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2.6: Multiplication of Rational Numbers

Difficulty Level: Basic Created by: CK-12
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Multiplication Property of –1

For any real number a, (-1) \times a = -a.

multiplicative identity property

The product of any number and one is the number itself.

Zero Property of Multiplication

For any real number a, \ (0) \times a = 0.

Associative Property

The associative property states that you can change the groupings of numbers being added or multiplied without changing the sum. For example: (2+3) + 4 = 2 + (3+4), and (2 X 3) X 4 = 2 X (3 X 4).

Commutative Property

The commutative property states that the order in which two numbers are added or multiplied does not affect the sum or product. For example a+b=b+a \text{ and\,} (a)(b)=(b)(a).

distributive property

The distributive property states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum. For example, a(b + c) = ab + ac.


The integers consist of all natural numbers, their opposites, and zero. Integers are numbers in the list ..., -3, -2, -1, 0, 1, 2, 3...

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as 4\frac{3}{5}.

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