Dividing by two digits example 2 | Multiplication and division | Arithmetic | Khan Academy

Let's divide 7,182 by 42.

And what's different
here is we're now

dividing by a two-digit
number, not a one-digit number,

but the same idea holds.

So we say, hey, how many
times does 42 go into 7?

Well, it doesn't really
go into 7 at all,

so let's add one
more place value.

How many times
does 42 go into 71?

Well, it goes into 71 one time.

Just a reminder, whoever's doing
the process where you say, hey,

42 goes into 71 one time.

But what we're really saying,
42 goes into 7,100 100 times

because we're putting this
one in the hundreds place.

But let's put that on
the side for a little bit

and focus on the process.

So 1 times 42 is 42,
and now we subtract.

Now, you might be able to do 71
minus 42 in your head, knowing,

hey, 72 minus 42 would be 30.

So 71 minus 42 would be
29, but we could also

do it by regrouping.

To regroup, you want to
subtract a 2 from a 1.

You can't really do that
in any traditional way.

So let's take a 10 from the
70, so that it becomes a 60,

and give that 10
to the ones place,

and then that becomes an 11.

And so 11 minus 2 is
9, and 6 minus 4 is 2.

So you get 29.

And we can bring down
the next place value.

Bring down an 8.

And now, this is
where the art happens

when we're dividing by
a multi-digit number

right over here.

We have to estimate how many
times does 42 go into 298.

And sometimes it might involve
a little bit of trial and error.

So you really just kind
of have to eyeball it.

If you make a
mistake, try again.

The way you know
you make a mistake

is, if say it goes into it 9
times, and you do 9 times 42

and you get a number larger than
298, then you overestimated.

If you say it goes into it
three times, you do 3 times 42,

you get some number here.

When you subtract, you get
something larger than 42,

then you also made a mistake,
and you have to adjust upwards.

Well, let's see if
we can eyeball it.

So this is roughly 40.

This is roughly 300.

40 goes into 300 the same
times as 4 goes into the 30,

so it's going to be roughly 7.

Let's see if that's right.

7 times 2 is 14.

7 times 1 is 28, plus 1 is 29.

So I got pretty close.

My remainder here-- notice
294 is less than 298.

So I'm cool there.

And my remainder is less
than 42, so I'm cool as well.

So now let's add
another place value.

Let's bring this 2 down.

And here we're just
asking ourselves,

how many times
does 42 go into 42?

Well, 42 goes into
42 exactly one time.

1 times 42 is 42, and
we have no remainder.

So this one luckily
divided exactly.

42 goes into 7,182
exactly 171 times.