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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
9,367 plus 2,459. So we can do this the exact
same way we've done in the last few videos. We start in the 1's place
or you can even think of it as the 1's column. So you're going to add the
seven 1's plus the 9 1's. So you're going to have 7
plus 9, which we hopefully know by now is 16. So what we do is we write
the 6 in the 1's place and we carry the 1. Let me switch-- if this 1 is
going to be the same thing as that 1 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 10's place. And when you write 16 you
have six 1's and one 10. If you view this as money,
what's the best way to get $16 in a world where
there weren't $5 bills? Where you only had $1
bills, $10 bills, $10 bills, and so on. Only multiples of 10. And we don't have any $5 bills. In that world you would
represent 16 as one $10 bill just like that. And then six $1 bills. So that's two $1 bills. That's two more $1 bills. And then that's two
more $1 bills. The whole reason why I'm
drawing it this way or I'm even using this analogy or drawing
the dollar bills is to show you what these places mean. When I say that this right
here is the 10's place, I'm essentially telling you how
many $10 bills do I have? If I've $16 and I'm doing it
as efficiently as I can in a world without $5 bills. I only have $1's, $10's,
and $100's and $1,000 bills and so forth. And this is the 1's. 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 is. And so when I have 7 plus 9 is
equal to 16 I say that I have six $1 bills and I
have one $10 bill. And I add that one $10
bill to everything else in the ten space. And the tens place is
essentially telling you how many-- that's the tens. I could write it like that or
I could write the 10's place. When I have 67-- 67 means
I have six $10 bills plus another seven $1's. So that's six 10's, five 10's. So I add up everything
in the tens place. So 1 plus 6 plus 5. Let me do that in a new color. 1 plus 6 plus 5 is equal
to-- 1 plus 6 is 7. 7 plus 5 is 12. So I write the 2 in the 10's
place because remember, this is twelve $10 bills because
we're in the 10's place. So I have two in the 10's place
and I put the 1-- I carried this 1 right here into
the 100's place. Because if I have twelve
$10 bills, I have $120. I have one $100 bill. And I have two $10 bills. I'll stop going to the dollar
bill analogy just 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 the left most digit up to the next column. And you just keep doing that. So let's do this
one right here. 1 plus 3 is 4. Let me write this down
in another color. 1 plus 3 plus 4. 1 plus 3 is 4. Plus 4 is 8. So 1 plus 3 plus 4 is 8. Nothing to carry. It was a one-digit number. And then finally,
I have 9 plus 2. That's equal to 11, so I
write the 1 down there. I write this 1 and then if
there was anything left here I would carry the 10's or the
other 1-- the 1 in the 10's place in 11-- I would carry it. But there's no where to
carry it to, so I write it down just like that. So 9.367 plus 2,459 is 11,826. 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 millions. Just to show you that
you can do any problem. So let's say we have 2,349,015. Let's throw a 0 in there. We have nothing in the
hundreds place there. And I want to add that to-- let
me switch colors just for fun. I want to add that to 7,--
let's put a 0 there-- 15,999. 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 5 plus 9. That's equal to 14. Write the 4 down
here, carry the 1. Then you go into
the 10's place. 1 plus 1 is 2. 2 plus 9-- let me
switch colors. 1 plus 1 is 2. 2 plus 9 is 11. Carry the 1. Now we're in the 100's 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. Now we're in the
10,000's place. 1 plus 4 is 5. And 5 plus 1 is 6. And there's nothing to carry. Now we're in the
100,000's place. 3-- we have nothing to carry,
so we just have the three 100,000's plus zero 100,000's. Well, that's just
three 300,000. And then finally, we're
in the millions place. 2,000,000 plus 7,000,000
is 9,000,000. Just like that. So this was a super
crazy number. 2,349,015 plus 7,015,999. 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 were able
to figure out that the answer is 9,365,014. So hopefully this gives
you a pretty good sense. And let me just do one more,
just to really make sure that we really understand how all of
this carrying business works. So let's do 15,999,001
plus 6,888,999. Let's just see how this
one's going to turn out. This seems like a like
a difficult problem. But once again, if we just
focus and don't get lost, we're going to get the
right answer hopefully. So 1 plus 9 is 10. Write the 0, carry the 1. 1 plus 0 plus 9 is 10. Write the 0, carry the 1. 1 plus 0 plus 9. That's 10 again. Write the 0, carry the 1. Now 1 plus 9 is 10, plus 8. 10 plus 8 is 18. Write the 8, carry the 1. 1 plus 9 is 10. Plus eight is 18. Write the 8, carry the 1. 1 plus 9 is 10. Plus 8 is 18. Write the 8, carry the 1. Now we're in the
1,000,000's place. 1,000,000 plus 5,000,000
is 6,000,000. Plus 6,000,000 is 12,000,000. Write the 200,000,000 and then
carry the 1 because 12,000,000 is 2,000,000 plus 10,000,000. 10,000,000 plus 10,000,000. This is one 10,000,000 plus
another one 10,000,000. That's 1 plus 1 is 2. And then we are done. 15,999,001 plus 6,888,999
is 22,888,000. So you just saw, we're just
doing 7 and 8 digit number additions, but you could apply
this-- if I had a number with 100 digits in it, you could
do the exact same thing. You just have to 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 one-digit
numbers, you just carry the 10's place. You just doing that and
work your way left. And if you make no errors,
you'll get the right answer.