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# Multiplying with area model: 78 x 65

CCSS.Math:

## Video transcript

I'm going to multiply 78 times 65 and a little less than standard way but hopefully it'll make some sense and you'll realize that there's multiple ways that you can multiply and this is actually the way that I multiply numbers in my head so 78 times 65 and then we're actually going to think about what the different parts of this process represent on this area model so 78 times 60 65 so I'm going to start just the way we normally start when we multiply I'm going to start with this five in this ones place and I'm going to say five times eight is 40 and instead of just writing a zero and carrying a four right over here I'm just going to write the number 40 so this was the five times the eight now I'm going to multiply the 5 times the 7 and we have to be a little bit careful here because 5 times this isn't just any 7 this is a 70 so what is 5 times 70 well 5 times 7 would be 35 so 5 times 70 is 350 so I'll write that down 350 so this does review 5 times 8 is 40 5 times 7 is 350 if you add these two together this is going to be 5 times 78 now let's go over to the 6 so let's multiply the 6 times the 8 now we have to be careful again this 6 is not just a regular 6 it's in the tens place this is a 60 60 times 8 well 6 times 8 is 48 so 60 times 8 is going to be 480 480 so it's going to be 480 and then 6 times 7 well that would be 42 but we have to be careful this is 60 times 70 so we're going to have two zeros at the end this is 4,200 not just 42 so 6 times 7 is 42 hundred 4,200 and now we can add everything together and this is a very similar process to what we do when we do the traditional method of multiplying I just made a little bit more explicit what parts are from what are from what multiplying which digits but we can add everything together in the ones place we have 0 in the tens place we have 4 plus 5 is not 9 9 plus 8 is 17 and now we can carry a 1 1 plus 3 is 4 4 plus 4 is 8 8 plus 2 is 10 carry 1 say regroup a 1 even and you have a 5 right over there so you get 5070 now I want to think about I want to visualize what was going on here using this area model so once again we had 78 so I'm going to make this vertical length represent 78 so this distance right over here this distance right over here represents the 70 that's the 70 and then we'll make this distance right over here represent the 8 let me make that a little bit cleaner so you see what I'm talking about so this distance right over here represents the 8 and we're going to multiply that times 65 so this distance right over here I it's not drawn perfectly to scale but it gives the idea this is 60 and then this distance right over here this distance right over here is the 5 so this whole distance is 65 this entire distance is 78 so when you multiply a 6 if you add a rectangle that's 68 you or 65 units wide and you multiplied it and it had a height of 78 units then its area is going to be 78 times 65 its area is going to be 5070 now each of these parts we can map to one part of this of this area model right over here when we multiplied the 5 times the 8 and got the 40 that was that was this section right over here 5 times 8 is equal to 40 when we multiplied 5 times 70 and got 350 that's this right over here 5 times 70 and we got 350 when we multiplied 60 the 6 and the tens place 60 times 8 and got 480 that's this right over here this is 60 times 8 is equal to 480 and then finally when we multiplied 60 times 70 and got 4,200 that's this area right over here this area is 60 wide detalle so this is sixty times 70 which is equal to 4200 and then when we added everything up to get 5070 we were essentially just adding up the areas of each of these tiles this big one is 4,200 that makes up most of the area then we get 480 from this magenta one then 350 from this kind of greenish yellow one and then 40 from this greenish blue one to get 5,000 70 so the area of this entire thing is 5070 square units