Commutative property of multiplication

The Commutative Property of Multiplication states that changing the order of the factors in a multiplication operation does not change the product. In other words, if $a$ and $b$ are any two numbers, then:

a \times b = b \times a

For example, $3 \times 4 = 4 \times 3 = 12$ . This property is fundamental in arithmetic and underlies many mathematical concepts and operations.

In this article

Part 1: Commutative property of multiplication

Sal explores what happens when we multiply numbers in different orders, for example 3x5 and 5x3.

Key Points of the Commutative Property of Multiplication:

Definition: The commutative property of multiplication states that changing the order of the factors does not change the product. In mathematical terms, $a \times b = b \times a$ .
Examples:
- $3 \times 5 = 15$ and $5 \times 3 = 15$
- $7 \times 2 = 14$ and $2 \times 7 = 14$
Visual Representation: Illustrate the property with arrays and grouping to show that rearranging factors leads to the same total.
Application: This property simplifies multiplication calculations and helps in mental math by allowing for rearrangement of numbers to make calculations easier.
Relation to Other Properties: The commutative property applies to addition as well, emphasizing a broader principle in arithmetic operations.
Importance in Algebra: Understanding this property is foundational for solving equations and manipulating expressions in algebra.

By grasping these key points, students can effectively utilize the commutative property in various mathematical contexts.

Commutative property of multiplication

Part 1: Commutative property of multiplication

Key Points of the Commutative Property of Multiplication:

Related topics

Multiplication as equal groups

Multiplication on the number line

Multiply using groups of objects

Multiplication with arrays