Multiplying number with 12
- Add zero on both side in multiplicand. eg : 67 => 0670
- now take 2 digits from left and multiply first digit with 2 and than add the second digit to it.
First two digits 0 and 6, so 0*2+6 = 6
Last Two digits 7 and 0 , so 7 * 2 + 0= 14
- Intermediate answer obtained is 6/19/14
- Now 1 from 19 is added to 6 as carry and 1 from 14 is added to 9 as carry , to give 7/10/4, now again 1 from 10 is added to previous digit 7 .Thus final answer is 804
similarly for 13 upto 19 we can find out products easily with only a single change instead of multiplying first digit with 2 multiply it with 3 if multiplier is 13 , 4 if 14 and so on upto 19
Examples :Multiplication with 12
231 * 12 = 2 7 7 2
write 0 2 3 1 0
assume 0 at end and start of number .
2 = 0*2+2(0,2 and multiplied with 2 as 12 is multiplier )
7 = 2*2 +3
7= 2*3 +1
2 = 2*1 + 0
Answer : 2772
another example
984 x 12 = 11808
09840
0*2+ 9= 9
9*2 +8=26
8*2+4=20
4*2+0=8
9 26 208
+ +
Answer : 11808
95432 x 12 = 1145184
0 9 5 4 3 2 0
0*2+9=9
9*2+5=23
5*2+4=14
4*2+3=11
3*2+2=8
2*2+0=4
9 23 14 1184
+ + +
1145184
Examples :Multiplication with 13 :
487 x 13 = 63128
04870
0*3+4=4(0,4 and 3 is used for multiplication as multiplier is 13)
4*3+8=20
8*3+7=31
7*3+0=21
Answer : 6331
similarly for others :
| multiplier | digit used to multiply |
| 14 | 4 |
| 15 | 5 |
| 16 | 6 |
| 17 | 7 |
| 18 | 8 |
| 19 | 9 |
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