The Distributive Property states that, for all real numbers *x*, *y*,
and *z*,

*x*(*y* + *z*) = *xy* + *xz.*

This very important property is frequently used in word problems.

**Example:**

Rico's MP3 player holds songs of three different genres: grindcore, zydeco, and kuduro. There are 5 times as many grindcore tracks as there are zydeco tracks, and there are 7 times as many kuduro tracks as there are zydeco tracks. Let *x* represent the number of zydeco tracks. Write an expression for the total number of tracks on the MP3 player, and simplify it.

Multiply the number of zydeco tracks by 5 to get the number of grindcore tracks.

5*x*

Multiply the number of zydeco tracks by 7 to get the number of kuduro tracks.

7*x*

Add up the numbers of all the tracks.

*x* + 5*x* + 7*x*

Simplify using the distributive property.

= (1 + 5 + 7)*x*

= 13*x*

So, Rico's MP3 player holds 13*x* tracks.