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## Staging content lifeboat

### Course: Staging content lifeboat>Unit 14

Lesson 39: Fractions as division

# Mixed numbers on a number line

Sal locates 3/2 on a number line. Created by Sal Khan.

## Video transcript

In the previous video, splitting this three-pack of soap with my wife, she cut it right down the middle. So we each got half of all three bars, or we got 3/2, or each of us got 3/2 bars of soap. Now, just to make sure that we really understand what 3/2 is-- and remember, 3/2 is really the same thing as 3 divided by 2. If someone says 3 divided by 2, you could say, hey, I'm going to represent that as 3/2. Or someone says 3/2, you could say, well, that's the same thing as 3 divided by 2. But just to really understand this number, let's actually think about where we would plot it on a number line, as well. So let me draw a number line here. I'm going to start that as 0. Let me draw a line, as straight a line as I am capable of drawing. And let's say that this right over here represents 1. So that would be 1 bar of soap in this example. And let's say that this right over here is 1/2 bar. This is 1/2 bar. And let's say that this is 1 and 1/2 bars. And let's say that this right over here is 2 bars of soap. So we have 3/2. So let's think about this. Remember, 3/2 is 3 times 1/2. Or, since we already split this into halves, we just have to go 3 of these halves. So let's do that. So this is 1/2. This is 1/2. Now we're going to have 2/2. That takes us to 1. And we know that because 2/2 is equal to 1. And now let's do our third half. Our third half is right over here. And so that is 3/2. And we see 3/2 is the exact same thing as 1 and 1/2. Now, just to hit that point home, we already saw that 3/2 is the same thing as 3 divided by 2. If you were to divide 3 by 2, you would get-- well, 2 goes into 3 exactly one time. And then what would you have left over? Well, you would have 1/2 left over. So 3/2 is the same thing as 1 and 1/2, which is exactly what we saw here. You could view this as we have 1 and 1/2 bars of soap. And this is where you would plot it on the number line. 3/2 is halfway in between 1 and 2.