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Algebra: Properties of Real Numbers


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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
Properties of Real Numbers - Identities and Inverses
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

Properties of Real Numbers - Closure and Density
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.
Commutative and Associative Property for Addition

Associative property for multiplication
Distributive property

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