Associative Property of Multiplication

The Associative Property of Multiplication states that when multiplying three or more numbers, the way in which the numbers are grouped does not change the product. In other words, if you have numbers \(a\), \(b\), and \(c\), then:

Example

Consider multiplying 2, 3, and 4:

• Grouping the first two numbers: \[ (2 \times 3) \times 4 = 6 \times 4 = 24 \]
• Grouping the last two numbers: \[ 2 \times (3 \times 4) = 2 \times 12 = 24 \]

In both cases, the product is 24, which illustrates the associative property.

Key Points

• Grouping Does Not Matter: You can change the grouping of the factors without affecting the outcome.
• Applies to Multiplication: This property is specific to multiplication (and addition has a similar associative property).
• Universal Validity: The property holds true for all real numbers, and in many other number systems as well.

This property is very useful in simplifying complex multiplication problems and in performing algebraic manipulations.

Latex

(a \times b) \times c = a \times (b \times c)