consider any digit number may it be 1,2,3,4,5 or beyond that, the trick for multiplying it with 11 remains same.
49*11=4 (4+9) 9 =>4(13)9 =>(4+1) 3 9 =539
here the first and last digit of the answer is the first and last digit of the number to be multiplied by 11 ie 49
so the first digit of the answer is 4 and the last digit is 9. In this case and the middle term is obtained by adding the first and last digit ie (9+4). As here the answer of 9+4 is 13 so 1 is considered as carry to the number before 1 ie 4. Thus it is added to 4 and answer obtained is 539.
for 3 digit number, the trick is same
394*11= 3 (9+3) (4+9) 4 =>3(12)(1 3)4 => 3 (1 2+1) 3 4 => 3(13)34=>(3+1)334=>4334
here as it is three digit number there are two middle terms.
- consider any 2 digit number say 49
49*11=4 (4+9) 9 =>4(13)9 =>(4+1) 3 9 =539
here the first and last digit of the answer is the first and last digit of the number to be multiplied by 11 ie 49
so the first digit of the answer is 4 and the last digit is 9. In this case and the middle term is obtained by adding the first and last digit ie (9+4). As here the answer of 9+4 is 13 so 1 is considered as carry to the number before 1 ie 4. Thus it is added to 4 and answer obtained is 539.
for 3 digit number, the trick is same
- consider any number say 394
394*11= 3 (9+3) (4+9) 4 =>3(12)(1 3)4 => 3 (1 2+1) 3 4 => 3(13)34=>(3+1)334=>4334
here as it is three digit number there are two middle terms.
- Here first and the last digit are 3 and 4 respectively
- First middle term i.e. (4+9) in this case
- The second middle term, in this case, is (9+3)
- Always start adding from last to first.
- Carry of the first middle term is forwarded to second middle term ie 1 of 13 is carry forwarded to 12 in this case.
- The carry of the second middle term is forwarded to first term ie 1 of 12 to 3 in this case.
The logic remains same for any number of any length.
Take multiplier 111 even than logic is same only the addition of three digits is to be done instead of 2
946 *111
0094600
0+0+9=9
0+9+4=13
9+4+6=19
4+6+0=10
6+0+0=6
9 13 19 106
+ + +
Answer - 105006
similarly, multiplication with the other numbers such as 1111 or such are done similarly only change is addition takes place of digit equal to the length of the multiplier.
Take multiplier 111 even than logic is same only the addition of three digits is to be done instead of 2
946 *111
0094600
0+0+9=9
0+9+4=13
9+4+6=19
4+6+0=10
6+0+0=6
9 13 19 106
+ + +
Answer - 105006
similarly, multiplication with the other numbers such as 1111 or such are done similarly only change is addition takes place of digit equal to the length of the multiplier.