Distributive Property

Date: 10/13/2001 at 08:10:12
From: Susan Kinney
Subject: Distributive property

We are learning the distributive property in school. Why do we have 
to learn this, and how will we use it, and when? 

Susan

Date: 10/13/2001 at 22:47:25
From: Doctor Peterson
Subject: Re: Distributive property

Hi, Susan.

This and similar properties are the foundation of all of algebra. Once 
you get into algebra you will have to be able to rewrite an 
expression, using these properties, to transform it into another 
expression that means the same thing, but is easier to work with in 
some way. By knowing how numbers work, you will know what changes you 
can make.

For example, suppose the letter x stands for some (unknown) number, 
and 2x means twice that number. Then if we know that

    x + 2x = 15

then we know that x is the same as 1x (1 times x), and we can use the 
distributive property to say that

    x + 2x = 1x + 2x = (1+2)x = 3x

So we can rewrite our equation as

    3x = 15

But now it's easy to find what x has to be; the number you can 
multiply by 3 to get 15 is 15 divided by 3, or 5.

The distributive property is really just common sense. My equation 
might mean

  I bought one CD for me and two for my big sister. The total cost was
  $15. I forget how much a CD costs. Can you tell me?

Well, one CD and two CDs is the same as 3 CDs; so 1 times the cost of 
a CD plus 2 times the cost of a CD is 3 times the cost of a CD. What I 
did to the equation is the same thinking without the words. 

Ultimately, algebra means solving problems with less thinking; and 
knowing the properties of numbers and their operations is what lets 
you do algebra.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/