Ekadhikena Purvena - Divide numbers in one line. Shortcut Division when Divisor Ending with 9 Sutra Used: Ekadhikena Purvena (1 more than the previous)(see more in Squares topic). Examples: 1/19 I: Method 1 (L --> R): For the denominator 19, the purva (previous) is 1. Hence Ekadhikena purva (one more than the previous) is 1 + 1 = 2. Now we will be using 2 for Division purpose. Write 1/19 as 1/20 (but remember they are not equal : )) Steps: Divide 1 by 2 which gives Quotient as 0(written with yellow) and Remainder as 1 (written on left side of Quotient with White) Now divide 10 by 2 which gives Quotient as 5(written with yellow) and Remainder as 0 (written on left side of Quotient with White) Now divide 05 by 2 which gives Quotient as 2(written with yellow) and Remainder as 1 (written on left side of Quotient with White) Similarly go on carrying this process till you find same pair of Quotient and Remainder is obtained. At the end we get 01, on dividing it by 2 we get Quotient as 0 and Remainder as 1. So that means same series (from blue dot to blue dot) will keep on repeating. So the series written in yellow color is final answer. II: Method 2 (R--> L): Here as well Ekadhikena Purvena is 2. BUT here we use 2 for multiplication purpose. Steps: (From R --> L) We start by putting 1. Multiply it 2 which gives 2. Now Multiply 2 by 2 which gives 4. Now Multiply 4 by 2 which gives 8. Now Multiply 8 by 2 which gives 16. Carry forward 1 (written in yellow). Now multipliy 6 by 2 and add the carry forward to it, gives 13. Carry Forward 1. Similarly go on carrying this process till you find same pair of Quotient and Remainder is obtained. Finally 0 will be obtained with carry forward 1. Multiplying 0 with 2 and adding carry forward gives 1 which repeats the series. So the series written in yellow color is final answer. III: Method 3 (More Shorter): Any of the above 2 methods are carried out till a certain criteria … [Read more...]