Creating a fraction through division

my wife and I have recently purchased an assortment pack of soap and we both want to experience all three bars and we are not willing to share soap with each other so we have a little bit of conundrum how do we share these three 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 I don't know 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 three bars so we're starting with three bars of soap and I'm going to divide it into two equal groups and I said how are we 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 it with her saw so she's cutting cutting the soap right over here so she has divided the soap into two equal groups so she's taking three bars and she's divided into two 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 cells cells share my wife took this top half well what do I have well I have I have one half I have another one half and I have another one half of a bar so I have three one halves of bars of soap or you could say that I have three times one half three times one-half bars of soap notice something very interesting happened here three divided by two is equal to three times one-half and we can make it even more interesting because we know two is the same exact same thing as 2 over 1 so 3 divided by 2 over 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 three half bars now but what's 3 times 1/2 well 3 times 1/2 is equal to is equal to 3 3 halves so just doing this little simple smelly soap example we 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 halves