# Relate place value to standard algorithm for multi-digit subtraction

## Video transcript

- [Instructor] What we're
going to do in this video is get some practice
subtracting multi-digit numbers I'm going to use 1000
minus 528 as our example. But really to understand
different methods and how they all fit together, why
it actually makes sense. So if you wanted to visualize
what this difference means, imagine something
that has a length of 1000 some type of units, so it's
length right over here is 1000 and we were to take away 528 from that. So 528 from that is what
we take away and so this difference would be well
what do we have left over. So this is equal to question mark. And I'm going to do it two different ways. I'm going to do it using
a table with place value and I'm also going to do
it using what's sometimes called the standard method
it's the way that people often learn to subtract numbers
like this especially if we're going to have to do some removing. So I'm actually going to
do them simultaneously for your benefit, alright. So let me just write out our
table with our place values. So first of all you have your
thousands place, thousands. And let me square off
the numbers here that are in the thousands place so
that 1000 right over there, that's one in the thousands place. Then you have your hundreds
place, hundreds place, and this number I have zero
hundreds right now here I have five hundreds. And then you have your
tens place, tens, zero tens right there in the tens place,
two tens right over there. And then of course you
have your ones place. Here I have zero ones,
here I have eight ones. Now let me also rewrite these
numbers and I'm going to do it using the standard method. So I have 1000 and then
I have zero hundreds I have zero tens and I have zero ones. And from that I am going to
subtract five hundreds, five hundreds, two tens, two tens,
and eight ones, eight ones. So let's do both of
these at the same time, make a little bit of a
table right over here. So that is my table. So let's start with what
we originally have, we have 1000 that's what we're subtracting from. Well on this table I would
just represent as that as 1000, now we want to take
five hundreds and two tens and eight ones from it, how do we do that? 'Cause right now we have no
hundreds, we have no tens, and we have no ones. And with the standard method
we have the same problem 'cause we start in the ones
place we say hey we want to take eight ones from zero
ones, similar problem here. How do we take eight ones here? Similarly we want to take
two tens from zero tens, how do we do that here and
the answer is regrouping. What we want to do is break
up this thousand and so we can start to fill in these
other categories it's like exchanging monies that's
sometimes an example used. So 1000 is how many hundreds? Well if we get rid of this
thousands I can break it up into ten hundreds, so one,
two, three, four, five, six, seven, eight, nine, ten. And so that's equivalent
of I could get rid of this 1000 or this one in the
thousands place and give myself ten hundreds. Well that starts to solve my
problem 'cause I could now take five hundreds from this,
I could take five from ten. Five hundreds from ten
hundreds, but I still have the problem in the tens
and the ones place. And so what I could do is I
could break up one of these hundreds and into ten
tens so let me do that. So I'm going to take, (mumbles)
so I'm going to take that one away and then that 100
is ten tens, one, two, three, four, five, six, seven, eight, nine, ten. And if I did that here,
well if I take away one of the hundreds I'm now going
to have nine hundreds left. Nine hundreds left, but now I
have ten, now I have ten tens. So I'm in good shape now
I can take some tens here but I still don't have any
ones, remember I want to take eight ones from here, so you
can imagine what's going on. I could take one of my tens
and that's going to give me one, two, three, four, five,
six, seven, eight, nine, ten ones and so over here I
could take away one of my tens so I'm now going to have nine
tens and I'm going to break that into ten ones, ten ones. And so now things are
pretty straightforward. What do I do? Well I can now take my eight
ones from the ten ones. So ten minus eight,
that is going to be two. How would I represent that over here? I'm going to do the subtraction
in this yellow color. I want to take away eight of
these ones, so I take away one, two, three, four, five,
six, seven, eight, and I am left with that two right over
there, that two is that two. Now I can move on to the tens place. If I have nine tens and I
take away two tens, I'm going to be left with seven, I'm going
to be left with seven tens. How would we see it over here? Well I have nine tens left
over, I'm going to take away two of them, so take a one
two and I am left with seven. Is that seven? One, two, three, four, five,
six, seven, yep that is seven tens right over there. We have two ones, seven tens
and so this seven is exactly this seven right over there same colors. I think you see where this
is going and the whole idea is not just to get the answer
but to understand how we got this answer. So in the hundreds place if I
have nine hundreds and I take away five hundreds then I'm
going to be left with four hundreds, same idea over here. I have nine hundreds, I take
away one, two, three, four five, I am going to be
left with four hundreds, this four and this four is the same. And so there you get the
general idea, with the standard method it sometimes seems
like magic of how we're regrouping things but all
we're doing is we're taking that thousand and saying
hey that's ten hundreds and then we take one of
those hundreds and we say hey that's ten tens and we take
one of those tens and we say that's ten ones and then
we are able to subtract.