 The next major operation that we're going to try and define is division, and our definition of division actually comes from our definition of multiplication. So the basic definition for the division of two whole numbers is suppose I have a multiplication A times B equal to C. Then every time I have a multiplication A times B equal to C, I also have a division A is equal to C divided by B. Now this assumes that we have a division that in the usual language comes out evenly, which is to say that C divided by B has to be equal to A with nothing left over. And so we'll actually look at division with remainders a little bit later on. Now this particular symbol that we have here for division is one of several symbols that we use. So there are other symbols for division, and we should regard the following as equivalent symbols, C divided by B, C slash B, and note the direction of that slash. It's important to note that if I reverse the direction of the slash, the backslash, it is not going to be considered the same as C divided by B. The backslash and the forwardslash represent two entirely different concepts in mathematics. So as usual, we'll start out by proving a division fact, for example, 24 divided by 6 is equal to 4. And once again, this is a proof problem, so we'll go back to our definition of division, which we'll have for reference. Once again, it's based on our definition of multiplication. If I have a multiplication, then I have a division. And again, we'll compare our definition to our statement. So here I have C must be the same as 24, so I'll make that replacement. I have B must be the same as 6, so I'll replace that. And then A is the quotient, and so I'll replace A with 4, and I'll make that replacement. And again, we'll add a little bit of words to make everything come out a little bit easier to read. And so I might say something like, since 4 times 6 is equal to 24, then 4 is equal to 24 divided by 6. And again, as a proof problem, what I have to include is the portions written in green.