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Let's do a bunch more of these addition problems.

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So let's say I have 9,367 plus 2,459.

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So we can do this the exact same way we've done in

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the last few videos.

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We start in the 1's place or you can even think of

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it as the 1's column.

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So you're going to add the seven 1's plus the 9 1's.

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So you're going to have 7 plus 9, which we hopefully

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know by now is 16.

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So what we do is we write the 6 in the 1's place

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and we carry the 1.

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Let me switch-- if this 1 is going to be the same thing

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as that 1 right there.

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And this might look like a little bit of a mystery or

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magic, and the whole reason we did that is that

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this is the 10's place.

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And when you write 16 you have six 1's and one 10.

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If you view this as money, what's the best way to

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get $16 in a world where there weren't $5 bills?

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Where you only had $1 bills, $10 bills, $10

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bills, and so on.

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Only multiples of 10.

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And we don't have any $5 bills.

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In that world you would represent 16 as one $10

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bill just like that.

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And then six $1 bills.

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So that's two $1 bills.

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That's two more $1 bills.

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And then that's two more $1 bills.

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The whole reason why I'm drawing it this way or I'm even

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using this analogy or drawing the dollar bills is to show

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you what these places mean.

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When I say that this right here is the 10's place, I'm

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essentially telling you how many $10 bills do I have?

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If I've $16 and I'm doing it as efficiently as I can in

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a world without $5 bills.

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I only have $1's, $10's, and $100's and $1,000

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bills and so forth.

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And this is the 1's.

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So when I write it this way I'm literally telling you, I have

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one $10 bill and I have six $1 bills.

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That's what $16 is.

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And so when I have 7 plus 9 is equal to 16 I say that I have

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six $1 bills and I have one $10 bill.

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And I add that one $10 bill to everything

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else in the ten space.

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And the tens place is essentially telling you how

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many-- that's the tens.

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I could write it like that or I could write the 10's place.

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When I have 67-- 67 means I have six $10 bills

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plus another seven $1's.

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So that's six 10's, five 10's.

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So I add up everything in the tens place.

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So 1 plus 6 plus 5.

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Let me do that in a new color.

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1 plus 6 plus 5 is equal to-- 1 plus 6 is 7.

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7 plus 5 is 12.

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So I write the 2 in the 10's place because remember, this

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is twelve $10 bills because we're in the 10's place.

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So I have two in the 10's place and I put the 1-- I carried

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this 1 right here into the 100's place.

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Because if I have twelve $10 bills, I have $120.

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I have one $100 bill.

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And I have two $10 bills.

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I'll stop going to the dollar bill analogy just so we can

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make sure we understand the process.

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But I think you see how it works.

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You start at the right, you add the two numbers up.

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If it's a two-digit answer you carry the left most digit

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up to the next column.

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And you just keep doing that.

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So let's do this one right here.

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1 plus 3 is 4.

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Let me write this down in another color.

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1 plus 3 plus 4.

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1 plus 3 is 4.

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Plus 4 is 8.

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So 1 plus 3 plus 4 is 8.

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Nothing to carry.

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It was a one-digit number.

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And then finally, I have 9 plus 2.

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That's equal to 11, so I write the 1 down there.

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I write this 1 and then if there was anything left here I

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would carry the 10's or the other 1-- the 1 in the 10's

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place in 11-- I would carry it.

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But there's no where to carry it to, so I write

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it down just like that.

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So 9.367 plus 2,459 is 11,826.

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And I just put that comma there because it's

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easier for me to read.

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Let me do a bunch more of these.

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Let's do a really, really daunting problem.

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Let's do something in the millions.

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Just to show you that you can do any problem.

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So let's say we have 2,349,015.

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Let's throw a 0 in there.

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We have nothing in the hundreds place there.

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And I want to add that to-- let me switch colors just for fun.

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I want to add that to 7,-- let's put a 0 there-- 15,999.

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Let's add these two numbers.

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It seems like a hard problem, but if we just focus on each

108
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of the places I think you'll find that it's not too bad.

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So we start off with 5 plus 9.

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That's equal to 14.

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Write the 4 down here, carry the 1.

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Then you go into the 10's place.

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1 plus 1 is 2.

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2 plus 9-- let me switch colors.

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1 plus 1 is 2.

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2 plus 9 is 11.

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Carry the 1.

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Now we're in the 100's place.

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1 plus 0 is 1.

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Plus 9 is 10.

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So we write the 0 from the 10, carry the 1.

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Let me switch colors again.

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1 plus 9 is 10.

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10 plus 5 is 15.

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Now we're in the 10,000's place.

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1 plus 4 is 5.

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And 5 plus 1 is 6.

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And there's nothing to carry.

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Now we're in the 100,000's place.

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3-- we have nothing to carry, so we just have the three

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100,000's plus zero 100,000's.

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Well, that's just three 300,000.

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And then finally, we're in the millions place.

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2,000,000 plus 7,000,000 is 9,000,000.

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Just like that.

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So this was a super crazy number.

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2,349,015 plus 7,015,999.

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Just by keeping track of our places and carrying the

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two-digit numbers or the second digit in the two-digit numbers

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as necessary, we were able to figure out that the

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answer is 9,365,014.

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So hopefully this gives you a pretty good sense.

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And let me just do one more, just to really make sure that

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we really understand how all of this carrying business works.

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So let's do 15,999,001 plus 6,888,999.

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Let's just see how this one's going to turn out.

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This seems like a like a difficult problem.

148
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But once again, if we just focus and don't get lost,

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we're going to get the right answer hopefully.

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So 1 plus 9 is 10.

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Write the 0, carry the 1.

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1 plus 0 plus 9 is 10.

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Write the 0, carry the 1.

154
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1 plus 0 plus 9.

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That's 10 again.

156
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Write the 0, carry the 1.

157
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Now 1 plus 9 is 10, plus 8.

158
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10 plus 8 is 18.

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Write the 8, carry the 1.

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1 plus 9 is 10.

161
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Plus eight is 18.

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Write the 8, carry the 1.

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1 plus 9 is 10.

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Plus 8 is 18.

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Write the 8, carry the 1.

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Now we're in the 1,000,000's place.

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1,000,000 plus 5,000,000 is 6,000,000.

168
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Plus 6,000,000 is 12,000,000.

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Write the 200,000,000 and then carry the 1 because 12,000,000

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is 2,000,000 plus 10,000,000.

171
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10,000,000 plus 10,000,000.

172
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This is one 10,000,000 plus another one 10,000,000.

173
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That's 1 plus 1 is 2.

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And then we are done.

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15,999,001 plus 6,888,999 is 22,888,000.

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So you just saw, we're just doing 7 and 8 digit number

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additions, but you could apply this-- if I had a number with

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100 digits in it, you could do the exact same thing.

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You just have to start at the right, go each column by each

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column, and then if you end up with a two-digit answer when

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you add the two one-digit numbers, you just

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carry the 10's place.

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You just doing that and work your way left.

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And if you make no errors, you'll get the right answer.