**Visualizing Number
Relationships****
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**Math
Models Home Page**

**Distributive
Property**
**The basic operations have some
properties that are interesting:**

**Their names are sort of
intimidating, but they really are quite simple if we use models to
understand just what they mean.**

**The Distributive Property
of Multiplication Over Addition**
**The distributive property means
that we can break up one factor of a multiplication problem into its
addends, multiply them by the other factor, and then add the products
together to get the whole answer. let's take a look at an example to
show what this means.**

**Suppose we consider the multiplication problem
5 x 12:**

**The idea is to make the problem easier to solve
in our heads, with numbers that are easier to use. We could just as
easily have done it this way:**

**This model can work for harder problems, and in
fact models another important cousin of the distributive property -
partial products. Let's see how it would look for 23 x
35:**

**In the above example, 600, 90, 100 and 15 are
the partial products of the 23 x 35 multiplication problem. The
partial products add up to the total product.**

**The Distributive Property
of Multiplication Over Subtraction**
**This same model can be used to ease mental
computation by using the idea of subtraction, too. Here's a simple
example for 12 x 19:**

**These properties seem almost self-evident, but
that does not lessen their fundamental importance. They are basic to
mental computation strategies and most useful in algebraic
computation. We will see examples of these in future
lessons.**