Level 4 Subtraction

Subtraction of multi-digit numbers involving borrowing

Welcome to the presentation
on level 4 subtraction.

Let's get started
with some problems.

First problem I have here
is 33,220 minus 399.

So this like we did with, I
believe,

that we also did borrowing in the level 3
subtraction,

we have to go through all of the digits in
the top number

starting with the top right digit and make
sure that

they are larger than the digit below it.

Because you can only subtract
a smaller number

from a larger number.

You can't do it the other
way, at least,

until we learn negative numbers.

So let's go through this and
check to

make sure all the top numbers are larger.

Well immediately, we see no.

Well this 0 is not
larger than 9.

So we have to borrow
to make the 0 bigger.

So what we do is we borrow
1

well some people say we're borrowing a 1.

Some people say, I mean,
borrowing a 1 from the 10's place

is really
like borrowing a 10.

So for simplicity let's just
say we're borrowing a 1.

So you borrow a 1 from this 2
and this 10

will become a,the 0 sorry, will become a 10.

And since we borrowed that
1, this 2 will become a 1.

We took 1 away from this 2 and
we gave it to the 0 to make 10.

We actually took 10 away
from this 2

because this 2's in the 10's place.

I don't want to
confuse you too much.

If just the mechanics of it are
we took 1 away from the 2

and we put it in front of
the 0 to make 10.

Now let's keep checking.

So now we have a
1 in this place.

1 is smaller than 9, so
we have to borrow again.

So we borrow 1 from this 2 now.

So this 2 now becomes 1.

And this 1 will
now become an 11.

So now we have a 10
is larger than a 9.

11 is larger than a 9.

1 is not larger than 3, so
we have to borrow again.

This is a good problem.

Maybe I should've warmed you
all up a little bit more.

It involves a lot of borrowing.

So in order to borrow we do
the same thing over again.

This 1 will become 11.

And it's going to borrow from
this 3, which will become a 2.

I think we're done now.

10 is larger than 9, 11 is
larger than 9, 11 is larger

than 3, 2 is larger than
nothing,

3 is larger than nothing.

So now we're ready to subtract.

This is the easy part.

10 minus 9 is 1.

11 minus 9 is 2.

11 minus 3 is 8.

2 minus nothing is 2.

3 minus nothing is 3.

So we get 32,821.

The only thing that makes this
harder than just normal subtraction

is that you have to
know how to do the borrowing.

And the way I do the borrowing
might be different than the way

you learned in school, but I
think it's easier

because you do all of the borrowing at once
instead of switching

back and forth between borrowing
and subtracting.

So all we did here, we said
that 0 is less than 9.

Let's borrow 1.

The 0 becomes a 10 because
we got this 1 right here.

We got this 1 from this 2
and this 2 became a 1.

I think you might see the
pattern

if we do a couple of more problems.

So let's do a couple of more.

If I had 25,633 ,let's see,minus 578.

So name drill.

Start at the top right and we
make sure that

the digits on top are larger than
the digit below it.

Immediately we see 3 is smaller
than 8, so we have to borrow.

So this 3 will become 13.

And then we borrow from this
3, which will now become 2.

We took a 1 away from this
3, it became a 2,

and this 1 is right here.

13 is now larger than 8, but
2 is now smaller than 7.

So we have to borrow again.

This 2 becomes a 12.

And this 6 will become a 5.

13 is larger than 8, 12 is
larger than 7,

5 is the same as 5, so you can actually
do the subtraction.

Because 5 minus 5 is 0.

As long as the top number's
not smaller

than the number below it.

And then obviously this 5
is larger than this 0

and this 2 is larger than
this nothing here.

So now we're ready to subtract.

13 minus 8 is 5.

12 minus 7 is 5.

5 minus 5 is 0.

5 minus nothing is 5.

Bring down the 2.

So the answer is 25,055.

So let's do a problem now that
I think will confuse you a little bit more

because the
borrowing isn't as easy.

You have to actually borrow
from a couple places.

Let's say I had 37,002
minus-- let's say I had 155.

So the same drill.

So this 2 is less than 5,
so we have to borrow.

So this 2 will become a 12.

But huh, there's a 0 here, so
you can't borrow from the 0.

Some people will let you borrow
from the 0

but I think that just confuses things

because you can't borrow from the 0, there's nothing there.

So instead of borrowing from
the 0 we look to this 0.

Well, there's still
nothing there.

So now we look, oh,
there's a 7 here.

So what we do is instead of
borrowing a 1 from the 0,

which is hard to do, we borrow 1 from
this 700, from this whole 700.

And what is 700 minus 1?

Right, it's 699.

So that 700 becomes 699.

Cross all of this out.

And now let's check
our numbers again.

12 is larger than 5, nine is
larger than 5, 9 is larger than 1

6 is larger than nothing,
and 3 is larger than nothing,

so we're ready to subtract.

12 minus 5 is 7.

9 minus 5 is 4.

9 minus 1 is 8.

6 minus nothing is 6.

3 minus nothing is 3.

So there, we're done.

The answer is 36,847.

I think we could have time
for one more problem.

Let's say I had 3,201
minus-- let's say it's 502.

Same drill.

1 is less than 2, so
we have to borrow.

Turn that into an 11.

But you can't borrow from the
0, so you're going to

have to borrow from this entire 20.

Well, what's 20 minus 1?

Right, it's 19.

This becomes a 19.

so,lets check again

11 is greater than 2.

Check.

9 is greater than 0.

Check.

Uh-oh.

1 is not greater than 5.

So we have to borrow again.

This 1 becomes an 11.

We borrowed from this
3, which becomes a 2.

11 is greater than 2, 9 is
greater than 0, 11 is greater than 5

2 is obviously greater
than nothing below it.

So we're ready to subtract.

11 minus 2 is 9.

9 minus 0 is 9.

11 minus 5 is 6.

And 2 minus nothing is 2.

So 3,201 minus 502
is equal to 2,699.

I think you're now ready to

try some of the level 4 subtraction problems.

You just always have to
remember,

do you're borrowing first.

Make sure all the numbers on
top are larger than,

or at least as large as all the
numbers on the bottom.

And then you can just do your
subtraction

like a normal subtraction problem.

I hope you have some
fun doing this.

Talk to you later.