 In some cases, we have multiple sets, each of which contain the same number of objects. For example, we might have five packs of hot dogs, each of which contains 12 hot dogs, or we might have six packs of hot dog rolls, each of which contains eight rolls. Find the total number when we have a collection of sets corresponds to a multiplication, and so we define a times b is the quantity corresponding to a sets of b. Now there is a problem in notation, because a times b means a sets of b, a is a number, but b might not be. So for now, when we write a times b, a should always be considered a number, regardless of how we write it, and b might or might not be a number. To avoid the notation problem, we'll begin by spelling out the first factor. For example, we might write four times three base five. Let's multiply three times two one four base six, and so we have three sets of two one four base six. That's two large, one medium, four small. And we have three sets like that. Since we're working base six, we'll look for sets of six to bundle and trade. So here's a set of six we can trade. And in fact, since this is the next larger unit, we'll move it to the appropriate column. We'll bundle and trade other sets of six. Again, for organizational purposes, let's put these in the right column. And there's another set of six we can bundle. And again, arithmetic is bookkeeping how many of which units we have one zero five zero base six. Now remember that in base n, the largest amount we can conceive is n. So what happens when we multiply by the base? Well, let's try it and find out. Let's try to find five times three two base five. And so we have five sets of three two base five. But if we bundle and trade, then every unit in every set appears five times. And so each of the three mediums becomes a large and each of the two small becomes a medium. And so we find that five times three two base five is three two zero base five. And this is true generally. And so we could say that we add a zero. But how you speak influences how you think and we shouldn't say that. What we're really doing is shifting the places. And so we can say that multiplying by the base shifts all digits one place. So for example, if we want to find four times one three two base four, multiplying by four means that every unit in every set appears four times. And so each unit in every set can be bundled for one of the next larger unit. And so our product is one three two zero base four.