Finding 1 on the number line

I'm here at the Khan Academy exercise called "Find One on the Number Line," and they're asking us to do exactly that. It says move the dot to one on the number line, and it's a little interactive dot that I could move around. So let's think about how I would do it. I always encourage you to pause this video and see at least how you think about doing it, or put your finger on the screen where you think one is, and then we'll work through it together.

All right, so they've told us where zero is, and they've told us where seven fourths is. One thing I could do is I could say, "Well, how many of these equal spaces does it take me to get from zero to seven fourths?" So let's see, it's 1, 2, 3, 4, 5, 6, 7. If it takes seven equal spaces to get to seven fourths, that means that each of these spaces is one-fourth. Because then it would be one-fourth, two-fourths, three-fourths, four-fourths, five-fourths, six-fourths, and seven-fourths.

All right, we're making some good progress. So where would one be? Well, one would be four-fourths. So we would go one-fourth, two-fourths, three-fourths, and then four-fourths. So that's where one is. The important thing to realize is the only way we knew that each of these gaps, or each of these spaces from one hash to the next, the way that we knew that each of those is a fourth is by saying, "Hey look, seven of those equal spaces get us to seven fourths." So each of these must be a fourth. Therefore, four of those four-fourths would be equal to one.

Let's do another example. So here we said we're told to move the dot to one on the number line. So put your finger on where that would be on the screen, pause the video, and do that. All right, in some ways this is a little bit easier because they told us that going from zero to the next little cross or hash, I guess you could say, whatever you want to call these things, is one-sixth. So what is one? Well, one or one whole is six-sixths.

So this is one-sixth, two-sixths, three-sixths, four-sixths, five-sixths, and then six-sixths. So there we go, that is where one is on this number line.