Multiplying by two digits mentally

As a child, I was amazed at the speed some people performed some long mathematical processes.  I did not know back then that there are so many nice tricks in math.  One of my favourites is the way an individual can obtain the answer of multiplying any big number by two digits as fast as five or six seconds.  So how does it work?

The simplest one to start with is multiplying any number by 11.  I'll start with an example to simplify matters.  So what if we were asked to get the answer to the following: 45326 x 11?  All we have to do is:

1) copy the first number as it appears

2) add each two digits starting with the first one at the far left to get the numbers in the middle

3) copy the last number as it appears

Hence, the answer would be: 4(4+5)(5+3)(3+2)(2+6)6 = 498586.

You might ask, though, what would happen if the sum is larger than 10?  Simply use the idea of "carrying over".  For example, what is 318432 x 11?

318432 x 11 = 3(3+1)(1+8)(8+4)(4+3)(3+2)2

= 3(4)(9)(12)(7)(5)2

We now how to carry over the "1" from the 12 to the 9.  So the answer becomes:

34(9+1)2752 = 3502752

What happens then if we're multiplying by a two-digit number different than 11?  Same story, but all we have to keep in mind is that there is an extra step involved.  Again, it would be best to illustrate with an example:

24321 x 13 = 2[(2*3)+4][(4*3)+3][(3*3)+2][(2*3)+1](1*3)

= 2(10)(15)(11)(7)(3)

= 316173

So the only difference here is that we multiply the first number in each sum and the very last digit by the "3", which is the "1's" digit in 13 and then proceed as before!!

This trick proves that math could be not only fun, but very easy to understand!