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Video transcript

so we're going to think about in this video is multiplying fractions so let's say that we wanted to take two thirds and we want to multiply it by four what is this going to be equal to pause this video and try to think about it on your own alright now let's work through this together and to help us I will use a number line and let's say that each of these hash marks represent a third so this is 0 this is one-third two-thirds three-thirds 4/3 5/3 six thirds 7/3 8/3 and 9/3 and so where is 2/3 times one well 2/3 times one is just going to be 2/3 we just take a jump of 2/3 so that is times 1 if we multiply by 2 or free to take 2/3 times 2 that'll be 2 jumps so 1 2/3 to 2/3 3 2/3 and then for 2/3 so we just took 4 jumps of 2/3 each you could view that as 2/3 plus 2/3 plus 2/3 plus 2/3 and where does that get us to it got us to 8/3 so notice 2/3 times 4 is equal to 8/3 now we could go the other way we could look at a number line and think about what are ways to represent what the number line is showing us and on Khan Academy we have some example problems that do it that way so I thought it would be good to do an example like that and so let's label this number line a little bit different instead of each of these lines representing a third let's say they represent a half so zero one half two halves three halves four halves five halves so why did I write five six my brain is going ahead five halves six halves seven halves eight halves and nine halves and let's say we were to see something like this so if you were to just see this representation so I'm going to try to draw like this so if you were to de-seed this representation what is that trying to represent what what type of multiplication is that time to trying to represent well you could view that as three halves plus another three halves plus another three halves because notice each of these jumps are three one halves or three halves so you could view this as three halves plus three halves plus three halves or another way of thinking about it is this is three jumps of three halves so you could also view this as being the same thing as three times three halves and what are these equal to well three halves plus three halves plus three halves or three times three halves it gets you to nine halves