Multiplication and division relationship for fractions

you are likely already familiar with the relationship between multiplication and division for example we know that 3 times 6 is equal to 18 but another way to express that same relationship is to say all right if 3 times 6 is 18 then if I were to start with 18 and divide it by 3 that would be equal to 6 or you could say something like this that 18 divided by divided by 6 is equal to 3 now we're just going to extend this same relationship between multiplication and division two expressions that deal with fractions so for example if I were to tell you that 1/4 divided by and I'm going to color code it divided by 2 is equal to 1/8 is equal to 1/8 how could we express this relationship but using multiplication well if 1/4 divided by 2 is equal to 1/8 that means that 1/8 times 2 is equal to 1/4 let me write this down or I could write it like this I could write that 1/4 is going to be equal to it's going to be equal to 1/8 times 2 times 2 and we could do another example let's say that I were to walk up to you on the street and I were to tell you that hey you 42 is equal to 7 7 divided by 1/6 in the future we will learn to compute things like this but just based on what you see here how could we express this same relationship between 42 7 and 1 6 but express it with multiplication pause this video and think about that well if 42 is equal to 7 divided by 1/6 that means that forty-two times 1/6 is equal to seven let me write that down this is the same relationship as saying that 42 times 1/6 1/6 is equal to 7 now let's say I walk up to you on the street and I were to say alright you I'm telling you that 1/4 divided by divided by 6 is equal to some number that we will express as T so can we rewrite this relationship between 1/4 6 and T but instead of using division use multiplication pause this video and try to think about it so if 1/4 divided by 6 is equal to T based on all of the examples we've just seen that means that if we were to take T times 6 we would get 1/4 so we could write it this way T times 6 times 6 is going to be equal to 1/4 if this isn't making sense I really want you to think about how this relationship is really just the same relationship we saw up here the only new thing here is instead of always having whole numbers we're having fractions and representing some of the numbers with letters