 We're going to start working out how to do multiplication and division in base 6 by building a times table for base 6. This will be our base when we start trying to solve multiplication and division problems in base 6. We're going to start by using some simple rules that you probably already know, and then we're going to do a whole lot of addition to fill in the rest of the table. So to begin with, we know that zero times anything is zero, so I can easily fill in the zero rows and column. Now one is almost as easy. One times anything is the anything. So I'm going to just write down whatever the other thing is in that row or column. Now I'm going to start doing a whole bunch of addition. I'm also going to take advantage of the fact that my table needs to be symmetrical along the diagonal. So for example my two here, one times two is equal to two times one. So I'm also going to expect five times three is equal to three times five. I'm primarily going to walk across the row just adding whatever this difference is at each time and making sure I stay within my base. So two plus two will give me four. But four plus two doesn't give me six, because I don't have any sixes in base six. Six is actually ten. So I get ten there. Ten plus two is twelve. Twelve plus two is fourteen. And fourteen plus two will give me twenty. So rather like you would expect, two times ten gives me twenty. Three times ten should give me thirty. All we're doing here is multiplying three by the one and then three times zero. So I get three and then zero. So here I'd have forty, fifty, but then I get one hundred because I don't have a sixty. And since our table is symmetrical, I'm going to go ahead and copy some of these across the diagonal. So now I'm down to nine more elements of which I only need to fill out six. So ten plus three will give me thirteen. Thirteen plus three won't give me sixteen, because I'm in base six. That will actually give me twenty. Twenty plus three will give me twenty-three. Down here I have twelve plus four, which will give me twenty. Then twenty plus four is twenty-four. Twenty-four plus four can kind of see that we're sort of repeating what we had over here, but with twenty added on, so twenty matches up here. Twenty-four, next will be thirty-two, and then the forty. So I'll copy my twenty-three and my thirty-two over here. And then I just have one more element which will be forty-one. So there's my times table in base six. We can build these for any arbitrary base you'd like. Six is small enough that we can write it on the board relatively easily though. Now we'll be able to use this to solve more complex problems in base six.