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Current time:0:00Total duration:5:10

Video transcript

we've already seen that a fraction like two ninths can be interpreted as 2/9 we do the two in the same color as 2/9 that if we have a fraction that it can be interpreted as the numerator divided by the denominator and this leads to all sorts of interesting conclusions some of which we've already seen and some of which are a little bit new so for example if I add the fraction if I had the fraction seven seventh 7/7 this can be interpreted now as seven divided by seven as our numerator nevah divided by our denominator and seven divided by seven is of course equal to one and this is consistent with what we've already seen 7/7 would get us to a whole and a whole is the exact same thing as one but we could do things a little bit more interesting as well we could take something like eighteen sixths eighteen six and realize that wow this is the same thing as 18 divided by six 18 divided by six which we know is equal to three is equal to three and we should do a little reality check does this make sense that 18 six should be equal to three well we could rewrite it we could rewrite 18 six 18 six let me write it make the sixth that same orange color that's going to be the same thing 18 is 6 plus 6 plus 6 and then all of that over 6 all of that over 6 and then that's the same thing that's the same thing as 6 over 6 plus 6 over 6 plus 6 over 6 and I could make this I could make this right over here in orange and we've already seen or we've seen many many videos ago that 6 6 just like seven sevens these are each equal to a whole these are each equal to one and we can now view this as 6 divided by 6 which is the same thing as 1 so this is one plus one plus one which is of course equal to three but this starts to raise an interesting question this will worked out just fine when because 18 is a multiple of six six divides evenly into 18 what happens if we're if we start having fractions where the new where the denominator does not divide evenly into the numerator let's say we have a fraction like 23 over 23 over 6 23 over 6 well we know that we can interpret this as 23 divided by 6 23 divided by 6 and if we actually divide 23 by 6 so let's do that so we divide 6 into 23 6 into 23 we know 6 goes into 23 3 times 3 times 6 is 18 and then when you subtract you end up with a remainder of 5 so we might say hey 23 divided by 6 23 divided by 6 6 is equal to 5 remainder 3 is equal to 5 remainder 3 but that's not that satisfying what do I do with this remainder this really isn't the number here this says we go this is just saying that we're going 5 times and then we have a little bit left over what we can do now is is manipulate this a little bit so that we can realize that this is a number and in particular a mixed number so for example we could start with a 23 over 6 and we could divide it in two or we could decompose the numerator into one part that is divisible by 6 evenly divisible by 6 and the remainder so for example 23 over 6 we can rewrite as 18 plus 5 over 6 over 6 notice I decomposed the 23 into one part that is multiple that is a multiple of 6 and it's the largest multiple that essentially fits into 23 or that is less than or equal to 23 and then the remainder the remainder when you divide 6 into 23 you get a room or five you could view it as I divided it into the remainder and everything else and the reason why this is interesting is because we know that this is going to be equal to 18 over six 18 over 6 plus 5 over 6 plus 5 over 6 well we already know that 18 over 6 is the same thing as 18 divided by 6 or 3 so this is the same thing as 3 so we know that 23 over 6 which is the same thing as 18 plus 5 over 6 is the same thing as 3 plus 5 6 or if we want to write it as a mixed number we could write it as 3 and 3 and 5/6