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I've written the same
subtraction problem twice.

Here we see we're
subtracting 172 from 629.

And all I did here is I
expanded out the numbers.

I wrote 629 as 600 plus 20
plus 9, and I rewrote 172,

the one is 100.

So that's there.

This is 7/10.

It's in the tens
place, so it's 70.

And then the 2 is 2 ones,
so it just represents 2.

And we'll see why this
is useful in a second.

So let's just start
subtracting, and we'll

start with the ones place.

So we have 9 minus 2.

Well, that's clearly just 7.

And over here we could
also say, well, 9 minus 2,

we have the
subtraction out front.

That is going to be 7.

Pretty straightforward.

But then something
interesting happens

when we get to the tens place.

We're going to try to
subtract 2 minus 7,

or we're going to try
to subtract 7 from 2.

And we haven't learned
yet how to do things

like negative numbers, which
we'll learn in the future,

so we have a problem.

How do you subtract a larger
number from a smaller number?

Well, luckily we have
something in our toolkit called

regrouping, sometimes
called borrowing.

And that's why this is valuable.

When we're trying to
subtract a 7 from a 2,

we're really trying to
subtract this 70 from this 20.

Well, we can't subtract
the 70 from the 20,

but we have other
value in the number.

We have value in
the hundreds place.

So why don't we take 100 from
the 600, so that becomes 500,

and give that 100
to the tens place?

If we give that 100 to the tens
place, what is 100 plus 20?

Well, it's going to be 120.

So all I did, I didn't
change the value of 629.

I took 100 from
the hundreds place

and I gave it to the tens place.

Notice 500 plus 120
plus 9 is still 629.

We haven't changed the value.

So how would we do
that right over here?

Well, if we take 100
from the hundreds place,

this 600 becomes
a 5, 500, and we

give that hundred
to the tens place,

it's going to be 10 hundreds.

So this will now become a 12.

This will now become a 12.

But notice, this 12 in the
tens place represents 12 tens,

or 120.

So this is just another
way of representing

what we've done here.

There's no magic here.

This is often called borrowing,
where you say hey, I took a 1

from the 6, and I
gave it to the 2.

But wait, why did
this 2 become a 12?

Why was I able to add 10?

Well, you've added
10 tens, or 100.

You took 100 from here, so
600 became 500, and then 20

became 120.

But now we're ready to subtract.

12 tens minus 7 tens is 5 tens.

Or you could say
120 minus 70 is 50.

And then finally, you
have the hundreds place.

5 minus 1 is equal to 4, but
that's really 500 minus 100

is equal to 400.

500 minus 100 is equal to 400.

And so you get 457, which
is the same thing as 400

plus 50 plus 7.