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.

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## 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

## Considerations

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.