Speed-Multiplication by 12

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 This is based on the method for multiplication by 11. Be sure you know the method for doing that on the pages which deal with that. If you can't do multiplication by 11 that way, and can only do it the "normal" way (no matter how well), you should go back to those pages and learn them now before going on.

 Once you understand them, the following will make sense to you:

• When multiplying by 12, instead of adding two digits next to each other, you will be adding the digit in the lower column to twice the digit in the next highest column. To understand why this works, click here (um, later, because that page isn't up yet. Sorry.)
  
• Because you will be adding one digit to two times another digit, and the highest digit is 9, you will find that the highest number you can arrive at would be 9 + (2 x 9), which would be 27.

Step 1: as usual, pretend there are two invisible zeroes, one in front, and one behind the number to be multiplied.	Step 2: Add the last zero to two times the digit in the ones column, and write the answer below the ones column.	Step 3: Add the digit in the ones column to two times the digit in the tens column and write the final digit of the answer below the tens column. Mentally (DO NOT WRITE IT DOWN!) carry the first digit (the 1) along to the next step.
Step 4: Add the digit in the tens column to two times the digit in the hundreds column, plus the carried 1, and write the final digit of the answer below the hundreds column. Mentally (DO NOT WRITE IT DOWN!) carry the first digit (the 2) along to the next step.	Step 5: Add the digit in the hundreds column to two times the imaginary 0 in the thousands column, (that will always be 0) plus the carried 2, and write the answer below the thousands column. (I know it is not necessary to multiply the final 0 by 2, but I wrote it like that for the sake of keeping it consistent in your mind.)

  This method works with any number, no matter how long or short, times 12. The next page will be about why it works and how you can use it to learn how to do other numbers. In the meantime practice it with a few long, random numbers times 12.

  After learning multiplication by 12, and 11, can you see a pattern developing? Can you think of the way this method might work for multiplication by 13? Try to figure it out and try some yourself to see if your method works before you go on to the lesson of how to multiply by 13. Then compare you method to the one described there.

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