In this lesson, we're going to look at converting fractions from one type to another type. First, let's review the different types of fractions. Some fractions represent less than a whole. We can see that we have three out of four parts of this circle shaded in orange, so we can represent it as three fourths. We call this type of fraction a proper fraction. So proper fractions represent less than one whole. And we can tell by looking at the fraction, even when we don't have the picture to look at, that it's a proper fraction because the numerator is always less than the denominator. The three in this case is less than the four. Some fractions represent more than a whole. So in this picture we have one whole circle and then a part of another circle. The first circle is completely colored in and then we have part or three fourths of the second circle. Now, there's two different ways that we can represent this amount as a fraction. The first way is by putting it all together in one fraction of seven fourths. We have seven parts altogether, four from the first circle and three from the other circle. So that's where the seven in the numerator comes from. But each circle is still split into four parts, so our denominator is still going to be four. So we can represent this as seven fourths. This type of fraction we call an improper fraction. Because the numerator is larger than the denominator, the seven is larger than the four. We can also represent the same amount a different way. Since the first circle is one whole and the second circle is three fourths, we can say that this is one and three fourths. This type of fraction is a mixed fraction because it has a whole number part, which is the one and then a fraction part, the three fourths. So first we're going to look at how we can convert an improper fraction to a mixed fraction. Because remember, these two types of fractions are the ones that represent more than one whole. So let's start off with that seven forths that we just saw. Remember, fractions really just represent division. So we can write this as seven divided by four, the numerator divided by the denominator. Now, to change this to a mixed fraction, our next step is going to be to solve this division problem using long division. So we'll set it up with our long division sign. So we know that four goes into seven one time. Four times one gives us four. Ssubtract and we have a remainder of three. Now each part of the answer that we get by solving through long division is going to give us part of our mixed fraction. So the whole number part of our answer, the one, becomes the whole number of our fraction. The remainder becomes the numerator of the fraction part. So we put the three as the numerator and then whatever our divisor is that becomes the denominator. Okay? So you can look to the divisor of your long division problem, or you can also look at the denominator of your original fraction, which is still the four. So as a mixed fraction becomes one and three fourths. And this time we're going to look at how we can convert a mixed fraction to an improper fraction. So we'll start off with our same mixed fraction of one and three four, and follow the steps to see how we can set it up as an improper fraction. The first thing that we're going to do is multiply the whole number times the denominator of the fraction part. So in this case, it's the one being multiplied by the four. The next step after that will be to add the numerator. So we're going to add that three. Now let's see what this gives us. One times four gives us four. Then add three to that and we get seven. That seven is going to be the numerator of our improper fraction. Okay? And then to figure out what the denominator is, we just look at the denominator of the fraction part of our original mixed fraction, which is the four. So we keep that same denominator. And now we're back at seven fourths as our improper fraction. So just to review, when we're converting an improper to a mixed fraction, we use division. So divide the numerator by the denominator and then we solve it by long division. The whole number in the quotient, which is the answer, becomes the whole number of the mixed fraction. Whatever the remainder is, that becomes the numerator of the fraction part. And then we just keep the same denominator going from a mixed to an improper fraction. We first multiply the whole number by the denominator and then add the numerator. Whatever we get from that becomes the numerator of the improper fraction. And then of course, just keep the same denominator.