Creating a fraction through division

My wife and I have recently purchased an assortment pack of soap, and we both want to experience all 3 bars. And we are not willing to share soap with each other. So we have a little bit of a conundrum. How do we share these 3 bars of soap so that we each get to experience all of the smells? So this might be a nice rose smell. This might be some type of ivory smell. I don't even know if that's a legitimate smell. This might be some type of sandalwood, which is always very nice. And my wife has an idea. She says, look I'm going to take these 3 bars, so we're starting with 3 bars of soap. And I'm going to divide it into 2 equal groups. And I said, how are you going to do that? And she says, well, I'm just going to take out some type of carving saw or carving knife, or who knows what it is, and I'm just going to cut it right down the middle, so right down this. This is my wife cutting the soap right over here with her saw. So she's cutting the soap right over here. So she has divided the soap into 2 equal groups. So she's taken 3 bars, and she's divided into 2 equal groups. So the interesting question here is, how many bars of soap do we each have now? And I encourage you to pause the video and think about that for a second. How many bars of soap do we each have now? Well, let's just visualize my share. Let's say I take this bottom half right over here. So this is Sal's share of the soap. Let me write this out. So this is Sal's share. My wife took this top half. Well, what do I have? Well, I have 1/2, I have another 1/2, and I have another 1/2 of a bar. So I have 3/2 bars of soap. Or you could say that I have 3 times 1/2 bars of soap. Notice, something very interesting happened here. 3 divided by 2 is equal to 3 times 1/2. And we could make it even more interesting, because we know 2 is the exact same thing as 2/1. So 3 divided by 2/1 is equal to 3 times 1/2. Notice we went from a division to a multiplication, and we took the reciprocal. And that makes complete sense. We have 3/2 bars now. But what's 3 times 1/2? Well, 3 times 1/2 is equal to 3/2. So just doing this little simple, smelly soap example, we've got a very interesting result. 3 divided by 2 is the same thing as 3 times 1/2, which is the same thing as 3/2.