# Laws of addition and multiplication

*
*

*Commutative laws of addition and multiplication.*

Associative laws of addition and multiplication.

Distributive law of multiplication over addition.

Associative laws of addition and multiplication.

Distributive law of multiplication over addition.

*
Commutative law of addition:
m + n = n + m . A sum isn뭪 changed at rearrangement of its addends.
*

*
Commutative law of multiplication:
m � n = n � m . A product isn뭪 changed at rearrangement of its factors.
*

*
Associative law of addition:
( m + n ) + k = m + ( n + k ) = m + n + k . A sum doesn뭪 depend on grouping of its addends.
*

*
Associative law of multiplication:
( m � n ) � k = m � ( n � k ) = m � n � k . A product doesn뭪 depend on grouping of its factors.
*

*
Distributive law of multiplication over addition:
( m + n ) � k = m � k + n � k . This law expands the rules of operations with brackets (see the previous section).
*