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# Multi-digit addition with regrouping

## Video transcript

let's do a bunch more of these addition problems so let's say I have nine thousand three hundred and sixty seven plus two thousand four hundred and fifty nine so we can do this the exact same way we've done in the last few videos we start in the ones place or you can even think of it as the ones column so you're going to add the seven ones plus the nine ones so you have 7 plus 9 which we hopefully know by now is 16 so what we do is we write the 6 in the ones place and we carry the 1 so if this one we switch good if this one is going to be the same thing as that one right there and this might look like a little bit of a mystery or magic and the whole reason we did that is that this is the tens place and when you write 16 you have six ones and one 10 if you view this as money how would what's the best way to get 16 dollars in a world where there weren't five dollar bills we only had one dollar bills \$10 bills hundred-dollar bills and so on only only multiples of 10 and we don't have any \$5 bills in that world you would represent 16 as one \$10 bill 1 \$10 bill just like that and then 6 \$1 bills let me so that's 2 \$1 bills that's two more \$1 bills and then that's two more \$1 bills and so 16 is so the whole reason why I'm drawing it this way I'm even using this analogy or drawing the dollar bills so to show you what these places mean when I say when I tell you when I say that this right here is the tens place I'm essentially telling you how many 10 dollar bills do I have if I have 16 dollars and I'm doing it as I'm I'm doing it as efficiently as I can in the world without five dollar bills I only have ones tens and a hundreds and thousand dollar bills and so forth and this is the ones so when I write it this way I'm literally telling you I have one \$10 bill and I have six \$1 bills that's what 16 dollars is and so when I have 7 plus 9 is equal to 16 however I say that's I have 6 \$1 bills and I have one ten dollar bill and I add that one ten dollar bill to everything else in the ten space and the tens place is essentially telling you how Mead that's the tens I'll write it like I can write it like that or I could write the tens place that when I have 6767 means I have six \$10 bills plus another seven ones so that's six tens five tens so I add up everything in the tens place so one plus six plus five let me do that in a new color one plus six plus five is equal to one plus 6 is 7 7 plus 5 is 12 so I write the two in the tens place because remember this is 12 \$10 bills right because we're in the tens place so I have two in the tens place and then I put the one I carry this one right here into the hundreds place because if I have 12 \$10 bills I have a hundred and twenty dollars I have \$100 bill and I have two \$10 bills and I'll stop going to the dollar bill analogy because so we can make sure we understand the process but I think you see how it works you start at the right you add the two numbers up if it's a two-digit answer you carry this the the leftmost digit up to the next column and you just keep doing that so let's do this one right here one plus three is four let me write this down in another color one plus three plus four one plus three plus four one plus three is four plus four is eight so one plus three plus four is eight nothing to carry it was a one digit number and then finally I have 9 plus 2 9 plus 2 that's equal to 11 so I write the 1 down there I write this one and then if there was anything left here I would carry the the tens or the the other one the one in the tens place in 11 I would carry it but there's nowhere to carry it too so I write it down just like that so nine thousand three hundred and sixty seven plus two thousand four hundred and fifty nine is 11 thousand eight hundred and twenty six and I just put that comma there because it's easier for me to read let me do a bunch more of these let's do a really really daunting problem let's do something in the million just to show you that you can do any any problem let's say we have two million three hundred and forty nine thousand and fifteen let's start a zero in there right we have nothing in the hundreds place there and I want to add that to switch colors just for fun I want to add that to 7 million seven million let's put a zero there fifteen thousand and nine hundred and ninety nine let's add these two numbers it seems like a hard problem but if we just focus on each of the places I think you'll find that it's not too bad so we start off with five plus nine five plus nine that's equal to fourteen right the four down here carry the 1 then you go into the tens place one plus one is two two plus nine let me switch colors one plus one is two two plus nine is 11 carry the one one now we're in the hundreds place 1 plus 0 is 1 plus 9 is 10 so we write the 0 from the 10 carry the 1 let me switch colors again 1 plus 9 is 10 10 plus 5 is 15 15 now we're in the ten thousands place one plus four is five and five plus one is six and there's nothing to carry now we're in the hundred thousands place 3 we have nothing to carry so we just have the 300,000 plus zero hundred thousands well that's just three hundred thousand and then finally we're in the millions place two million plus seven million is nine million just like that so way this is a super crazy number two million three hundred forty nine thousand and fifteen plus seven million 15999 just by keeping track of our places and carrying the two-digit numbers or the second digit in the two-digit numbers as necessary we're able to figure out that the answer is nine million three hundred and sixty-five thousand and fourteen so hopefully this gives you a pretty good sense let me just do one more just to really make sure that we we really understand how all of this carrying business works so let's do fifteen million nine hundred ninety nine thousand and one plus six million eight hundred and eighty eight thousand nine hundred and ninety nine let's just see how this one's going to turn out this is this seems like a like a difficult problem but once again if we just focus and don't get lost we're going to where we're going to get the right answer hopefully so one plus nine is ten right the zero carry the 1 1 plus zero plus 9 is 10 right the zero carry the 1 1 plus 0 plus 9 that's 10 again right the zero carry the 1 now 1 plus 9 is 10 plus 8 10 plus 8 is 18 right the 8 carry the 1 1 plus 9 is 10 plus 8 is 18 right the 8 carry the 1 1 plus a 9 is 10 plus 8 is 18 right the 8 carry the 1 now we're in the millions place 1 plus 1 million plus 5 million is 6 million plus 6 million is 12 million right the 2 million and then carry the 1 because 12 million is 2 million plus 10 million 10 million plus 10 million right this is 110 million plus another 110 million right it's 1 plus 1 is 2 and then we are done 15 million nine hundred ninety nine thousand and one plus six million eight hundred and eighty eight thousand nine hundred ninety nine is 22 million eight hundred and eighty eight thousand so you know you just saw we're just doing we're doing seven and eight digit number additions but you could apply this if I had a number with a hundred digits in it you could do the exact same thing you just have to go start at the right go each column by each column and then if you end up with a two-digit answer when you add the two-digit when you add the two one digit numbers you just carry the tens place you just keep doing that and work your way left and if you make no errors you'll get the right answer