The Associative Laws (or Properties) of Addition and Multiplication

The Associative Laws (or the Associative Properties)

The associative laws state that when you add or multiply any three real numbers , the grouping (or association) of the numbers does not affect the result.

The Associative Law of Addition:

$(a + b) + c = a + (b + c)$

Example 1:

$\begin{array}{l} (2 + 3) + 5 = 5 + 5 = 10 \\ 2 + (3 + 5) = 2 + 8 = 10 \end{array}$

The Associative Law of Multiplication:

$(a b) c = a (b c)$

Example 2:

$\begin{array}{l} (5 \cdot 7) \cdot 6 = 35 \cdot 6 = 210 \\ 5 \cdot (7 \cdot 6) = 5 \cdot 42 = 210 \end{array}$

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