Faster way to multiply any number with numbers from 12-19

The basic recipe for multiplying any number by 12-19 is to “multiply one’s digit of the number from 12-19 with all the digits of the other number one by one and add to its neighbor on the right.”

Let’s multiply 346 by 17.

Start with the right-most digit, 6. Multiply 7 with 6 and add the neighbor (none in this case, as 6 is the right-most digit). We get 42.  
Write down 2, and carry the 4. -----> 2

Move left to the next digit, 4. Multiply 7 with 4 to get 28, add the neighbor to right 6, to get 34, and add the carry 4, to get 38.

Write down the 8, and carry the 3. -----> 82

Move left to the next digit, 3. Multiply 7 with 3 to get 21. Add the neighbor, 4, and we get 25. Add the carry 3, to get 28.

Write down the 8, and carry the 2. -----> 882

Now add the carry 2 to the left most digit 3 which gives us 5. Finally, Write down 5. -----> 5882

So, our answer is 5882.

Let’s try another example: 123456×13.

First digit is 6. Multiply 3 with 6 + no neighbor  ---------> (3x6+0) = 18. Write 8 and carry 1. ---> 8

Next digit is 5. Multiply 3 with 5 + neighbor 6 + carry 1 (3x5+6+1) = 22. Write 2 and carry 2. ---> 28

Next digit is 4. Multiply 3 with 4 + neighbor 5 + carry 2 (3x4+5+2) = 19. Write 9 and carry 1. ---> 928

Next digit is 3. Multiply 3 with 3 + neighbor 4 + carry 1 (3x3+4+1) = 14. Write 4 and carry 1. ---> 4928

Next digit is 2. Multiply 3 with 2 + neighbor 3 + carry 1 (3x2+3+1) = 10. Write 0 and carry 1. ---> 04928

Next digit is 1. Multiply 3 with 1 + neighbor 2 + carry 1 (3x1+2+1) = 6. Write 6 and no carry. ---> 604928

Finally, the left-most digit 1 + no carry = 1. Write down 1. ---> 1604928

The answer is 1604928.

One more example: 35246×15

5 x 6 = 30. Write down 0, carry 3. -------------> 0

5 x 4 + 6 + 3 = 29. Write down 9, carry 2. ---> 90

5 x 2 + 4 + 2 = 16. Write down 6, carry 1. ---> 690

5 x 5 + 2 + 1 = 28. Write down 8, carry 2. ---> 8690

5 x 3 + 5 + 2 = 22. Write down 2, carry 2. ---> 28690

3 + 2 = 5. Write down 5. -------------------- > 528690

So, 35246×15 = 528690