## Using the Distributive Property

### The Distributive Property

The **distributive property** is a characteristic of numbers that involves both addition and multiplication. It is used often in algebra, and we can use it now to obtain exact results for a multiplication.

Suppose we wish to compute . We can proceed in either of two ways, one way which is known to us already (the order of operations), and a new way (the distributive property).

Compute using the order of operations.

Operate inside the parentheses first: .

Now multiply 3 and 7.

Compute using the distributive property.

We know that multiplication describes repeated addition. Thus,

Let's look again at this use of the distributive property.

The 3 has been *distributed* to the 2 and 5.

This is the distributive property. We distribute the *factor* to each *addend* in the parentheses. The distributive property works for both sums and differences.

#### Sample Set A

Using the order of operations, we get

Using the order of operations, we get

Source: Rice University, https://cnx.org/contents/XeVIW7Iw@4.6:Gmai8dss@2/Mental-Arithmetic-Using-the-Distributive-Property

This work is licensed under a Creative Commons Attribution 4.0 License.