What is the Identity Property of Multiplication?

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There are four properties, or standard rules, that make it easier to perform multiplication problems: commutative, associative, distributive and identity. The identity property is the most straightforward to recognize and use.

Identity Property of Multiplication Definition

This property is also known as the multiplication property of 1. It states that the result of multiplying any real number by 1 is the number itself. In other words, multiplying any number by 1 doesn’t change the number’s value. A tip for remembering this property is that multiplying any number by 1 allows the number to keep its identity.

Theory behind the Multiplication Identity Property

All multiplication operations break down to a series of additions. When you multiply any number by the identity value of 1, it is equivalent to adding the number to 0 once.

General Identity Property of Multiplication Example

1 × a = a × 1 = a

Numeric Identity Property of Multiplication Example

1 × 3 = 3 × 1 = 3

Algebraic Identity Property of Multiplication Example

1(2x) = (2x) × 1 = 2x


Some math textbooks and online references list additional multiplicative properties, including the inverse property and the multiplicative property of zero. However, the identity property is universally agreed upon as a fundamental multiplicative property.