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## Addition and subtraction greater than 1000

# Multi-digit subtraction with regrouping twice

## Video transcript

We've got 9,601 minus 8,023. And immediately when we try to
start subtracting in our ones place, we have a problem. This 3 is larger than this 1. And we also have that
problem in the tens place. This 2 is larger than this 0. So we're going to have to
do some type of borrowing or regrouping. And so the way I like
to think about it-- I like to go to the
first place value that has something to give. Obviously, the tens
place is in no position to give anything
to the ones place. It needs things itself. And so we're going to go
to the hundreds place. And the hundreds place
has an abundance of value that it can regroup into
the tens and ones place. This 6 right over
here represents 600. So why don't we take
100 from that 600-- so then this will become
500-- and then give that 100 over to the tens place. Now, if we give 100 to
the tens place, how would I represent that
in the tens place? Well, I have zero 10's. And now I'm going to give 100. 100 is the same
thing as 10 10's. It's going to be 0 plus 100. 100 in the tens
place is just 10. So let me write it this way. So this right over here is now
going to be rewritten as 10. Now, you might be
saying, wait, wait, wait. What's going on here, Sal? You took 100 from
the hundreds place. That's why it became 500. Now, why did this
become 10 and not 100? Now remember, this is 10 10's. So this is still
representing 100. You have not changed the
value of this top number. Before, the value was
9,000 plus 600 plus 1. Now it's 9,000 plus 500 plus
100-- 10 10's is 100-- plus 1. I have not changed
the value here. Now, we're still not done yet. We don't want to just
subtract because we still have the problem
with the ones place. The ones place still
doesn't have enough value. Now, the good thing is we've
given some value to the tens place. So why don't we take
10 from the tens place? So if you have 10 10's,
and you take one 10 away, you're going to be left
with nine 10's, or 90. And then we can take that 10
and give it to the ones place So let's do that. You take that 10 we
just took from there, and you give it
to the ones place. You now have 11 here. And now we are
ready to subtract. 11 minus 3 is 8. 9 minus 2-- and this is
really 90 minus 20-- is 70. But in the tens place,
we represent that as a 7. 500 minus zero hundred is
500, represented as a 5 in the hundreds place. 9,000 minus 8,000 is 1,000. And we're done. And just to make
things really clear, I'm going to redo
this problem now but with things expanded out. So this first number is 9,000
plus 600 plus zero 10's plus 1. And this number right here,
we're subtracting 8,000. We're subtracting zero 100's. We're subtracting two
10's, which is 20. Subtracting 20. And subtracting three 1's. So I have just rewritten
this exact same statement. But the regrouping
and the borrowing is going to become a
little bit clearer now. So the same exact
thing-- we said, hey, we can't subtract the 3 from
the 1 or the 20 from the 0. But we have a lot of value
right over here in the 600. So why don't we
take 100 from that? So this becomes 500. And we give that 100
to the tens place. So this becomes 100. Notice, the value
has not changed. This is 9,000 plus
500 plus 100 plus 1. That's the same thing as
9,000 plus 600 plus 1. We've just put the value
in different places. And here we have
explicitly written 100. But when we represent it
in the tens place, 10 10's is the same thing as 100. Now, we aren't done
regrouping just yet. We want to give some
value to the ones place. So we can take 10 from the tens
place-- and this becomes a 90-- and give that 10
to the ones place. 10 plus 1 is 11. So notice, I did
the exact borrowing, the exact regrouping,
that I did here. I just represented it
a little bit different. This 500 was represented by
a 5 in the hundreds place. This 90 was represented
by a 9 in the tens place. But either way, we're
ready to subtract now. 11 minus 3 is 8. 90 minus 20 is 70. Write a plus there. 500 minus 0 is 500. And then 9,000 minus
8,000 is 1,000. And we got the same
result because 1,000 plus 500 plus 70
plus 8 is 1,578.