Laws of addition and multiplication

Commutative law of addition:    m + n = n + m . A sum isn’t changed at rearrangement of its addends.

Commutative law of multiplication:    m · n = n · m . A product isn’t changed at rearrangement of its factors.

Associative law of addition:  ( m + n ) + k = m + ( n +  k ) = m + n + k . A sum doesn’t depend on grouping of its addends.

Associative law of multiplication:  ( m · n ) · k = m · ( n ·  k ) = m · n ·  k . A product doesn’t 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).