In my blog relating to Fun with numbers,I mentioned about cyclic number 142857.When you multiply this number with 2,3,4,5 and 6,you will get 285714,428571,571428,714285 and 857142 with the digits readjusting their places but following the same pattern left to right.When you multiply the number with 7 you will get 999999.
It is easy to remember /realise the correct answer by remembering what should be last digit in each case.i.e when you multiply with 6,you must have 2 as the last digit because 6 times 7(the last digit in 142857) is 42.etcetc.
Now let me tell you a calculation trick using these results.One will be able tell immediately or in the beginning a few minutes later what the result will be when you multiply the number say with 16 or,345.or 6305 or any other number.
In fact the results are 2285712,.....49285665 900713385....Let me explain how these results become easy to find.
As you get 999999 by multiplying with 7 viz 'one million less one' you should get 2 million less 2 when multiplying with 14,....8 million less 8 when multiplying with 56 (which is 8 times 7) etc etc.
Now as 16 equals 14 plus 2 (viz 2 times 7 plus 2),you can find the results of multiplication with 14 and 2 and add them together for getting what the result should be when multiplying with 16.viz it should be 2 million less 2 plus 285714 i.e 2285714 less2 i.e 2285712 as mentioned earlier by me.
Similarly for 345 you will notice by dividing it with7 that it is 49 times 7 plus 2,So the result of multiplication with 345 is obtained by adding the results of multiplication with 49 times 7 and the result of multiplication with2 viz it is 49 million less 49 plus 285714 viz 49285714 less 49 viz it is 49285665 as mentioned by me.
For 6305 you can see that it is 900 times 7 plus 5 so the result should be 900 million less 900 plus 714285 viz it is 900714285 less 900 i.e 900713385 as mentioned by me.
The calculations would seem to be difficult for a beginner but by practicing with smaller numbers first one can easily master the technique.
The result of multiplication with say 23641286 will be 3377326 million less 3377326 plus 571428 viz 3377323194102.
Read the complete process a couple of times to get yourself familiarised with the technique. .....
It is easy to remember /realise the correct answer by remembering what should be last digit in each case.i.e when you multiply with 6,you must have 2 as the last digit because 6 times 7(the last digit in 142857) is 42.etcetc.
Now let me tell you a calculation trick using these results.One will be able tell immediately or in the beginning a few minutes later what the result will be when you multiply the number say with 16 or,345.or 6305 or any other number.
In fact the results are 2285712,.....49285665 900713385....Let me explain how these results become easy to find.
As you get 999999 by multiplying with 7 viz 'one million less one' you should get 2 million less 2 when multiplying with 14,....8 million less 8 when multiplying with 56 (which is 8 times 7) etc etc.
Now as 16 equals 14 plus 2 (viz 2 times 7 plus 2),you can find the results of multiplication with 14 and 2 and add them together for getting what the result should be when multiplying with 16.viz it should be 2 million less 2 plus 285714 i.e 2285714 less2 i.e 2285712 as mentioned earlier by me.
Similarly for 345 you will notice by dividing it with7 that it is 49 times 7 plus 2,So the result of multiplication with 345 is obtained by adding the results of multiplication with 49 times 7 and the result of multiplication with2 viz it is 49 million less 49 plus 285714 viz 49285714 less 49 viz it is 49285665 as mentioned by me.
For 6305 you can see that it is 900 times 7 plus 5 so the result should be 900 million less 900 plus 714285 viz it is 900714285 less 900 i.e 900713385 as mentioned by me.
The calculations would seem to be difficult for a beginner but by practicing with smaller numbers first one can easily master the technique.
The result of multiplication with say 23641286 will be 3377326 million less 3377326 plus 571428 viz 3377323194102.
Read the complete process a couple of times to get yourself familiarised with the technique. .....
Wow thatha, you are making it sound simple, but you got to be a genius to come up with this technique.
ReplyDelete