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.

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.