Mixed number or improper fraction on a number line

Move the orange dot to 9/4 on the number line. Let's think about this number line right here. This is 0. This is 3. So this must be 1 and 2. We need to go to 9/4. So there's two ways of thinking about 9/4. One way is to try to convert it to a mixed number. 4 goes into 9 two times. And you'll have 1 left over. So this you could do as 2 and 1/4. So you could say, this is 1, 2. And then, we have to go 1/4 of the way between 2 and 3. So that looks like about 2 and 1/4. So you could think about it that way. Or you could even view it as an improper fraction. So let's go by 1/4's. So that's 1/4, 2/4, 3/4, 4/4, which is a whole, 5/4, 6/4, 7/4, 8/4, which is equal to 2 wholes. 8 divided by 4 is 2. And then, we go from 8/4 to 9/4. Either way, we get to that exact same point on the number line. Let's do a few more of these. Move the orange dot to 11/5 on the number line. So we can do it both ways again. 5 goes into 11 two times. And then, you have 1 left over. So you could call this 2 and 1/5. So we could go 1, 2, and then 1/5. Or we could just think of it in terms of 1/5's as an improper fraction. 1/5, 2/5, 3/5, 4/5, 5/5 is a whole, 6/5, 7/5, 8/5, 9/5, 10/5. 10 divided by 5 is 2. 10/5 is two wholes. 10/5 and 11/5-- I'm having more fun than I expected to with this exercise. Let's do one more. Orange dot to 5/2 on the number line. So this is 1/2. This is 2/2, which is a whole. This is 3/2. This is 4/2, which is two wholes. This is 5/2. Another way you could have thought about it-- 2 goes into 5 two times with a remainder 1. So this is 2 and 1/2 as a mixed number-- 1, 2, and 1/2 as a mixed number.