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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.

057
Take last digit.
7
057
Take last 2 digits.
5+7=12.
That is, 2 with carry 1.
carry=127
057
Take 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.
057
Moving further, we have only 2 digits remaining and take those.
0+5=5.
5 plus carried 1 is 6.
6327
057
Take 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.

00476
Take last digit.
6
00476
Take last 2 digits.
7+6=13.
That is, 3 with carry 1.
carry=136
00476
Take last 3 digits.
4+7+6=17.
17 plus carried 1 is 18.
That is, 8 with carry 1.
carry=1836
00476
Take last 4 digits.
0+4+7+6=17.
17 plus carried 1 is 18.
That is, 8 with carry 1.
carry=18836
00476
Take 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.
00476
Moving 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
00476
Take remaining 3 digits.
0+0+4=4.
4 plus carried 1 is 5.
5288836
00476
Take remaining 2 digits.
0+0=0.
05288836
00476
Take remaining digit.
005288836

Answer $= 005288836$

Case 2: Number of Digits ≥ Number of Ones

Example: Calculate 12 × 11

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

Answer $= 132$

Example: Calculate 752 × 111

752
Take last digit.
2
752
Take last 2 digits.
5+2=7.
72
752
Take 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.
752
Moving 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
752
Take remaining digit.
7 plus carried 1 is 8.
83472

Answer $= 83472$

Example: Calculate 1257 × 1111

1257
Take last digit.
7
1257
Take last 2 digits.
5+7=12.
That is, 2 with carry 1.
carry=127
1257
Take last 3 digits.
2+5+7=14.
14 plus carried 1 is 15.
That is, 5 with carry 1.
carry=1527
1257
Take 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.
1257
Moving further, we have only 3 digits remaining and take those.
1+2+5=8.
8 plus carried 1 is 9.
96527
1257
Take remaining 2 digits.
1+2=3.
396527
1257
Take remaining digit.
1396527

Answer $= 1396527$

Example: Calculate 1245 × 11

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

Answer $= 13695$

Example: Calculate 2573 × 111

2573
Take last digit.
3
2573
Take last 2 digits.
7+3=10.
That is, 0 with carry 1.
carry=103
2573
Take 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.
2573
Take next 3 digits.
2+5+7=14.
14 plus carried 1 is 15.
That is, 5 with carry 1.
carry=15603
2573
Moving further, we have only 2 digits remaining and take those.
2+5=7.
7 plus carried 1 is 8.
85603
2573
Take remaining digit.
285603

Answer $= 285603$

Comments(19)

profileHimanshu
2015-09-11 03:09:34 
i didn't get ans. of this
938*111 pls solve
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profileRaj
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
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profiletejaswini
2015-08-22 08:31:27 
by using the above method i need the answer for
6752×111
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profilejay
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
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profileJay
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
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profiles
2014-09-02 05:02:54 

Calculate is for  1257 * 1111 not  1257 * 111

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profilehemant
2014-06-11 16:38:03 
see here is another method

111*1257 --- add those numbers

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
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profileJay
2014-06-10 10:22:49 
3rd example is 1257 * 1111 = 1396527 which is correct
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profilesan
2014-03-07 03:47:31 
  1. 19385679*1111=?(how to solve
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profileJay
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

ie 21537489369 is the answer
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