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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
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we've done in the last few videos.
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We start in the 1's place
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or you can even think of it as the 1's column.
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So you're going to add the 7 1's plus the 9 1's.
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So you're going to have 7 plus 9,
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which we hopefully 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
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the same thing as that 1 right there.
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And this might look like a little bit of a mystery or magic,
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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
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to get $16 in a world where there weren't $5 bills?
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Where you only had $1 bills, $10 bills,
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$100 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
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as one $10 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
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or I'm even using this analogy or drawing the dollar bills
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is to show you what these places mean.
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When I say that this right here is the 10's place,
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I'm essentially telling you
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how many $10 bills do I have?
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If I've $16 and I'm doing it
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as efficiently as I can in a world without $5 bills.
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I only have $1's, $10's, and $100's
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and $1,000's 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,
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I have 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
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I say that I have six $1 bills and I have one $10 bill.
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And I add that one $10 bill
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to everything else in the ten space.
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And the tens place is essentially telling you
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how many-- that's the tens.
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I could write it like that
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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+5 is 12
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So I write 2 in the tens place.
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Because, remember, this is twelve $10 bills.
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Right 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--
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I carried 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
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just so we can 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 2 numbers up.
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If it's a 2-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
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I would carry the 10's or the other 1--
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the 1 in the 10's place in 11-- I would carry it.
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But there's no where to carry it to,
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so I write 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
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because it's 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
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-- let me switch colors just for fun.
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I want to add that to 7 million,
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-- 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,
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but if we just focus on each of the places
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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,
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so we just have the three 100,000's
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plus zero 100,000's. Well, that's just 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
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and carrying the 2-digit numbers
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or the 2nd digit in the 2-digit numbers as necessary,
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we were able to figure out
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that the 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,
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just to really make sure that we really understand
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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.
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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.
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1 plus 0 plus 9.
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That's 10 again.
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Write the 0, carry the 1.
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Now 1 plus 9 is 10, plus 8.
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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.
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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.
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Plus 6,000,000 is 12,000,000.
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Write the 2,000,000 and then carry the 1
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because 12,000,000 is 2,000,000 plus 10,000,000.
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10,000,000 plus 10,000,000.
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This is one 10,000,000 plus another one 10,000,000.
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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,
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we're just doing 7 and 8 digit number additions,
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but you could apply this--
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if I had a number with 100 digits in it,
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you could do the exact same thing.
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You just have to start at the right,
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go each column by each column,
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and then if you end up with a two-digit answer
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when you add the two one-digit numbers,
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you just 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,
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you'll get the right answer.