 Alright, well let's take a look at division with mixed numbers. This is actually the most complicated of the operations because, no surprise, division is the most complicated of our elementary operations. So again, the idea that we might work with is that we can, if we want to, convert our mixed numbers into improper fractions. So again, the check we might make, the numbers here are fairly small, so it might be worth trying to do that. So let's see, three and a third is three times three plus one, ten-thirds, one times eight plus three, eleven, eight, and that is now a fraction divided by another fraction. And so we have a nice algorithm that says you're going to do that, invert and multiply. And I can multiply two fractions, no problem, 80 over 33. And again, I want to give my final answer the same dialect that I gave the question in. So the question, mixed numbers. So when I give the final answer, I should also express it as a mixed number. So this reduces to and fourteen-thirty-thirds. And again, the numbers involved ten, eight, three, and eleven aren't too big. 80 over 33, not too difficult to work with. So it seems reasonable to use the method of converting to improper fractions for this problem. However, every problem is not a nail. Suppose it takes up to like this, forty-seven and two-thirds, divided by seven and five-eighths. And if I were to convert these to improper fractions, forty-seven and two-thirds, one-forty-three-thirds, seven and five-eighths, sixty-one-eighths, I have two fractions, invert and multiply, and I end up with a horrible mess at the end of the day that I really don't want to have to deal with. So is there another way that I can do this? And again, the thing to keep in mind, every method that we have of doing a division can be applied to this division. And even though it's not our favorite method to use, we might consider using long division as long as we remember what we're actually doing when we do that long division. So again, we'll rewrite our mixed number as a whole number plus a fraction. And we could start in almost the same way that we do a standard long division. Problem seven goes into forty-seven. I don't know how many times, how about six? So I'll write my dividend and I'm going to subtract six-sevens and also six-five-eighths. So I'm going to multiply six by seven is forty-two, six by five-eighths is thirty over eight, and no reason to make our life difficult. Thirty over eight can be pretty quickly reduced to a whole number plus a left over that's three plus six-eighths. And again, I can reduce this to three-quarters. This is forty-five. So that product gives me forty-five and three-quarters. Now I need to do the subtraction. So I'm going to take this, I'm going to subtract this amount, and how do you do the subtraction? Well again, any method that you want to use, I feel like doing counting up because I think that's going to be the easiest. So if I start at forty-five and three-quarters and count up to this, I first go up by a quarter that takes me to forty-six, one more to take me to forty-seven, two-thirds more to take me to forty-seven and two-third. And I'll go ahead and add these fractional parts because I can, it's not too difficult, one plus eleven-twelve. And the thing that's worth noting at this point, the remainder is less than the divisor. And so I can express the quotient as six and the compound fraction remainder over divisor. So there's my remainder that amount. Now I don't want to leave the answer in that form, that's going to be pretty horrible. And so let's see what we can do about this. One way we can get rid of compound fractions is if we multiply by a common multiple of the two denominators here, that would be twelve and the eight, we can clear all of our fractions at the same time. So let's multiply by twenty-four. So that's going to be, give us this, again, multiplying by the same term gives us an equivalent fraction and that gives us twenty-four, one sixty-eight, twenty-four times eleven-twelve, twenty-two, twenty-four times five-eighths, is fifteen. Add those things together, that's forty-six, one eighty-thirds. Remember that's the remainder. So our actual quotient is going to be six and forty-six, one eighty-third, six and forty-six, one eighty-thirds.