# Long Division - Organised 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 units.

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

 1,000 x 6 = 6,000 too small 2,000 x 6 = 12,000 too big

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:

 1,100 x 6 = 6,600 too small 1,200 x 6 = 7,200 too small 1,300 x 6 = 7,800 too big

So, somewhere between 1,200 and 1,300. Let's move on to the tens:

 1,210 x 6 = 7,260 too small 1,220 x 6 = 7,320 too small 1,230 x 6 = ...

Stop! It is getting to be very tedious doing all this long multiplying ...

...there should be a simpler way

Backtrack:

We already know that 1,200 lots of 6 is close, so why don't we just reduce 7,698 by that:

7,698 - 6 × 1,200 = 7,698 - 7,200 = 498 left to solve

That's better, it gets easier the more you work at it!

So, where were we? That's right, working on the tens, but aiming for 498 now:

 10 x 6 = 60 too small 20 x 6 = 120 too small ... 80 x 6 = 480 too small 90 x 6 = 540 too big

So, 8 lots of ten.

We can now further reduce the question:

498 - 480 = 18 left to solve

Aiming for 18 now:
 1 x 6 = 6 too small 2 x 6 = 12 too small 3 x 6 = 18 BINGO!

We did it.

So what did we do? We had 1 lot of a thousand, 2 hundreds, 8 tens and 3 units = 1,283.

Better just test it out:

 1,283 x 6 = 7,698 ... YES!

So the moral of the story is:

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

## Let's try that again, but neatly:

 Thousands 1,000 x 6 = 6,000 too small 2,000 x 6 = 12,000 too big

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

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

 Hundreds 100 x 6 = 600 too small 200 x 6 = 1,200 too small 300 x 6 = 1,800 too big

So the answer for hundreds is 200 x 6.

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

 Tens 80 x 6 = 480 too small 90 x 6 = 540 too big

So the answer for tens is 80 x 6

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

 Units 3 x 6 = 18 perfect!

So the answer for units is 3 x 6

Our Answer: 1,000 x 6 + 200 x 6 + 80 x 6 + 3 x 6 = 7,698, and the answer is 1,283 !

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

 What We Did: Should be Written:

And that is how you do Long Division.

Now look at this Long Division page.