Associative property of multiplication

Definition

The associative property of multiplication states that the way numbers are grouped in a multiplication problem does not change the product. Mathematically, for any real numbers $a$, $b$, and $c$, $(a \cdot b) \cdot c = a \cdot (b \cdot c)$.

5 Must Know Facts For Your Next Test

1. The associative property applies to multiplication but not to subtraction or division.
2. It ensures that the product remains constant regardless of how the factors are grouped.
3. This property is essential when simplifying expressions involving multiple multiplications.
4. It is one of the fundamental properties of real numbers and helps in understanding more complex algebraic structures.
5. The associative property can be used in conjunction with other properties like the commutative and distributive properties.

Review Questions

• What is the mathematical expression for the associative property of multiplication?
• Does the associative property apply to operations other than multiplication? Give an example.
• How can you use the associative property to simplify $(2 \cdot 3) \cdot 4$?

Related terms

Commutative Property: States that changing the order of factors does not change their product: $a \cdot b = b \cdot a$.

Distributive Property: States that multiplying a number by a sum is equivalent to multiplying each addend individually and then adding the products: $a(b + c) = ab + ac$.

Identity Property of Multiplication: States that any number multiplied by one remains unchanged: $a \cdot 1 = a$.