The Al Gore Rhythm by Anne N. Convenient Ruth

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I’m tipping my mitt a little early, because the intermediate multiplication lessons are not finished yet. But I thought people should have easy access to the basic method for advanced multiplication. This is the tip of the iceberg, but everyone should at least be able to do this method. Anything less than that is either merely standard or substandard.

Here’s the “mystery algorithm” for 26 * 31, or any other set of two-digit numbers. Keep in mind that the description is much longer than the problem should take. After a little practice, it should take no longer than 10 seconds to do a problem like this in your head.

Step 1:
Multiply the digits in the ones columns of both numbers together. That would be the 1 ( of 31) and the 6 (of 26). That gives you 6. That’s the final digit of the product.

Steps 2a, 2b and 2c:
a) Now multiply the digit in the ones column of one number by the digit in the tens column of the other. Let’s use the 2 (from the 26) and the 1 (from the 31). 2 x 1 is 2. Keep that number in your head while
b) you multiply the digit in the ones column of one OTHER number (the 3 from the 31) by the digit in the tens column of the first number (the 6 from the 26). 3 x 6 = 18.
c) Add that to the 2 in your head. That gives you 20. The 0 from the 20 belongs in the tens column of the answer.

Keep the 2 (from the 20) in your head now. (At no point do you ever keep more than one number in your head, so don’t worry that it’s “too hard”.)

So far, we have the tens and ones columns of the product.

Note: The only step that people occasionally find “hard” is step 2. That is because most people cannot automatically add two 2-digit numbers in their heads. That is very easy to correct. I have written a booklet, “The See-Say-Write Method of Addition“, which is available at Mathmojo.com, and simply deals with making that skill automatic. It is a breeze to learn, and is worthwhile to investigate, even if you think you can add quickly.

It also contains the most amazing way to check your answers you have ever seen! This is the probably the single most important thing you can learn in beginning speed-math. We will build on this skill in future booklets, but you can begin to learn and use it immediately upon reading it. This is great stuff!

Step 3:
Multiply the digits in the tens columns of both numbers together (3 x 2 = 6) and add that to the 2 in your head, giving you 8. That 8 is the answer to the hundreds place in the product.

Step 4:

There is no step 4. You are done.

This was a very simple example. There is a bit more carrying with larger numbers, like 67*89, but it all works the same.

That was lot of writing for something that takes a few seconds to do! Try it with a few examples, and you will freak yourself out. You will amaze everyone you show this to. When I demonstrate this live to people, jaws drop. It is much easier to show than to write the recipe above for. Try it.

VERY IMPORTANT: Keep the stuff in your head that belongs in your head. Don’t write it. It takes a little effort in the beginning, but not much. After a short time, you will wonder why the heck people past the 3rd grade have to write simple carries.

By the way, the formula for the above looks like this:
ab * cd = 100(ac) + 10(ad + bc) + bd (although that doesn’t give you all the nuances of the algorithm).
Beats the poop out of the “standard” algorithm, dudn’t it?

One more thing. Although this method beats the pickles out most methods, doing something as simple as 26 x 31 only requires that you multiply 26 by 3 in your head (any 3rd grader should really be able to do that, if we didn’t treat them like simps), stick a 0 at the end. That’s 780. Mentally add 26 to that, and Bob’s your uncle.

Standard algorithm my ass.

Let me know how you do with this.

Yes, this method can be done from left to right, as well, but that is beyond the scope of this post. No, this is not “the one best algorithm”. (Is there such a thing?) Yes, there are even more ways to streamline the procedure, but that is also beyond the scope of this post.

I’m sure you’ll have questions:

“Does this work with larger numbers?”
Yes, it can be done with larger digits. (There is more to it for larger numbers, but not much.) I can do it with up to four digits times four digits in my head. That didn’t take as long to learn as it took me to learn the standard algorithm when I was in school. With numbers larger than four digits I simply need to write the carries down, nothing else.

“What about decimals?”
It works just like the standard algorithm with decimals. Try it with 5.6 * 9.2 . There are a total of two digits behind the decimal points. Do the multiplication normally, and just make sure there are two digits behind the decimal point in the product (answer).

“What about showing ‘the work’?”
Um, what work? Yeah, this is a dilemma. Let me make an analogy. In the “olden days” you had to crank up the motor of a car by hand with a crank in the front of the car before it would start. Along comes a “new fangled” automobile that doesn’t need a crank. Imagine how stupid it would be to say, “Hey, that new thing is no good, it doesn’t have a crank.”
Same thing as showing the work.
But, life and schools being what they are, you have realize that you may have to be graded by people who still hand-crank their brains.

Consider this: I am not teaching you how to get grades. I’m teaching you how to think. If you want good grades, you have to give the person grading you what they want. You’ll probably have to do things the way they want you to in school. It doesn’t pay to fight them. Just take it easy. If you learn this way, the standard way will be a piece of cake for you, because learning a new way and having a new perspective always helps you do the other way better. Of course, you won’t be able to help resenting being graded on something inferior. But you can handle that. It is a great skill and sign of maturity.

This method has many of the same advantages that the “standard” algorithm has over using a calculator. It also has those same advantages over the “s.a.” For example:

If you have to multiply numbers like the above, and you can’t do the standard algorithm, you’re in trouble if you don’t have a calculator, or a someone who isn’t an idiot with you, whom you can ask for help.

By the same token, if you have to multiply numbers like the above, and you can’t do the the method I have shown you, you’re in trouble if you don’t have pencil and paper at hand, or a friend who knows the better method.

In other words, you can use the same arguments that the people who argue for the “standard algorithm” use, against those same people. They want standards that are higher than poorer methods. So do we, right?

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