Multiplication by 11 using Speed Mathematics

In this chapter you are going to see how you can easily multiply any number with 11 .The principles in these tutorials are taken from various systems like Indian Vedic Mathematics and the German Trachtenberg System.

Example 1

Question : Calculate 12 * 11

Solution

Step 1 : The last digit of 12 is 2. Write it down as the right most digit of the answer. So we have

2

Step 2 : The last digit of 12 is 2. Its left neighbor digit is 1. Add these two. That is 2 +1 = 3. Write it as the second last digit of the answer. So we have

32

Step 3 : The left most digit of 12 is 1. Write it as the left most digit of the answer. So we have

132

This is the answer. That is 12*11 = 132

Example 2

Let's take a bigger number this time. Say we need to do 1245 * 11

Solution

Step 1: The last digit of 1245 is 5. Write it down as the right most digit of the answer. So we have

5

Step 2: The last digit of 1245 is 5. Its left neighbor digit is 4. Add these two. That is 5 +4 = 9. Write  it as the second last digit of the answer. So we have

95

Step 3: The second last digit of 1245 is 4. Its left neighbor digit is 2. Add these two. That is 4 +2 = 6. Write it as the third last digit of the answer. So we have

695

Step 4: The third last digit of 1245 is 2. Its left neighbor digit is 1. Add these two. That is 2 +1 = 3. Write it as the fourth last digit of the answer. So we have

3695

Step 5: The left most digit of 1245 is 1. Write it as the left most digit of the answer. So we have

13695

Yes, this is the answer. 1245 * 11 = 13695.

Example 3

Let's take a another bigger number this time. Say we need to do 472385 * 11

Solution

Step 1: The last digit of 472385 is 5. Write it down as the right most digit of the answer. So we have

5

Step 2: The last digit of 472385 is 5. Its left neighbor digit is 8. Add these two. That is 5 +8 = 13. Take 3 from it as the second last digit of the answer and treat the 1 as carry.So we have

35  (Carry = 1)

Step 3: The second last digit of 472385 is 8. Its left neighbor digit is 3. Add these two. That is 8 +3= 11. We have a carry 1. Add this to 11. So 11+1 = 12. Take 2 from it as the third last digit of the answer and treat the 1 as carry.So we have

235   (Carry = 1)

Step 4: The third last digit of 472385 is 3. Its left neighbor digit is 2. Add these two. That is 3 +2= 5. We have a carry 1. Add this also. That is 5+1=6. Write it as the fourth last digit of the answer. So we have

6235

Step 5: The fourth last digit of 472385 is 2. Its left neighbor digit is 7. Add these two. That is 2 +7= 9. Write it as the fifth last digit of the answer. So we have

96235

Step 6: The fifth last digit of 472385 is 7. Its left neighbor digit is 4. Add these two. That is 7 +4= 11. Take 1 from it as the sixth last digit of the answer and treat 1 as carry. So we have

196235   (Carry = 1)

Step 7 : The left most digit of 472385 is 4. Add the carry to this. that is 4+1 = 5. Write it as the left most digit of the answer. So we have

5196235

Yes, this is the answer. 472385 * 11 = 5196235.

Summary

Don't you see this as a simple process? Once you remember this pattern, you can do these calculations mentally.

 
 
 
Comments(44) Sign in (optional)
showing 1-10 of 44 comments,   sorted newest to the oldest
aban
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!
(0) (0) Reply
Arkajyoti
2014-12-19 18:00:05 
these shortcuts and tricks are very important but many people read this and then forget.
(0) (0) Reply
dreamBlitzer
2014-11-24 15:29:21 
15285966*11 = 152859660 + 15285966
(0) (0) Reply
chetan
2014-07-02 10:47:03 
please check for 385*92  i am not getting correct answer which is 35420
(0) (0) Reply
anu
2014-08-26 16:32:44 
these multiplications are only for 11 ,not with 92
(0) (0) Reply
san
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
(0) (0) Reply
Sharath
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
(0) (0) Reply
H.G. Moliya
2015-02-14 14:42:17 
19*11= 190+19 = 209

1249*11= 12490+1249 = 13739
(0) (0) Reply
abc
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...
(0) (0) Reply
Alex
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

(0) (0) Reply
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