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CCSS.Math:

let's multiply six times seven thousand nine hundred and eighty one and the way we're going to do it right now is just to represent or expand out seven thousand nine hundred eighty-one as 7,000 7,000 plus 900 plus nine hundred plus 80 plus 80 plus one plus one and so multiplying six times seven thousand nine hundred eighty-one is the same thing as multiplying six times seven thousand plus six times nine hundred plus six times eighty plus six times one you would essentially distribute the 6 and to help us keep track of things let me draw a little grid right over here so this is the six and we're going to have to think about what six times 7,000 is six times nine hundred six times eighty and six times one so I'll make a little square for a rectangle for each of them let me do that so here we go and so we just need to think about what is six times 7,000 well 6 times 7 is 42 so 6 times 7,000 is 42,000 6 times 900 well once again 6 times 9 is 54 so 6 times 900 is 5,400 6 times 80 well 80 is eight tens so 6 times 8 is 48 but since it's 6 times 80 or eight tens this is going to be 48 tens or 480 and then finally 6 times one of course is equal to is equal to 6 so to find what this product is we just have to take the sum of each of these numbers what's 6 times 7,000 is plus 6 times 900 plus 6 times 80 plus 6 times 1 so let's do that right over here so it's going to be forty two thousand plus five thousand four hundred plus 480 480 plus six plus six and we get let's see in the ones place we had just have a six in the tens place we just have an eight in the hundreds place for plus four is eight and the thousands plays 2 plus 5 is 7 and then finding the ten-thousands place we still have a 4 so we get 47,000 886 this is equal to forty seven thousand 886 and what I encourage you to do is to think about how this this is really underlying what we're doing here it's not that different than what you might have done with the traditional multiplication techniques and this is a useful way of thinking about it because now you really understand what's going on and actually when you start doing things like this in your head at least for myself this is actually how I try to tackle the multiplication problem someone says six times seven thousand nine hundred eighty-one if I was just looking at this and I didn't have any paper I would say okay what's 6 times 7 thousand suni that's 42,000 I'll try to remember that what's six times nine hundred well that's five thousand four hundred well if I add that to the 42,000 I get forty-seven thousand four hundred then what's six times eight 480 you have to add that to the forty-seven thousand four hundred to get to forty seven thousand eight eighty and then what's 6 times 1 well that's six we'll add that to the forty seven thousand eight hundred eighty which I've been keeping in my brain and that's going to be forty-seven thousand eight hundred and eighty six so this helps you understand what's really going on when you multiply multiple digits and it's a useful technique for doing mental multiplication