Fast multiplication n-digits (on certain situations)


Please note that this blog has been moved.

Now it has its own domain: mynixworld.info🙂

If you want to read the latest version of this article (recommended) please click here and I open the page for you.

I found another technique of multiplying numbers which respect the following conditions:

  • have the same number of digits
  • the first digit of both numbers is equal
  • the sum of last digit of both numbers is 10

Example for applicable numbers could be: 56 x 54, 21 x 29, 37 x 33, 112 x 118, etc.

The algorithm:

56 x 54:

  • the next ordinal number that comes after that 5 is 6; so we multiply 5×6 = 30, so we got the first two digits of our product
  • the last step is to multiply the units numbers, I mean: 6 x 4 which is 24; so 24 is the last two digits of our product

This mean that 56 x 54 = 3024.

Another example:

21 x 29:

  • the next ordinal number that comes after that 2 is 3; so we multiply 2×3 = 6, so we got the first two digits of our product
  • the last step is to multiply the units numbers, I mean: 1 x 9 which is 9; because is small than 10 we write down 09 instead of 9

This mean that 21 x 29 = 609.

Another example:

112 x 118:

  • the next ordinal number that comes after that 11 is 12; so we multiply 12×11 = 132, so we got the first two digits of our product
  • the last step is to multiply the units numbers, I mean: 2 x 8 which is 16

This mean that 112 x 118 = 13216.

When the above conditions are not meet you can still use the other method explained here and here.

About Eugen Mihailescu

Always looking to learn more about *nix world, about the fundamental concepts of arithmetic, algebra and geometry. I am also passionate about programming, database and systems administration.
This entry was posted in Algebra, Maths and tagged , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s