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Inverse property of multiplication

Video transcript

let's say that I have five lemons so that's one two three four five lemons and I were to ask you what do I have to multiply times five to get one or in this case what I have to multiply times five lemons to get one lemon and so another question you might ask because really multiplication and division are two sides of the same coin is what would I have to divide five by to get to one lemon or yellow circle or whatever I've drawn right over here well if you have five things and if you divide by five you're going to have five groups of one so if you divide by five you're going to have one two three four five groups so you could say five divided by five is equal to one you don't take five things divide it into five groups each group is going to have one in them or you could say five times one-fifth is equal to one and I used the dot for multiplication I could also say five times one-fifth is equal to one these are all really saying the same thing maybe what's kind of interesting here although it's not some huge some huge learning it's it's really just another way of writing what you've already probably known is this idea that if I have a number and I multiply times its multiplicative inverse and most of the time when people talk about inverses in mathematics they're talking about the multiplicative inverse then I'm going to get one so five times one-fifth is equal to one but that's the same that's just because five times one-fifth is the same thing as 5 divided by 5 if you would actually multiply this out if you actually take five times one-fifth this is equal to 5 over 1 times 1 over 5 you multiply the numerators 5 times 1 is 5 multiply the denominators 5 1 times 5 is 5 so you have five fifths and five fifths is the exact same thing as one so if someone were to ask you a question they said hey I have the number 217 and I want to multiply it by something and I want to get one after multiplying it by that something well you say well look if I took 217 and I divide it by 217 that would get me one and dividing by 217 is the exact same thing as multiplying by 1 over 217 multiplying by its multiplicative inverse which is once again a word that is fancier than the actual concept you're just multiplying by the inverse of this number another way to think about it is if I have five things and if I were to take one fifth of those five things how many things do I have well if I take one fifth of five things I have exactly one thing right over here but the general idea is super duper duper simple if I have some crazy number eight thousand three hundred and forty five that's actually not so crazy let's me turn into something in the millions and 271 so eight eight million three hundred forty-five thousand two hundred seventy-one and I say what do I have to multiply that and I'll use this multiplication symbol right now what do I have to multiply that by in order to get one well I just have to multiply by the inverse of this the multiplicative inverse of this so one over eight million three hundred and forty five thousand two hundred and seventy-one