 So let's take a look at multiplication, and we'll start out with what I call the Abbott and Costello problem. Find 7 times 13, and you might wonder why it's called the Abbott and Costello problem. You can google it. It's actually a rather entertaining little skit. But in any case, our beginning is that this product 7 times 13, that's equal to the sum of 713. So here I put down 713, and whatever this sum is, is going to be equal to the product. Now again, what I can do is I can decompose each of these 13s into a 10 and a 3. So I'll go ahead and do that, and each one of those 13s is a 10 and a 3. And so what do I have? Well I have 710s, and I have 7 threes. So if I put those together, this sum 710s and 7 threes is the same as 713s. And so this is actually an example of a really general theorem, which is known as the distributive property. So in general, if I have a bunch of real numbers, a, b, and c, then the product a times the sum of b and c is just a times b plus a times c. And if I try to apply that to this case, what I have is 7 times 13. I'm going to break that 13 into 10 and 3. My distributive property allows me to rewrite that 7 times 10 plus 7 times 3. And the advantage to this is both of these products are much easier than the original. So this is going to be 70 plus 21, and addition is pretty easy, so I can add that and get 91 as my product. And the important thing to realize here is that when you use the distributive property, it's whatever works, whatever you happen to feel comfortable with working with. Again, the only requirement here is eventually you're going to have to do a multiplication. So let's consider the product 7 times 27. And so one possibility, we could break 27 into 20 and 7. And so I can apply the distributive property 7 times 27, 7 times 20 plus 7. And I'll multiply that out 7 by 20 and 7 plus 7. And again, I can do those multiplications much more easily. This is 7 times 20 is 140. 7 times 7 is 49. And add those two together to get the product 189. And this is a perfectly good way of doing that multiplication. On the other hand, some people think in quarters. And you might note that 27 here is 25 plus 2. So here I've rewritten 27, and I've decomposed it into 25 and 2. And the advantage to this is when I expand it, that's seven quarters and 14. So that's 175 plus 14. Again, 189. And so the important thing is no matter how you break up this 27, whether you think of it as 20 and 7, or you think of it as a quarter and two cents, the distributive property is going to give you the same answer in both cases. And the only choice you have to make is do you want to work in quarters, or do you want to work in tens?