Speed-Multiplication by 12

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.

In this case, because the highest sum you will ever get while multiplying by 12 will be 27, the most you will ever have to carry would be 2. Each time that happens, you write the ones digit in the answer column below the digit you are working on, but you mentally (do not write it down!) carry a one or a two to the next addition. The movie clip will illustrate the steps

As you read the steps, click the start button to illustrate them.

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 .

You've reached the end of the speed-multiplication lessons for 11 and 12.

I'm working on a sequel to "Numbers Juggling - Times without the Tables" (which is an amazingly simple and effective way to learn multiplication from 1-15). It will be about how to multiply huge whole numbers, quickly and accurately in your head, and how to estimate and check in seconds.

If you are want me to hurry up and finish that booklet, make sure you're signed up for the Math Mojo Monthly Newsletter at the top left of this page. As soon as the booklet is published, it will be announced there, with a discount coupon only available from the Math Mojo Monthly.