# 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 **2**00 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**

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

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.