Why carrying works

Now, let's do the exact
same addition problem

that we did in the last video.

But I'm going to expand out
these numbers so that we really

understand what's
going on when we're

doing all of this carrying.

So this 5 is in
the hundreds place.

So it really represents
5 hundreds or 500.

3 represents 3 tens because
it is in the tens place.

So it represents 30.

And the 6, well, it just
represents 6 ones or 6.

Likewise, this 3 represents 300.

This 9 is 9 tens or 90.

And this 8 just
represents 8 ones or 8.

And now we can add these two up.

Now let's start in the
right-most column-- this ones

column.

6 plus 8, we've
already figured out,

is equal to 14, which is
the same thing as 10 plus 4.

So let's write the
part that's not

a multiple of 10 in
this ones column.

So let's put that 4 there.

And the part that
is a multiple of 10,

we can now carry into
this tens column.

And that's just to keep track
of it-- just to make sure

that we don't lose
that 10, we're

putting it into the tens column.

Now we can add all the tens.

10 plus 30 plus 90, we've
already figured out is 130.

Well the part that is
not a multiple of 100,

we can write in this tens
column-- so the 30 part.

And then the part that
is a multiple of 100,

we can put in the
hundreds column.

So we could put the
100 right over here.

Notice, we've just
carried the 1.

But essentially, we've carried
100, because we put a 1

in the hundreds place.

10 plus 30 plus
90 is 100 plus 30.

This is equal to 100 plus 30.

That's all we've done.

Now we can add the hundreds.

100 plus 500 plus 300 we've
already figured out is 900.

So we can write it as 900.

And we're done!

We've figured out that
500 plus 30 plus 6,

plus 300 plus 90 plus 8, is
equal to 900 plus 30 plus 4,

which is the same thing as 934.

So hopefully this gives
you a little bit more sense

of what we're doing when we
"carry the 1" every time.

6 plus 8 is 14.

We carried the 1.

That 1 represents 10.

It represents this
10 right over here.

Just so we don't
lose track of it.

Then we say that 10 plus
30 plus 90 is equal to 130.

So that's 30 plus 100.

Then we add the hundreds
together and we get 900.