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Multiplication by 11 (Speed Math)

Example 1: Calculate 12 × 11

Add digits of $12$ like this

$1\quad 1+2\quad 2$

Rewrite with the sum of digits

$1\quad 3\quad 2$

answer $=132$

Example 2: Calculate 1245 × 11

Add digits of $1245$ like this

$1\quad 1+2\quad 2+4 \quad 4+5\quad 5$

Rewrite with the sum of digits

$1\quad 3\quad 6 \quad 9\quad 5$

answer $=13695$

Example 3: Calculate 472385 × 11

Add digits of $472385$ like this

$4\quad 4+7\quad 7+2 \quad 2+3\quad 3+8\quad 8+5\quad 5$

Rewrite with the sum of digits

$4\quad 11\quad 9 \quad 5\quad 11\quad \class{bd p-5}{1}3\quad 5$

In $13$ shown above, take $1$ as carry. Add this $1$ to its left neighbor number $11.$ Thus $11$ becomes $12$

$4\quad 11\quad 9 \quad 5\quad \class{bd p-5}{1}2\quad 3\quad 5$

In $12$ shown above, take $1$ as carry. Add this $1$ to its left neighbor number $5.$ Thus $5$ becomes $6$

$4\quad \class{bd p-5}{1}1\quad 9 \quad 6\quad 2\quad 3\quad 5$

In $11$ shown above, take $1$ as carry. Add this $1$ to its left neighbor number $4.$ Thus $4$ becomes $5$

$5\quad 1\quad 9 \quad 6\quad 2\quad 3\quad 5$

answer $=5196235$

Comments(44)

profileaban
2015-03-25 16:27:17 
Why it works? If you write the numbers in 2 lines (your number on top of 11) and then do a simple multlipication, you will quickly and easily see why this method works for any number no matter how large!

19*11 =

19 *
11
------
 19
19
-----
209

The more fun is playing with two numbers having all ones, like: 11111111111111111*11111111111111111
I can give you the answer without writing a single digit down, just by looking at the numbers!
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profileArkajyoti
2014-12-19 18:00:05 
these shortcuts and tricks are very important but many people read this and then forget.
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profiledreamBlitzer
2014-11-24 15:29:21 
15285966*11 = 152859660 + 15285966
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profilechetan
2014-07-02 10:47:03 
please check for 385*92  i am not getting correct answer which is 35420
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profileanu
2014-08-26 16:32:44 
these multiplications are only for 11 ,not with 92
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profilesan
2014-03-05 04:20:54 
what about using your method for below numbers

19*11=

1249*11=

we don't get proper answers when we apply your method.Pls Reply
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profileSharath
2015-03-28 17:03:38 
START FROM LEFT SIDE 
                           (9+4=13 SO KEEP 3  ADD ONE NEXT SUM)9
                                        (2+4+1=7)39
                                                    (1+2=3)739
                                                               (1)3739
                                                                 13739
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profileH.G. Moliya
2015-02-14 14:42:17 
19*11= 190+19 = 209

1249*11= 12490+1249 = 13739
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profileabc
2015-01-07 14:49:32 
19*11 as per method:
last digit of 19 is 9
neighbour of 9 is 1 add 9+1=10
 then add left part of 10 with left part of 19 i.e-1+1=2
now put all together i.e 209 similarly it follows 29*11,39*11...
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profileAlex
2014-12-27 15:03:50 
19*11
1)9
2)9+1=10=0  (carry1)
3)1+1(carry)=2
Ans: 209

1249*11=
1)9
2)9+4=13=3  (1carry)
3)4+2+1(carry)=7
4)2+1=3
5)1
Ans: 13739

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