Editing Distributive property (section)

=== Other examples ===

* [[Ordinal arithmetic#Multiplication|Multiplication]] of [[ordinal number]]s, in contrast, is only left-distributive, not right-distributive.
* The [[cross product]] is left- and right-distributive over [[vector addition]], though not commutative.
* The [[Union (set theory)|union]] of sets is distributive over [[Intersection (set theory)|intersection]], and intersection is distributive over union.
* [[Logical disjunction]] ("or") is distributive over [[logical conjunction]] ("and"), and vice versa.
* For [[real number]]s (and for any [[totally ordered set]]), the [[maximum]] operation is distributive over the [[minimum]] operation, and vice versa: <math display="block">\max(a, \min(b, c)) = \min(\max(a, b), \max(a, c)) \quad \text{ and } \quad \min(a, \max(b, c)) = \max(\min(a, b), \min(a, c)).</math>
* For [[integer]]s, the [[greatest common divisor]] is distributive over the [[least common multiple]], and vice versa: <math display="block">\gcd(a, \operatorname{lcm}(b, c)) = \operatorname{lcm}(\gcd(a, b), \gcd(a, c)) \quad \text{ and } \quad \operatorname{lcm}(a, \gcd(b, c)) = \gcd(\operatorname{lcm}(a, b), \operatorname{lcm}(a, c)).</math>
* For real numbers, addition distributes over the maximum operation, and also over the minimum operation: <math display="block">a + \max(b, c) = \max(a + b, a + c) \quad \text{ and } \quad a + \min(b, c) = \min(a + b, a + c).</math>
* For [[Binomial (polynomial)|binomial]] multiplication, distribution is sometimes referred to as the [[FOIL Method]]<ref>Kim Steward (2011) [http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut28_multpoly.htm Multiplying Polynomials] from Virtual Math Lab at [[West Texas A&M University]]</ref> (First terms <math>a c,</math> Outer <math>a d,</math> Inner <math>b c,</math> and Last <math>b d</math>) such as: <math>(a + b) \cdot (c + d) = a c + a d + b c + b d.</math>
* In all [[semirings]], including the [[complex number]]s, the [[quaternion]]s, [[polynomial]]s, and [[matrix (mathematics)|matrices]],  multiplication distributes over addition: <math>u (v + w) = u v + u w, (u + v)w = u w + v w.</math>
* In all [[Algebra over a field|algebras over a field]], including the [[octonion]]s and other [[non-associative algebra]]s, multiplication distributes over addition.