The Trachtenberg Speed Math System provides a simple method and a fast method of long division both different from the traditional long division method you were or are being taught at school.
Simple Long Division
The first method is for those who just don't get the normal long division and it seems just too hard. It requires very little mathematical skill, as long as you can add two numbers together and do simple subtraction you have all the skills required. This Simple Long Division is very simple and is a very easy method to remember. If you also use the error checking as you go it is almost foolproof.
Granted it is not the fastest way to do long division but it will get you the answer. Although it is not very fast it is likely to be faster than the conventional long division if your math skills are lacking.
Fast Long Division
The second method is for those who are adept at math or have at least some interest in math. This is a very different method of doing long division and once learnt is faster than the conventional method.
Unlike multiplication when doing the long division you are approximating the answer as you go and there will be times that you have "guessed" to high or too low and need to back track slightly to adjust. This is not as difficult as it sounds and there are obvious signs to look out for as you progress.
Once you finish the long division a good habit to get into is to use one or both of the casting methods to check and double check your results.
There is also an article where we discuss several methods of division, mainly using one or two digit divisors, so you can compare how the Trachtenberg division compares against the conventional long division as well as a Vedic long division method. For good measure we also have a quick look at short division. You can read further in How to do Division.