Associative Property

Property For any real numbers $a$, $b$, and $c$, you can change how the numbers are grouped in addition and multiplication: $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$.

Examples Regrouping in addition: $(1 + 2) + 3 = 1 + (2 + 3)$. Regrouping in multiplication: $(3 \cdot 4) \cdot 7 = 3 \cdot (4 \cdot 7)$. Regrouping with variables: $d + (e + f) = (d + e) + f$.

Explanation This is the 'grouping' or 'friendship' property. In a long chain of addition or multiplication, you can change which numbers 'associate' in parentheses first. Regrouping terms helps you find convenient pairs to simplify, turning a complex problem into something much more manageable. The final answer will always be the same, no matter the grouping.