About this video
Sal shows that 3/2 bars of soap is the same as 3 divided by 2. He plots 3/2 on a number line by counting three halves from 0 and shows it lands at 1 and 1/2, halfway between 1 and 2.
You'll be able to
- explain that a fraction like 3/2 means the same as 3 divided by 2.
- plot a fraction greater than 1 on a number line by counting unit fractions.
- write 3/2 as the mixed number 1 and 1/2.
Key words
- number line
- A straight line with numbers placed in order at equal spaces.
- mixed number
- A whole number and a fraction together, like 1 and 1/2.
- half
- One of two equal parts of a whole, written 1/2.
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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.