Distributive Definition
In mathematics, a distributive property is a rule that allows one to perform the same operation on each member of a group of numbers and then add up the results. The distributive property is often used to simplify calculations with large numbers by breaking them down into smaller groups. For example, when multiplying 7 x 12, one could first multiply 7 by 10 to get 70, then multiply 7 by 2 to get 14, and then add these two results together to get 84.
The distributive property can be applied to addition and multiplication, but not subtraction or division. It also only applies to real numbers; it does not work with imaginary numbers or variables. Additionally, the distributive property is not associative, meaning that the order in which the operation is performed matters. For example, 3 x (4 + 5) is different from (3 x 4) + (3 x 5).
The distributive property is a fundamental rule of algebra that is often used without being stated explicitly. It is useful for simplifying equations and performing operations on large numbers. Understanding how and when to use the distributive property can be helpful in solving mathematical problems more efficiently.
