Saturday, September 8, 2012

Quick Multiplication

My nephew, Harsh, who is in class three has taught me a quick multiplication method which is in form
999....99*any number.
For example multiply a random number, say 27689878 with 99999999 in following manner.
Write down the number just before of the selected random number and then thereafter write down the difference of the number one by one i.e (9-2), (9-7), (9-6), (9-8), (9-9), (9-8), (9-7), (10-8).
It will constitute the product of the required random number.
So
         99999999*27689878 = 2768987772310122, where 27689877 is the number just before of the selected random number and thereafter 7 is the difference of 9and 2; 2 is the difference between 9 and 7; 3 is difference between 9 and 6 and so on and in the last 2 is the difference between 10 and 8.

Multiply 999 with 27.
999*27 = 26(9-0)(9-2)(10-7)
             = 26973.
Another example.
Multiply 9999 with 267.
9999*267 = 266(9-0)(9-2)(9-6)(10-7)
                 = 2669733.
Multiply 99999 with 54321.
99999*54321 = 54320(9-5)(9-4)(9-3)(9-2)(10-1)
                       = 5432045679.