Commutative property of multiplication

The commutative property of multiplication states that changing the order of the factors does not affect the product. In other words, if $a$ and $b$ are any two numbers, then:

a \times b = b \times a

For example, $3 \times 4 = 4 \times 3$ , both yielding the result of 12. This property highlights that multiplication is flexible in terms of the sequence in which numbers are multiplied.

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.

Here are the key points to learn about the commutative property of multiplication:

Definition: The commutative property of multiplication states that changing the order of the factors does not change the product.
Mathematical Expression: If $a$ and $b$ are any numbers, then $a \times b = b \times a$ .
Examples:
- $2 \times 3 = 3 \times 2 = 6$
- $5 \times 7 = 7 \times 5 = 35$
Applications: This property allows for flexibility in computations, making it easier to rearrange factors for mental math or simplification.
Visual Representation: Can be illustrated using area models or arrays, showing that the arrangement of rows and columns does not affect the total area (product).
Relation to Other Properties: It is one of the foundational properties of multiplication, along with the associative property and distributive property.
Real-World Relevance: Useful in everyday situations such as budgeting, calculating areas, and other tasks that involve multiplication.

Understanding these points will help grasp the commutative property of multiplication and its importance in mathematics.

Commutative property of multiplication

Part 1: Commutative property of multiplication

Related topics

Multiplication as equal groups

Multiplication on the number line

Multiplication as groups of objects

Multiplication with arrays

Multiplication in contexts