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### What is the Distributive Property?

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Date: 4 Mar 1995 14:54:38 -0500
From: Anonymous
Subject: Math Questions

What is the distributive property?
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Date: 5 Mar 1995 00:42:41 -0500
From: Dr. Ken
Subject: Re: Math Questions

Hello there!

The distributive property is a pretty cool thing.  When we talk about
the distributive property, we always talk about the distributive
property of one thing over another, like of multiplication over addition
or of multiplication over subtraction.  If you know what exponents are,
you can also talk about the distributive property of exponentiation over
multiplication.

Basically, what it says is this:  if we have a number times the sum of
two numbers, we can DISTRIBUTE the first number across the sum and
multiply it by each of the second numbers, and then do the adding.

For instance, if you have 6 x (4 + 3), you can DISTRIBUTE the 6 over to the
4 and the 3, to get 6x4 + 6x3, and you'll get the same answer you would have
gotten if you had done the problem the original way.  To check this case,
compute the first answer: it's 6 x 7, which is 42, and compute the second
answer: it's 24 + 18, which is also 42.  Whew, it worked!

If you've studied some algebra, here's how the distributive property
works out in algebraic symbols: x(y + z) = xy + xz.  It's something that
will come up a whole lot in the future, so you'll want to make sure
you're pretty solid on it.

Thanks for the question!

-Ken "Dr." Math
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Associated Topics:
Middle School Algebra

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