Commutative and Associative Properties

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Commutative Property of Multiplication: The product of a group of numbers is the same regardless of the order in which the numbers are arranged.

 Commutative Property of Addition: The sum of a group of numbers is the same regardless of the order in which the numbers are arranged

 $a\ +\ b\ =\ b\ +\ a$  

 $a\times b\ =\ b\times\ a$  

 $a\ -\ b\ \ne\ b\ -\ a$  

 $a\ \div\ b\ \ne\ b\ \div\ a$  

Associative Property of Addition: The sum of a set of numbers is the same no matter how the numbers are grouped.

Associative Property of Multiplication: The product of a set of numbers is the same no matter how the numbers are grouped.

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

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

 $\left(a\ \div\ b\right)\ \div\ c\ \ne\ a\ \div\ \left(b\ \div\ c\right)$  

 $\left(a\ -\ b\right)\ -\ c\ \ne\ a\ -\ \left(b\ -\ c\right)$