About this video
Point A is at -1 and point B is at 3 on a number line. To find point C, 2/3 of the way from B to A, Sal finds the distance from B to A (4), takes 2/3 of it (8/3, or 2 2/3), and moves that far from B towards A, landing at 1/3.
You'll be able to
- find the distance between two points on a number line.
- find a point that is a given fraction of the way from one point to another.
- pay attention to the starting point and direction when dividing a segment.
Key words
- distance
- How far apart two points are, always a positive amount; on a number line it is the absolute value of their difference.
- mixed number
- A whole number and a fraction together, like 2 2/3.
Transcript
- [Instructor] We're told on the following number line, point A is at -1, we can see that there, and point B is at 3, all right? What is the location of point C, which is 2/3 of the distance from point B to point A? So pause this video and see if you can figure that out before we do this together.
All right, now let's do this together. So if we're going 2/3 of the distance from point B to point A, so we're gonna start at point B. And if we went all the distance to point A, we would go all of that way. But we don't wanna go the whole distance, we wanna go 2/3 of this distance.
But to figure out how far we should go, we first have to figure out what this distance is going to be. So we're going from 3 to -1 here. So one way to think about it, you could take your end point and subtract your starting point and you get -4, and you're like, "How is that a distance?"
Well, you could view that as you're going 4 down. The distance here, if you just think of it in absolute terms, is 4, so the distance here is 4. Another way to think about it is you go 3 to get to 0 and then you go another one, so that is 4 to get to -1. So we wanna go 2/3 of the way down this 4.
So what is 2/3 of 4? So 2/3 x 4, well that is the same thing as 2/3 x 4/1, which is the same thing as 8/3. And if we wanna write that as a mixed number, 3 goes into 8 two times with the remainder of 2. So this is 2 2/3. So we want to go down 2 2/3 of a whole. So let's go down one, go down two, and now we're going to go down 2/3.
And luckily, this is split into thirds. So we're gonna go down another third and then 2/3. So point C is going to be right over there and we are done.
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