5. Trick - More Multiplication

This trick is an extension of the previous trick. It empowers you to multiply two numbers that can be expressed as z|y and z|(10-y).

The result of multiplication of the two numbers is z(z+1)|y(10-y)

To illustrate by an example,

37 * 33 = 3(3+1)|7*3 = 1221
141 * 149 = 14(15)|1*9 = 210|09 = 21009

Hmm... what do you say? Isn't maths really a fun!

4. Trick - Squaring numbers ending in 5

The sutra (formula) that empowers me to do so at ease is "Ekadhikena Purevena", meaning by one more than the previous one.

To calculate square of any number ending in 5, say z5 is z(z+1)|25, ie, multiply z by z+1 and attach 25 next to it.

For example, 75² is:

752 = 7(7+1)|25 = 5625

Simple and powerful, isn't it? Now, let us see what goes behind it. It's simple algebra.

(10x + 5)2 = 100x2 + 100x + 25
  = 100x(x+1) + 25
  = x(x+1)|25

3. Trick - Multiplication

Today we will learn about multiplication... once again, the same trick but with a difference.

The trick that I will tell you now will give you more power. After this, you will never need to know any table more than 5x5. I call this extension as "10's complement".

10's complement of any digit x is 10 - x. In two numbers that you are multiplying, take 10's complement of any digit greater than 5 and increase the digit next to it (higher significant value) by one. Reverse this process while calculating final value. The digits whose complements are taken shall be called "barred".

Calculation with barred digits will be considered as being done with negative numbers. For example, bar-4 * 4 = bar-16 and bar-8 + 3 = bar-5.

Now, I shall demonstrate it with an example:

    478*129 = 522*131

    522
   x131
 --------
   53342
   11
 --------

  = 62342 = 61662