numbers, the answer is also real.

When you multiply real numbers, the answer is also real.

Density Property of Real Numbers

Between any two real numbers, we can always find another real number.

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