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Laws of addition and multiplication


Commutative laws of addition and multiplication.
Associative laws of addition and multiplication.
Distributive law of multiplication over addition.

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

Commutative law of multiplication:    m ∑ n = n ∑ m . A product isnít changed at rearrangement of its factors.

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

Associative law of multiplication:  ( m ∑ n ) ∑ k = m ∑ ( n ∑  k ) = m ∑ n ∑  k . A product doesnít 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).

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