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Distributing Values

You know about addition and you know about multiplication. When those two operations combine, you get a third law that is very useful. The Distributive Law combines both functions. You'll use this law all of the time in Algebra. Here's an example...

3 * (4 + 5) = ?
• Using the law we can do this...
(3 * 4) + (3 * 5) = ?

Did you see that? All of the terms split apart! The 3 from the multiplication part of the problem was distributed to each of the addends. Think of it this way: you wind up with the same answer if you multiply a sum by a number or if you multiply each of the addends separately and then add the products together. Here's the example worked out...

3 * (4 + 5) = 3 * 9 = 27
(3 * 4) + (3 * 5) = 12 + 15 = 27

Here's one more example to see how you can use the law. We don't expect you to be able to use it this way right now, just watch how it helps solve problems.

8 * 256 = ?
8 * (200 + 50 + 6) = ?
• See how we broke the value up into an addition problem?
(8 * 200) + (8 * 50) + (8 * 6) = ?
• The distributive law split it up.
1600 + 400 + 48 = ?
• We solved each multiplication problem in the parentheses.
2048

We did that one without a calculator and with no carrying or regrouping. The distributive law is the best!

And Then There Were Zero and One

For multiplication, zero and one are special numbers. Whenever you multiply a number by 0 you get zero. Some examples...

5 * 0 = 0
35 * 0 = 0
256,781,247 * 0 = 0.
52 * 48 * 1,598 * 32,598 * 157,859 * 0 = 0

If there is one zero in there, the product is zero. It only takes one.

The general idea with variables that represent any possible numbers...


What about 1? One is special, because any number multiplied by 1 is the original number. Some examples...

5 * 1 = 5
358 * 1 = 358
5,943 * 1 = 5,943

The general idea with variables that represent any possible numbers...


There are a few more laws that work with multiplication, but we're not going to cover them here. The rules that let you move the numbers around will be useful tools for most of arithmetic.

Learn about more multiplication rules in part one.

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