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:
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! All this multiplying is taking too long ...
...there should be an easier way
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:
Answer so far  Number left 
1,000 x 6 = 6,000  7,698  6,000 = 1,698 
Now (remembering we have chopped off 1,000 x 6) we can continue, but we work on 1,698 now.
Guesses  Compared to 1,698 
100 x 6 = 600  too small 
200 x 6 = 1,200  too small 
300 x 6 = 1,800  too big 
Now we can take 200 x 6 = 1,200 from 1,698: 1,6981200 = 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
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
Ones  3 x 6 = 18  perfect! 
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, and the answer is 1,283 !
Check: 1,283 x 6 = 7,698
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.