# Long Division Index

Long Division is easy, once you get the idea.
Hopefully some of these pages will "click" with you, and you will be a master!

## Why Long Division

The simplest way to do division is by repeated subtraction:

### Example: What is 48 / 12?

• Start with 48, subtract 12, we get 36
• Repeat: 36-12 = 24
• Repeat: 24-12 = 12
• Repeat: 12-12 = 0

We did 4 subtractions, so 48 / 12 = 4

But this could take a long time for something like 3768 / 12

### Example: What is 3768 / 12?

• Start with 3768, subtract 12, we get 3756
• Repeat: 3756-12 = 3744
• Repeat: 3744-12 = 3732
• Repeat: 3732-12 = 3720
• ... oh No! This will take a long long time!

Maybe we could do 100 subtracts in one go

• Start with 3768, subtract 100 lots of 12, we get 3768-1200 = 2568
• Repeat: 2568-1200 = 1368
• Repeat: 1368-1200 = 168

Now lets move to 10 subtracts in one go

• 168, subtract 10 lots of 12, we get 168-120 = 48

Now lets move to singles:

• 48, subtract 12, we get 36
• Repeat: 36-12 = 24
• Repeat: 24-12 = 12
• Repeat: 12-12 = 0

So we did 3 lots of 100, 1 lot of 10 and 4 single subtracts of 12, which is a total of 314 subtracts of 12

So 3768 / 12 = 314

That is the Idea behind Long Division

Long division looks like this:

0314
12 )3768
0
37
36
16
12
48
48
0

It may look a little strange at first, but can you see the "3768" near the top?

And then the "12" at its left, and the actual answer of "314" at the top.

That shows us we worked out 3768 / 12 = 314

• Now look down for the "36": That is where we tackled the 100s (3 × 12 = 36)
• And a bit below that is the "12", which is where we did the 10s (1 × 12 = 12)
• And at the bottom is the "48" (4 × 12 = 48)

So we tackled the 100s, then the 10s, then the units, just like above.

And the "0" at the bottom means that after all the subtracts there is nothing left over.

Continue on and learn how to do this yourself!

## Understanding Long Division

Long Division - Introduction

Long Division - How It Works