# 3rd Grade Homework – The Distributive Property

February 21st, 2016 by Math Tricks | Filed under 3rd Grade Homework.

My son came home from school recently with some 3rd grade math homework that he was having trouble with.  The homework assignment involved the Distributive Property, which for many of us has been long forgotten about.  Anyways, the homework assignment perked my interest because it showed students how the Distributive Property can be used to make difficult multiplication problems very easy.

First, to refresh your memory, the Distributive Property is an algebraic property that describes how a multiplication problem such as A(B + C) can be solved.   Simply, the number outside of the parentheses must be distributed across the numbers within the parentheses:

A(B + C) = AB + AC

Does this look familiar?  I hope so.  So, how does this help us to solve tough multiplication problems?  Let me give you an example:

8(3 + 5)

Of course you can just add 3 to 5 and get the answer 64 very quickly if you know your multiplication tables.  Now, by using the Distributive Property:

8(3 + 5) = 24 + 40 = 64

So, we got the same (correct) answer using the Distributive Property.  So how can we use this property to solve difficult multiplication problem?  Well, if you use the method illustrated above in reverse, you can!  Here is an example:

8 x 13

Well, not very difficult, but a good example on how to apply the technique.  First, we can break down the “13” portion of the problem to “10 + 3”:

8 x (10 + 3)

By the Distributive Property:

8 x (10 + 3) = (8 x 10) + (8 x 3)

So the problem now becomes WAY more easier than 8 x 13:

(8 x 10) + (8 x 3) = 80 + 24 = 104

So, how about a herder problem?  Let’s try 7 x 1066.  Here, we will break up 1066 into more than two parts:

7 x 1066 = 7(1000 + 10 + 50 + 5 + 1) = (7000 +70 + 350 + 35 + 7)

This is a rather simple addition problem that you can solve with pen and paper, or even do in your head, with the answer being 7462.  Cool!!

4 x 528

9 x 156

8 x 252

11 x 1287