These lessons, with videos, examples, and solutions, explain the properties of real numbers: Additive Identity Property, Multiplicative Identity Property, Additive Inverse Property, Multiplicative Inverse Property, Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication, Distributive Property.

**Related Pages**

Real Numbers

The Real Number System

More Topics for GMAT

Free Math Worksheets

The following table gives the Properties of Real Numbers. Scroll down the page for more examples and solutions using the properties of real numbers.

**Properties of Real Numbers**

Defines the properties of real numbers and then provides examples of the properties by rewriting and simplifying expressions.These include the distributive property, factoring, the inverse properties, the identity properties, the commutative property, and the associative property.

**Examples:**

Use the properties of real numbers to rewrite and simplify each expression.

State which properties apply.

- 4(7 + 5)
- (3 + 9) + (-9)
- 8 - (11 + 6)
- 3/4 • (7/9 • 4/3)
- 100[0.23 + (-1.78)]

**Introductory Algebra - Properties Of Real Numbers**

Commutative Law of Addition

Commutative Law of Multiplication

Associative Law of Addition

Associative Law of Multiplication

Distributive Law

**Properties of Real Numbers**

Additive Identity Property, Multiplicative Identity Property, Additive Inverse Property, Multiplicative Inverse Property, Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication, Distributive Property, Absolute Value.

**Properties of Real Numbers**

Additive Identity Property, Multiplicative Identity Property, Additive Inverse Property, Multiplicative Inverse Property, Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication, Distributive Property.

**Properties of Real Numbers**

When analyzing data or solving problems with real numbers, it can be helpful to understand the properties of real numbers. These properties of real numbers, including the Associative, Commutative, Multiplicative and Additive Identity, Multiplicative and Additive Inverse, and Distributive Properties, can be used not only in proofs, but in understanding how to manipulate and solve equations.

How to define the properties of real numbers?

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