TRECHTENBERG

Trachtenberg Speed Math 

Jwww.socialhapp.blgspot.comakow Trachtenberg spent years in a Nazi concentration camp and to escape the horrors he found refuge in his mind developing these methods. Some of the methods are not new and have been used for thousands of years. This is why there is some similarity between the Trachtenberg System and Vedic math for instance. However, Jackow felt that even these methods could be simplified further. Unlike Vedic math and other systems like Bill Handley's excellent Speed Math where the method you choose to calculate the answer depends on the numbers you are using, the Trachtenberg System scales up from single digit multiplication to multiplying with massive numbers with no change in the method.

The Trachtenberg Speed System of Basic Math can be taught to children once they can add and subtract. They do not need to have learned the multiplication tables before being able to multiply using this system. The basic multiplication method taught in this system is ideal for children and for adults who feel they are poor at multiplying. The rules are easy to learn and it does not take much practice to become proficient.

Once a child or adult is comfortable with the multiplication tables there is the direct method of multiplication. When multiplying a two digit number by a two digit number, and also when squaring two digit numbers, the Trachtenberg System makes use of binomial expansion to make the calculation easier and faster than the more traditional method of multiplication.

A two digit number, say 43 can be split into .
To generalize this for any two digit number we can replace the numbers with letters.
If we replace  with  and the  with  we get .
Squaring this number we can represent as 
If we multiply this two digit number with another, which we can represent as  then it becomes 

Binomial Expansion of 

  

Binomial Expansion of 

  

The methods for squaring two digit numbers and multiplying a two digit by two digit number make use of the expanded equations to create the rules you follow to do the calculation.

Don't be alarmed if you do not yet understand this very, very short explanation you do not need to know this to use the method but be assured what you are doing is solid math that always works and not a trick that may work in only some cases.

Once you start using the direct method of multiplication you find that the numbers you are having to mentally add up can get quite large and the totals also can run into several digits when multiplying by numbers with three or more digits. Jakow Trachtenberg also realized this and again he wondered if there was a way to make this easier. There was, and it is the masterpiece of the Trachtenberg System, it is the tens and unit method of multiplication. The tens and unit method is also referred to as the two finger method as you can use two fingers to help keep track of the calculation as you go along.

The calculation only uses only either the unit digit or the tens digit from a two digit result from multiplying two one digit numbers together. This greatly reduces the size of the numbers you are having to add up in your head.
Once learnt the two finger method will allow you to multiply any two numbers together and simply write the answer down as you mentally solve the equation.