October / November 2015 Newsflash: Tips & Techniques

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 + c) by a, you get same answer as when you multiply each part (b and c) individually by a, and add the results (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 = ____________