Commutative property of multiplication

Definition

The commutative property of multiplication states that the order in which two numbers are multiplied does not affect 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 only applies to multiplication and addition, not subtraction or division.
2. This property is fundamental in simplifying algebraic expressions and solving equations.
3. It allows for the rearrangement of factors in a multiplication problem without changing the result.
4. An example of this property is $3 \times 5 = 5 \times 3$, both equaling $15$.
5. Understanding this property can help identify errors in algebraic manipulations.

Review Questions

• What does the commutative property of multiplication state?
• Provide an example using numbers that demonstrates the commutative property of multiplication.
• Does the commutative property apply to subtraction? Explain why or why not.

Related terms

Associative Property: A property stating that how numbers are grouped in addition or multiplication does not change their sum or product. For example, $(a + b) + c = a + (b + c)$.

Distributive Property: A property indicating that multiplying a number by a sum is the same as doing each multiplication separately. Mathematically, $a(b + c) = ab + ac$.

Identity Property: A property stating that multiplying any number by one leaves it unchanged: $a \times 1 = a$.