06: MULTIPLY BY 12, 13, 14, ..., 19

SUTRA (Algorithm):

Multiply by Unit's Digit only; from Right to Left
Multiply each digit & ADD RightSide digit, if any.
Repeat for every digit ... ... Finally PUT down last (Left-most) digit.
Normal Carry-Over rule

Demonstration (1): 413 x 12 = ?

2 x 3 is 6 Result: 6
2 x 1 is 2Add Rtside digit 3Result: 56
2 x 4 is 8Add Rtside digit 1Result: 956
 Finally Left last digit 4Result: 4956
So 413 x 12 = 4956

Demonstration (2): 413 x 19 = ?

9 x 3 = 27 Carry 2Result: 7
9 x 1 = 9+ Rtside digit 3 & carried 2; Get 14Carry 1Result: 47
9 x 4 = 36+ Rtside digit 1 & carried 1; get 38Carry 3Result: 847
 Finally Left last digit 4+ carry 3Result: 7847
So 413 x 19 = 7847

Demonstration (3): 413 x 14 = ?

4 x 3 is 12; So, Carry 1; Result 2
4 x 1 is 4; + 3 + 1; Get 8. So Result 82
4 x 4 is 16; + 1; Get 17. Carry 1; Result 782
Last Left digit 4; + 1; Get 5. Result 5782.

So 413 x 14 = 5782

Demonstration (4): 2598 x 17 = ?

7 x 8 = 56; Carry 5; Result: 6
7 x 9 = 63; +8 +5 = 76 Carry 7; Result: 66
7 x 5 = 35; +9 +7 = 51 Carry 5; Result: 166
7 x 2 = 14; +5 +5 = 24 Carry 2; Result: 4166
2; = +2; = 4 Result: 44166

Verify The following, by Actual Working:

  1. 23 x 13 >> 299
  2. 23 x 18 >> 414
  3. 28 x 16 >> 448
  4. 637 x 14 >> 8 29 21 28
  5. 589 x 17 >> 10 50 71 63
  6. 3206 x 14 >> 4 14 8 8 24