Tag: vedic methods of multiplication

5555  × 9 = 5555 (10 - 1)
= 55550 - 5555
= 49995

1111  × 9 = 1111 (10 - 1)
= 11110 - 1111
= 9999

9999  × 99 = 9999 (100 - 1)
= 999900 - 9999

1111  × 9 = 1111 (10 - 1) = 11110 - 1111

9999  × 99 = 9999 (100 - 1)
= 999900 - 9999
= 989901

12345  × 99 = 12345 (100 - 1)
= 1234500 - 12345

12345  × 99 = 12345  × (100  - 1)
= 1234500 - 12345
= 1222155

9999  × 9 = 9999 (10 - 1) = 99990 - 9999

For 103^3, the base is 100 and deviation is +3. The formula is (number + 2*deviation) | (3*deviation^2) | (deviation^3), which gives (103 + 6) | (3*9) | 27 = 109 | 27 | 27 = 1092727.

The deviations from base 100 are -2, -3, and -1. The product is calculated by (98-3-1) | ((-2*-3) + (-3*-1) + (-1*-2)) | (-2*-3*-1), which is 94 | (6+3+2) | -6. Adjusting the -6 gives 94 | 11 | -6 = 94 | 10 | 94 = 941094.