Commutative property of multiplication

Definition

The commutative property of multiplication states that changing the order of the factors does not change the product. Mathematically, for any real numbers $a$ and $b$, $a \times b = b \times a$.

5 Must Know Facts For Your Next Test

1. The commutative property holds for all real numbers.
2. This property is fundamental in simplifying algebraic expressions.
3. It is one of the basic properties of multiplication along with associative, distributive, and identity properties.
4. The property can be visualized using arrays or geometric representations such as area models.
5. It is crucial for rearranging terms when solving equations.

Review Questions

• Does the commutative property apply to subtraction? Explain why or why not.
• If $3 \times x = x \times 3$, what algebraic principle does this illustrate?
• Provide an example showing the commutative property of multiplication using negative numbers.

Related terms

Associative Property: States that the way in which factors are grouped in multiplication does not change the product: $(a \times b) \times c = a \times (b \times c)$.

Distributive Property: States that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products: $a(b + c) = ab + ac$.

Identity Property of Multiplication: $1$ is the multiplicative identity because any number multiplied by $1$ remains unchanged: $a \times 1 = a$.