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# Using area model and properties to multiply

CCSS.Math:

## Video transcript

what I hope to do in this video is get a little bit more practice and intuition when we're multiplying multi digit numbers so let's say that we wanted to calculate what 7,000 times 6 is 7,000 times 6 now for some of you you might did might just jump out at you that hey look if I have 7 of anything and here I have 7 thousands and I multiply that by 6 I'm now going to have 7 times 6 of that thing or 42 of that thing and in this case we have 42 thousands so you might just be able to cut to the chase and say hey look six times seven thousands is going to be 42 thousands and that's great if you can just cut to the chase like that and another way to think about is like look 6 times 7 is 42 and then since we're talking about thousands we're not just talk about 7 when I'm at 7 thousands I have 3 zeros here so I'm going to have 42 thousands 3 zeros there but I want to make sure that we really understand what is going on here this will also help us a little bit of practice of our multiplication properties so 7,000 is the same thing as 1,000 times 7 or 7 times 1000 it's seven thousands or you could view it as a thousand sevens either way so this is the same thing as a thousand times 7 times 6 times times 6 and so you could view it as you could do the thousand times seven first which would be seven thousand and then times 6 or you could do the 7 times 6 first and this is this right over here this is the associative property of multiplication it sounds very fancy but just say it says that hey look we can multiply the 7 times 6 first before we multiply by the thousand so we could rewrite this as 1,000 times x and if we going to do the 7 times 6 first we could put the parenthesis around that times 7 3 times 7 times 6 7 times 6 notice it's 1,000 times 7 times 6 I could do a thousand times 7 first to get 7,000 or I could do the 7 times 6 first to get and you know where this is going so if you multiply the 7 times 6 first you're going to get forty-two and you're going to have a thousand times 42 1000 times 42 so you could view this as a thousand forty twos or maybe a little bit more intuitively you could view this as 40 mm so once again we get to 42 40 mm and so the whole reason some of y'all might have just been able to do this immediately your head and that's all good but it's good to understand what's actually going on here and the reason why I also broke it up that way this way is that the exercises on Khan Academy make you do this to make sure that you really are understanding how to break up these numbers and how you can reassociate how when you multiply them let's do another one let's say that we wanted to figure out let's say that we wanted to figure out let me get our give ourselves some space let's say that we wanted to figure out what 56 56 times 8 is and there's a bunch of different ways that you could do it you could say that look 56 this is the same thing as 55 tens that's 50 plus 6 ones plus 6 ones so 50 plus 6 and all of that times 8 all of that times 8 and then you can distribute the 8 and you could say look this is going to be 50 times 8 so it's going to be 50 times 8 plus 6 times 8 plus 6 times 8 plus 6 times 8 and 50 times 8 well 5 times 8 is 40 but not we're not just saying 5 we're saying 5 tens so 5 10 times 8 is going to be 40 tens or it's going to be 400 another way to think about it 5 times 8 is 40 but we're not talking about 5 we're going about 5 tens so it's going to be 40 tens so 50 times 8 is 400 and then 6 times 8 is of course equal to 48 so this is going to be equal to 400 448 and this is actually how I do things in my head when I do it in my head I have to see I'm not writing things down like this but I think okay 56 56 times 8 I could break that up into 50 and six and eight times 50 well that's four hundred or forty tens you could say eight times five tens is going to be 40 tens or four hundred and then eight times six is going to be 48 so it's going to be four hundred plus 48 once you get some practice you're going to be able to do things like things like this in your head and if it helps we can also visualize this looking at an area of a rectangle so imagine this rectangle right over here and let's say that let's say that this dimension right over here is eight it is eight units tall so that's the eight and this entire dimension this entire length this entire length here is 56 so the area of this rectangle is going to be 56 times 8 which is what we set to figure out and to do that what we could break it up into is 50 and 6 so this first section right over here this first section right over here this has length we could say this has length 50 that has length 50 and then the second section this has length 6 this has length 6 and the reason why we broke it up this way is because we can maybe in our heads or without too much work figure out what 8 times 50 is and then separately figure out what 8 times 6 is so separately figure out the areas of these two pieces of the big rectangle and then add them together so what's 8 times 5 tens well it's going to be 40 tens or 400 this is going to be 400 square units it's going to the area of this yellow part and then what's 8 times 6 well we know that's going to be 48 square units so the entire rectangle is going to be the eight times the 50 or the 50 times the 8 the 400 this area the yellow area plus the magenta area plus the 8 times the 6 the 48 which is 448 448 is going to be the area of the whole thing 8 times 56