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# Multiplication by Ones (Speed Math)

This method can be used to multiply any number by $11, 111,$ etc. It can be divided into two cases, as explained below. (Note: speed math calculator can be used to practise problems using this method.)

## Case 1: Number of Digits < Number of Ones

### Example: Calculate 57 × 111

Number of digits in $57$ is less than number of digits in $111.$ Therefore, write $57$ as $057$ by making number of digits equal.

 057Take last digit. 7 057Take last 2 digits.5+7=12.That is, 2 with carry 1. carry=127 057Take last 3 digits.0+5+7=12.12 plus carried 1 is 13.That is, 3 with carry 1. carry=1327 We have taken up to 3 digits, equal to the count of ones in 111. Now start taking 3 digits each by moving left successively. 057Moving further, we have only 2 digits remaining and take those.0+5=5.5 plus carried 1 is 6. 6327 057Take remaining digit. 06327

Answer $=06327$

### Example: Calculate 476 × 11111

Number of digits in $476$ is less than number of digits in $11111.$ Therefore, write $476$ as $00476$ by making number of digits equal.

 00476Take last digit. 6 00476Take last 2 digits.7+6=13.That is, 3 with carry 1. carry=136 00476Take last 3 digits.4+7+6=17.17 plus carried 1 is 18.That is, 8 with carry 1. carry=1836 00476Take last 4 digits.0+4+7+6=17.17 plus carried 1 is 18.That is, 8 with carry 1. carry=18836 00476Take last 5 digits.0+0+4+7+6=17.17 plus carried 1 is 18.That is, 8 with carry 1. carry=188836 We have taken up to 5 digits, equal to the count of ones in 11111. Now start taking 5 digits each by moving left successively. 00476Moving further, we have only 4 digits remaining and take those.0+0+4+7=11.11 plus carried 1 is 12.That is, 2 with carry 1. carry=1288836 00476Take remaining 3 digits.0+0+4=4.4 plus carried 1 is 5. 5288836 00476Take remaining 2 digits.0+0=0. 05288836 00476Take remaining digit. 005288836

Answer $= 005288836$

## Case 2: Number of Digits ≥ Number of Ones

### Example: Calculate 12 × 11

 12Take last digit. 2 12Take last 2 digits.1+2=3. 32 12Take remaining digit. 132

Answer $= 132$

### Example: Calculate 752 × 111

 752Take last digit. 2 752Take last 2 digits.5+2=7. 72 752Take last 3 digits.7+5+2=14.That is, 4 with carry 1. carry=1472 We have taken up to 3 digits, equal to the count of ones in 111. Now start taking 3 digits each by moving left successively. 752Moving further, we have only 2 digits remaining and take those.7+5=12.12 plus carried 1 is 13.That is, 3 with carry 1. carry=13472 752Take remaining digit.7 plus carried 1 is 8. 83472

Answer $= 83472$

### Example: Calculate 1257 × 1111

 1257Take last digit. 7 1257Take last 2 digits.5+7=12.That is, 2 with carry 1. carry=127 1257Take last 3 digits.2+5+7=14.14 plus carried 1 is 15.That is, 5 with carry 1. carry=1527 1257Take last 4 digits.1+2+5+7=15.15 plus carried 1 is 16.That is, 6 with carry 1. carry=16527 We have taken up to 4 digits, equal to the count of ones in 1111. Now start taking 4 digits each by moving left successively. 1257Moving further, we have only 3 digits remaining and take those.1+2+5=8.8 plus carried 1 is 9. 96527 1257Take remaining 2 digits.1+2=3. 396527 1257Take remaining digit. 1396527

Answer $= 1396527$

### Example: Calculate 1245 × 11

 1245Take last digit. 5 1245Take last 2 digits.4+5=9. 95 1245Take next 2 digits.2+4=6. 695 1245Take next 2 digits.1+2=3. 3695 1245Take remaining digit. 13695

Answer $= 13695$

### Example: Calculate 2573 × 111

 2573Take last digit. 3 2573Take last 2 digits.7+3=10.That is, 0 with carry 1. carry=103 2573Take last 3 digits.5+7+3=15.15 plus carried 1 is 16.That is, 6 with carry 1. carry=1603 We have taken up to 3 digits, equal to the count of ones in 111. Now start taking 3 digits each by moving left successively. 2573Take next 3 digits.2+5+7=14.14 plus carried 1 is 15.That is, 5 with carry 1. carry=15603 2573Moving further, we have only 2 digits remaining and take those.2+5=7.7 plus carried 1 is 8. 85603 2573Take remaining digit. 285603

Answer $= 285603$ Himanshu
2015-09-11 03:09:34
i didn't get ans. of this
938*111 pls solve 0 0 reply Raj
2015-09-11 11:32:38
938*111

9  (9+3)  (9+3+8)  (3+8)  8

9  (2, c=1)  (0, c=2)  (1, c=1)  8

10  4  1  1  8

i.e., 104118 0 0 tejaswini
2015-08-22 08:31:27
by using the above method i need the answer for
6752×111 0 0 reply jay
2015-08-25 21:43:11
6752×111

6 (6+7) (6+7+5) (7+5+2) (5+2) 2
6 3(c=1) 8(c=1) 4(c=1) 7 2
7 4 9 4 7 2

Ans is 749472 0 0 Jay
2014-06-08 10:50:51
3rd examples answer is wrong as 1257*111=139527....so is der any fault in d method with 4 digit no or der is any other method 2 solve it 0 0 reply s
2014-09-02 05:02:54

Calculate is for  1257 * 1111 not  1257 * 111 0 0 hemant
2014-06-11 16:38:03
see here is another method

1257+12570+125700 ---- add one zero from the second digit of 111

suppose 11111*1257 ---- add those numbers

1257+12570+125700+1257000+12570000 ---- add one zero from the second digit of 11111 0 0 Jay
2014-06-10 10:22:49
3rd example is 1257 * 1111 = 1396527 which is correct 0 0 san
2014-03-07 03:47:31
1. 19385679*1111=?(how to solve 0 0 reply Jay
2014-03-07 20:24:28
19385679*1111

1    1+9         1+9+3     1+9+3+8   9+3+8+5   3+8+5+6  8+5+6+7  5+6+7+9  6+7+9    7+9         9
1     10             13           21           25              22           26               27         22           16           9
1     (c=1) 0    (c=1) 3    (c=2)1    (c=2) 5       (c=2) 2     (c=2) 6       (c=2) 7  (c=2)2     (c=1) 6    9
1+1   0+1        3+2          1+2        5+2          2+2            6+2            7+2        2+1          6         9
2       1             5              3             7               4                8                9            3            6        9 0 0