Distributive Property

Date: 10/29/97 at 23:49:03
From: Nicole
Subject: Distributive Property

I am in a ninth grade algebra class, although I am only in the 8th 
grade.  I am really stuck on this Distributive Property thing. I don't 
understand it at all. Can you help me?

Date: 11/04/97 at 15:10:29
From: Doctor Pipe
Subject: Re: Distributive Property

The Distributive Property is one of the basic properties of the real 
numbers. You are wise to keep trying to understand it.

Try this. To distribute something means to hand it out. If you 
distribute a test paper to your class, you give a test to each person 
in the class.

The Distributive Property says that if a, b, and c are real numbers, 
then

     a x (b + c) = (a x b) + (a x c)

Both b and c share a on the left side of the equation; on the right 
side of the equation the a has been distributed to b and c.

Let's take a specific case: 5 x (2 + 3).  The distributive property 
says that this is the same as (5 x 2) + (5 x 3).  When we write:

     5 x (2 + 3) = (5 x 2) + (5 x 3)

we say that we have distributed the five to the two and the three.  
Both sides of the equation are equal so they will work to the same 
answer:

      5 x (2 + 3)             (5 x 2) + (5 x 3)
    = 5 x 5                 = 10 + 15
    = 25                    = 25

Using our example, the Distributive Property says that five times the 
sum of two plus three is equal to the product of five times two plus 
the product of five times three.

Using coins to show this, take twenty-five pennies. First, make five 
stacks of two pennies and five stacks of three pennies. This 
represents the righthand side of the equation above: five times two 
plus five times three (or written mathematically: (5 x 2) + (5 x 3)).  

Now pair each stack of two pennies with a stack of three pennies.  
This represents the left side of the example above: five groups, two 
plus three in each group (or written mathematically: 5 x (2 + 3)).

What a strange world it would be if you could take twenty-five pennies 
and have more or less than 25 based on how you grouped them!

Keep trying - you WILL understand this - and more!  You might even 
have fun ....

-Doctor Pipe,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/