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I thought that we could talk about fractions. So , for instance, one over two. Also known as one half. Okay, so another one would be two over five, or two fifths. And then there are more complicated ones, like eighteen over forty-two, and, well, you know that there is something a little wrong here, which is that the top and the bottom, you can both divide them by two, and then you get that this is nine over twenty-one. And, oh, Im not done. And so its three sevenths. I wanted to do this example because all the fractions Im going to consider are going to be reduced like this. Namely, its going to be of the form p over q, where p and q are integers, and they are what we call coprime, namely that they have no common divisor. [Brady]: Weve cancelled them down as far as they can go. [Dr. Bonahon]: Thats completely correct, yes. And now, if you remember, with fractions you can do things: you can add them up, or you can multiply them. And multiplication is fairly easy because if I want
