 To divide, the ancient Egyptians use the fact that the quotient A divided by B is the answer to how many Bs do I need to make A? This means they could use their multiplication tables as division tables. So let's say we want to divide 225 by 45. And this is the same as asking the question, how many 45s do we need to make 225? So we want to know how many 45s are needed to make 225, so we'll make a table of multiples of 45. So one of the 45s is 45. We'll double the amount, so two of the 45s is 90. Doubling again four of the 45s is... Now we could keep doing this, but the thing to notice here is if we double again, we'll get more than 225, and we don't need to. So we want to add to 225, so let's pick this largest piece first, that'll give us 180. Now we want 225, so we need some more, so we'll pick the next piece that fits. This piece here is going to be too big, that'll give us 90 more, but this last piece here, that'll give us 45 more, and that'll take us right up to 225. So we'll go to the checkout counter, and we'll say we want this piece, and this piece, and so all together that's 5 of the 45s, and that works out to be 225. And so 225 divided by 45 is 5. Or let's take something like 6885 divided by 153. So again, we want to know how many 153s we need to make 6885. So we'll start by constructing our table, one of the 153s is 153. Now we want to make 6885, so we're going to need a lot of the 153s, so let's start by taking 10 of the 153s. So 10 of the 153s is 1530. Now we can also double this a few times. So if my package of 10 is 1530, a package of 20, twice as many is going to be. And I can double again, and that's going to be a package of 40 is going to be 6120. And again, it's worth pointing out that if I double again, I'll have too much, we'll get more than we need. Now it's possible that we got lucky, and on the shelf we have everything that we need to make 6885. Don't count on it. Let's take a look. This package is 6120. If I take the next package, 3060, that's going to be too much. If I take the next one, that's still going to be too much. And the next smaller size on the shelf is not enough. So let's take our initial packet here, one 153. I can double that size, and that's going to get me two 153s. And if I double it again, I'll get four 153s. And now let's select. So if I take this packet, that's 6120. If I take this packet, that's 612 more. And if I take this packet, that's 153 more. And if I add these three together, I get the 6885 I want. And so that means I need 40, 4, and 1, 45 of the 153s. So 6885 divided by 153 is 45. It's worth comparing our work to our earlier problem of multiplying 153 by 45. And the thing to notice here is they produce essentially the same table. The only real difference between the two is whether we're looking on the left-hand side, which is what we do when we're multiplying, or whether we're looking on the right-hand side, which is what we do when we're dividing.