The distributive property is the ability of multiplication to "distribute" over another operation inside parenthesis. Multiplication distributes over addition or subtraction, such that x(a+b) = xa + xb.
This means we can distribute the factor outside the set of parenthesis to each item inside, and then add the results.
Example: 5(2+3) is equivalent to 5*2 + 5*3 because the multiplication by five was distributed across the addition inside the parenthesis.
Division is not distributive over addition or subtraction
Example: 10/(5-3)`!=` `10/5-10/3`
The Distributive Property can be used in arithmetic to make multiplication easier, breaking up one of the numbers and multiplying two parts separately and then add the products.
In Algebra, the Distributive Property helps you simplify expressions with parenthesis.
Example: a(b+c) = ab+ac