Distributive Property of Multiplication

The distributive property is an important mathematical property that students begin learning during early algebra. This property shows students that the complicated task of multiplying a number by a group of numbers added together can be simplified down to doing each multiplication separately. Use the resources on this page to gain a better understanding of the distributive property and help your child become an expert.

The distributive property is just a fancy name for multiplication with parentheses. Let’s start with a more simple example:

6 × (3 + 4)

Following the order of operations, we would start by adding the two numbers inside the parenthesis before multiplying that product by 6:

6 × (7) = 42

The distributive property states that we can solve this problem a different way since we have a single term being multiplied by a group of two or more terms added together. Looking at the same example from before, the distributive property says that we can remove the parentheses from our problem by multiplying each term on the inside by the term on the outside:

6 × (3 + 4) → 6 × 3 + 6 × 4

If we then follow our order of operations and perform the multiplication first and then the addition, we get the following:

18 + 24 = 42

This answer is the same as the one we found before, but it was achieved using a different method. This property becomes even more helpful in higher level algebra with the introduction of variables. Let’s look at a different example:

2 × (3x + 5)

In this problem, we can’t follow our order of operations because 3x and 5 do not add. Therefore, we have to use our distributive property to simplify the expression:

2 × (3x + 5) → 2 × 3x + 2 × 5 = 6x + 10

The distributive property is an important algebraic property for students to learn since it is so widely used in upper level math. Education.com’s many resources on the subject will have your student mastering the concept of distributive property in no time!