associative property
When you add three numbers, you really add two at a time, so you must choose which pair to combine first. The associative property promises this choice does not affect the result: (a + b) + c = a + (b + c). Whether you group 2 + (3 + 4) or (2 + 3) + 4, you reach 9 either way.
The same holds for multiplication: (a × b) × c = a × (b × c). This is why we can drop the parentheses entirely and write a + b + c or abc without ambiguity — every grouping gives the same answer. It is the property that makes a long chain of additions or products well-defined.
Like commutativity, this property fails for subtraction and division. (10 − 3) − 2 = 5, but 10 − (3 − 2) = 9, so grouping changes a difference. Associativity is strictly about how factors or addends are grouped, and should not be confused with the commutative property, which is about their order.
To compute 25 × 4 × 7, group the easy pair first: (25 × 4) × 7 = 100 × 7 = 700, instead of 25 × (4 × 7) = 25 × 28.
Regrouping a product lets you compute the convenient pair first; the answer is unchanged.
Commutative changes order; associative changes grouping. A handy memory: “associate” suggests gathering into groups, so the associative property is the one about parentheses.