DISTRIBUTIVITY Meaning and
Definition
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Distributivity is a mathematical property that describes how operations distribute over each other in a given mathematical system. It refers to the ability of operations to be applied to a group of numbers or variables together and then distributed individually to each element within the group.
In arithmetic and algebra, distributivity is often associated with the distributive property. This property states that when a certain operation, such as multiplication, is performed on two numbers or variables within parentheses, it can be distributed over the terms within the parentheses. For example, in the equation a(b + c) = ab + ac, the multiplication is distributed over the addition, resulting in the product of a and the sum of b and c being equal to the sum of the products of a and b, and a and c.
Distributivity can also apply to other operations, such as addition and subtraction. In these cases, the operation is distributed over a group of numbers or variables, resulting in the sum or difference being applied to each element individually.
The distributive property is a fundamental property in mathematics and plays a crucial role in simplifying algebraic expressions, solving equations, and performing calculations efficiently. Understanding the principles of distributivity allows mathematicians and students to manipulate expressions and equations, making computations more manageable and understandable.
Etymology of DISTRIBUTIVITY
The term "distributivity" is derived from the noun "distribution", which comes from the Latin word "distributio", meaning "distribution". It, in turn, is derived from the verb "distribuere", which combines "dis-" (meaning "apart" or "away") with "tribuere" (meaning "to assign" or "to allocate"). Therefore, "distributivity" refers to the property or concept of distributing or allocating something, particularly in mathematics where it describes the property of an operation over a set of elements or expressions.
