Distributive Property

Date: 12/11/97 at 20:04:52
From: Kerry
Subject: Distributive property

What is the distributive property?

Date: 12/11/97 at 20:21:43
From: Doctor Tom
Subject: Re: Distributive property

The distributive property usually means that multiplication (*)
distributes over addition (+). It is stated in the form of the 
following formula:

   a*(b+c) = a*b + a*c,

where a, b, and c can be any numbers.

In other words, you can either add b and c together first and then 
multiply by a, or you can multiply a by b and a by c, and add those 
products, and the result will be the same in either case.

Using numbers, for example:

   5*(7+3) = 5*7 + 5*3

since

    5*(10) = 35 + 15

        50 = 50

In the math you encounter before you go to college, this is exactly 
what the distributive law means, but there's a more general sense in 
that if you invented other operations besides addition and 
multiplication, those operations could distribute over each other.

That may not make sense, but let me give you a concrete example. 
I will show you that division (/) does NOT distribute over addition 
(+).

In other words,

   a/(b+c) is not equal to a/b + a/c.

To check, just plug in some numbers:

   5/(7+3) is not equal to 5/7 + 5/3, since

   5/(7+3) = 5/10 = 1/2,

but 5/7 + 5/3 = 15/21 + 35/21 = 50/21, which is not equal to 1/2.

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