October / November 2015 Newsflash: Tips & Techniques

Oct 13, 2015

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 = ____________

 

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