**Mental Math: The Distributive Property Meets Wholes and Parts**

Whether you’re working on arithmetic or algebra, a strong understanding of the **distributive property** is a valuable tool to have in your mental math toolkit. Here’s our favorite way to look at this.

The distributive property says:

** a**(

**+**

*b***) =**

*c***+**

*ab*

*ac*In plain English, this says that when you multiply the *whole* (** b** +

**) by**

*c***, you get same answer as when you multiply each**

*a**part*(

**and**

*b***) individually by**

*c***, and add the results (**

*a***+**

*ab***).**

*ac*

Here are some examples of this in action:

**1.** *Find the total value of 5 pennies and 5 dimes.*

If we look at this problem in terms of the distributive property:

5(1¢ + 10¢) = (5 x 1¢) + (5 x 10¢)

You can either:

- Add 1¢ + 10¢ (i.e. add the value of each
*part*to make a*whole*) and multiply by 5: 11¢ x 5 =**55¢**_{. (The left–hand side)}

… Or:

- Find the value of each “
*part*” by multiplying 5 x 1¢ and 5 x 10¢. Add the answers: 5¢ + 50¢ =**55¢**._{(The right–hand side)}

*Try this*: Find the total value of 6 nickels and 6 dimes.

**2. ***Solve: 4 x 26*

4(26) = (4 x 25) + (4 x 1)

You can either*:*

- Think of 26 (the
*whole*), four times_{. (The left–hand side)}

… Or:

- Break “26” into
*parts*by thinking of it as “25 + 1”. Multiply each part by 4 (“4 x 25” and “4 x 1”), and add the answers: 100 + 4 =**104**_{. (The right–hand side)}

*Try this*: 4 x 2 ½ = ____________