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.
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
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.
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.
Don't you see this as a simple process? Once you remember this pattern, you can do these calculations mentally.
19*11 =
19 *
11
------
19
19
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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!
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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