Fractions greater than 1 on the number line

We're asked to move the dot to 7/6 on the number line, so pause this video. I can move this dot right over here, but I encourage you: pause the video and put your finger on where 7/6 would be on the number line.

All right, now let's work on this together. So what they're saying is, from 0 to this point on the number line, right over there, that gets us to 1/6. Each of these spaces are a sixth. So we go 0, 1/6, 2/6, 3/6, 4/6, 5/6, 6/6, 7/6. Let me make sure I got that: each of these are a sixth. So we have 1, 2, 3, 4, 5, 6, 7/6.

So that's 7/6 on that number line. Now they have other ways of getting at the same idea. For example, they say which point is at nine-fourths on the number line, and they ask us to choose one answer. We can look at the choices here. So which choice shows nine-fourths on the number line? Pause this video and see if you can pick that.

All right, now let's look at each of these. It looks like in choice A, the space between zero and one is split into one, two, three, four equal spaces. So as we go from zero to this next line, that's a fourth, and it seems like it keeps going.

So this is one-fourth, two-fourths, three-fourths, four-fourths, five-fourths, six-fourths, seven-fourths, eight-fourths. Nine-fourths is here; that's what we're looking for. But the dot is not at nine-fourths—it's at ten-fourths, eleven-fourths, twelve-fourths—so I don't like choice A.

Let's see choice B. Let's see what this is. We have divided the space between zero and one into one, two, three, four, five, six equal spaces. So each of these are a sixth. To go from zero to one, you've already gone six-sixths, and then seven-sixths, eight-sixths, nine-sixths.

So this is nine-sixths, not nine-fourths. Let's look at this last choice. I'm already feeling like it should be the answer, but we can see that the spaces are the same as in our first choice.

So these are each fourths, once again—I know that because the space between zero and one, or any two whole numbers, is divided into four equal spaces. So to go from zero to one, you go four-fourths, and then five-fourths, six-fourths, seven-fourths, eight-fourths, and nine-fourths.

So choice C is definitely looking good. Let's do one more example. Here they say what fraction is located at point A on the number line. Pause this video and see if you can answer that.

All right, so between whole numbers, how many equal spaces do we have? It looks like we have one, two, three, four, five, six equal spaces. So things are divided into sixths: 1/6, 2/6, 3/6, 4/6, 5/6, 6/6—which is equal to 1—and then 7/6.

So this is 7 over 6, just like that, and we are done.