Associative property of multiplication
from class:
College Algebra
Definition
The associative property of multiplication states that the way in which numbers are grouped in a multiplication problem does not change the product. Mathematically, for any real numbers $a$, $b$, and $c$, $(a \cdot b) \cdot c = a \cdot (b \cdot c)$.
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5 Must Know Facts For Your Next Test
- The associative property allows for the regrouping of factors without affecting the product.
- It is valid for all real numbers.
- This property simplifies complex calculations by allowing flexibility in grouping.
- It is different from the commutative property, which involves changing the order of factors.
- Understanding this property helps in factoring and simplifying algebraic expressions.
Review Questions
- What is the associative property of multiplication?
- Does $(2 \cdot 3) \cdot 4$ equal $2 \cdot (3 \cdot 4)$? Explain why or why not.
- How can the associative property be used to simplify $(5 \cdot x) \cdot y$?
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