Long Division - Organized Guessing

So, how does Long Division work?

It works by breaking up the big number and solving it a section at a time.

Thousands, Hundreds, ...

To illustrate, let us try guessing the answer to 7,698 ÷ 6, but following a special method.

We will start at the thousands, then move to the hundreds, then tens, then ones.

OK, starting at the thousands: How many 6 lots of a thousand can we fit into 7,698 ? Well, just one, really. Two is too much:

We have made progress of sorts. We can guess that the answer is between 1,000 and 2,000.

Now let's move onto the hundreds. Let's add a hundred at a time:

So, somewhere between 1,200 and 1,300.

Let's move on to the tens:

Stop! All this multiplying is taking too long ...

At the start, when we worked on the thousands, why not chop off what we know already?

We could chop off 1,000 x 6 = 6,000 and get:

Now (remembering we have chopped off 1,000 x 6) we can continue, but we work on 1,698 now.

Now we can take 200 x 6 = 1,200 from 1,698: 1,698 − 1200 = 498

And now we are only working on 498 ...

We can continue like this, following this idea:

Don't work on the entire number every time,
just work on whatever is left.

Let's try the whole thing from the start, working neatly:

Start with 7,698

So the answer for thousands is 1,000 x 6.

7,698 − 1,000 x 6 = 1,698 left to figure out:

So the answer for hundreds is 200 x 6.

1,698 − 200 x 6 = 1,698 - 1,200 = 498 left to figure out

So the answer for tens is 80 x 6

498 - 80 x 6 = 498 − 480 = 18 left to figure out

So the answer for ones is 3 x 6

Our Answer: 1,000 x 6 + 200 x 6 + 80 x 6 + 3 x 6 = 7,698

Which is: 1,283 x 6 = 7,698

But instead of using all those words, we write it down like this:

What We Did		Best Written
1,283  6 )7,698    -6,000     1,698    -1,200       498      -480        18       -18         0		1283  6 )7698     6     16     12      49      48       18       18        0

And that is how you do Long Division.

Now look at this Long Division page.