A property of an operation where changing the grouping of operands does not change the result. For addition and multiplication: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).
From Latin 'associatus,' past participle of 'associare' meaning to join or unite. The mathematical usage emerged in the 19th century during the systematic study of algebraic structures, as mathematicians recognized grouping as a fundamental aspect of operations.
The associative property is what makes mental math possible - it allows us to regroup numbers for easier calculation, like computing 25 × 4 × 7 as 25 × 4 × 7 = 100 × 7! This property is so fundamental that it's one of the defining axioms for mathematical structures called groups, which appear throughout modern mathematics and physics.
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