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Current time:0:00Total duration:6:58

Video transcript

in this video I'm going to multiply 87 times 63 but I'm not going to do it just by using some some process by just showing you some steps instead we're just going to use the distributive property to actually try to calculate this thing so first what I'm going to do let me rewrite 87 let me rewrite so this is the same thing as 87 but instead of writing 63 like that I'm going to write 63 as 60 60 plus 360 plus 3 now what is this going to be equal to well 87 times 60 plus 3 that's going to be the same thing as let me actually copy and paste this so this is going to be the same thing as so it's going to be 87 times 60 87 times 60 Plus 87 plus 87 times 3 plus 87 times 3 you could say that we've just distributed we have just distributed the 87 we're multiplying 87 times 60 Plus 3 that's 87 times 60 Plus 87 times 3 I could put parentheses here to make it a little bit clearer well fair enough but then how do you calculate what this is well now we can rewrite 87 as 80 plus 7 so let's rewrite that so this is the same thing actually let me write it this way I can swap them around so this is the same thing as 60 times 87 but I'll write that as 60 60 times 80 plus 7 like this 80 plus 7 plus plus 3 times 80 plus 7 or 3 times 87 let me write let me just copy and paste that so I don't have to keep switching colors plus 3 times 80 plus 7 so copy and then let me paste it and then you have it just like that so all I did just to be clear all of what you see right over here 87 87 times 60 well that's the same thing as 60 times 87 which is the same thing as 60 times 80 plus 7 all that you see are 87 times 3 that's the same thing as 3 times 87 which is the same thing as 3 times 80 plus 7 that's just that over here but look we can distribute again we can distribute the 60 times sine times 80 plus 7 so this is going to be 60 I'm going to do that same color color changing is hard this is 60 times 80 times 80 plus 60 plus 60 times 7 times times 7 plus plus 3 times 80 plus 3 times 80 plus 3 times 7 so plus plus 3 times 3 times actually let me do it 3 times 7 right over here so notice what we really did is we thought about what each of these digits represent 8 represents 87 represents 7 6 represents 60 because it's in the tens place the 8 was in the tens place as well this 3 is in the ones way so it's just 3 and we just multiplied them all together we multiplied the 80 times the 60 we multiply the 80 times the 3 we multiply the 7 times the 60 right over here we multiply the 7 times the 3 and then we add them all up together and this will actually give us our product so for example this right over here 6 times 8 is 48 but this isn't 6 eighths this is 60 80s so this is going to be 4,800 we've got 2 zeros right over here so 48 followed by the 2 zeros this right over here 60 times 7 is 4420 6 times 7 is 42 there's going to be ten times as much because this is a 60 and then 3 times 80 well same logic 3 times 8 is 20 four so this is going to be 240 and then finally 3 times 7 is 21 and then to get the product we can add these two together and you might be saying a Sal I know faster ways of doing this but the whole reason I'm doing this is to show you that that fast way you knew how to do it it's just it's not some magical formula or some magical process you're doing it just comes out of really distributive property and hopefully a little bit of common sense so what is this going to be equal to well we could add them all up 4,800 plus 420 + 240 + 21 where you get a 1 here let's see 20 plus 40 plus 20 is 80 let's see 800 plus 400 is 1200 plus 2 more 200 more is 1400 or 1400 and so you get five thousand four hundred and eighty one it's equal to five thousand four hundred and eighty one and you might say gee you know this was this was a bit of a pain to have to do the distributive property over and over again is there a simpler way to maybe visualize this and there is you could actually write this as a grid so we could say we're multiplying eighty seven times 63 we can write it like this we could say it's 80 plus seven eighty plus seven times 60 60 plus three plus three and then you can set up a grid like this so let me set up a little box here it's two digits by two digits so it's going to be a 2x2 grid two rows and two columns and then you just have to calculate well what 60 times 80 well we already calculated that that's 4,800 what is 60 times seven well that's going to be 400 400 and 220 what is three times 80 we already calculated that that is 240 I don't do that same color 240 and finally what is 3 times 721 you add them all together you get five thousand four hundred and eighty-one and I encourage you to now just do this this the same multiplication problem the same 87 times 63 the way that you might have traditionally learned it and see and look at the different steps and why they are making sense and why at the end of the day you really are doing the same thing that you just did in this video you're just doing in a different way and the whole point of this whole exercise this whole video is so that you really get the understand so you're not just blindly doing some type of steps to find the product of two numbers but you can actually understand why those steps work and how those numbers relate to each other