distributive law


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distributive law.

In mathematics, given any two operations, symbolized by * and +, the first operation, *, is distributive over the second, +, if a*(b+c)=(a*b)+(a*c) for all possible choices of a, b, and c. Multiplication, ×, is distributive over addition, +, since for any numbers a, b, and c, a×(b+c)=(a×b)+(a×c). For example, for the numbers 2, 3, and 4, 2×(3+4)=14 and (2×3)+(2×4)=14, meaning that 2×(3+4)=(2×3)+(2×4). Strictly speaking, this law expresses only left distributivity, i.e., a is distributed from the left side of (b+c); the corresponding definition for right distributivity is (a+bc=(a×c)+(b×c).

distributive law

[di′strib·yəd·iv ′lȯ]
(mathematics)
A rule which stipulates how two binary operations on a set shall behave with respect to one another; in particular, if +, ° are two such operations then ° distributes over + means a ° (b + c) = (a ° b) + (a ° c) for all a,b,c in the set.
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In Year 7 according to the Australian Curriculum: Mathematics, students should "apply the associative, commutative and distributive laws to aid mental and written computation" and "extend and apply the laws and properties of arithmetic to algebraic terms and expressions".