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.

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**
Cool. Was a tad bit confusing at first sight, but yeah its cool. Maths is cool.

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