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:

$\left(a+b\right)+c=a+\left(b+c\right)$

Example 1:

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

The Associative Law of Multiplication:

$\left(ab\right)c=a\left(bc\right)$

Example 2:

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