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
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:
Start with 7,698
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.