# 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:

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