Math Mojo - Making Math Meaningful

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This is the explanation for how the speed-method of multiplying by 9 works. It is a supplemental lesson to the Math Mojo Monthly (Issue #1), "Multiplication of the Week" chapter. Please refer to that issue as you read along here.

You may remember that I said it is important to know why the method I taught you works. You can only really begin to get deep knowledge of something after you have begun to investigate the "why" of it.

The "why" of how this method works is based on the Idea that anything multiplied by 9 is the same thing as multiplying it by 10, and subtracting the original number from that product.

But it is hard to do, say, (452 x 10) – 452 in your head .Let's look at how it would work on paper, the way you already learned to do it.

If you wrrte it out, (and I suggest you do that now, so you can follow this more easily) with the 4,520 above the 452, and lined up the columns as you would in a normal subtraction problem, you would be subtracting like shown below (if you did it from right to left, like you were probably taught in school):

1) Ones (or units) column:
You would subtract the 2 in the subtrahend (lower number) from the 0 in the minuend (upper number). Of course you can’t, because 2 is less than 0) so you would borrow from the 2 in the tens column of the subtrahend (making it a 1). That makes the answer (also called the "difference") of the units column 10 minus 2, which is 8.

This is the same step as subtracting 2 from 10 in our speed method.

2) Tens column:
Subtract the 5 in the subtrahend from the 1 in the minuend (remember that 1 used to be a 2). Of course, you can’t do this either, so you have to borrow from the 5 in the hundreds column of the subtrahend, making it a 4). Now, instead of subtracting 5 from 1, you are subtracting 5 from 11, which gives you 6 as the difference in the tens column.

This is the same step as subtracting 5 from 11 in our speed method.

3) Hundreds column:
Subtract the 4 in the subtrahend from the 4 (which used to be a 5), and get 0 as the difference.

This is the same step as subtracting 4 from 4 in our speed method.

4) Thousands column:
Since you didn’t borrow anything from the 4 in the minuend, it is still a 4. There is nothing in the thousands column of the subtrahend, so you subtract nothing (0) from 4. 4 - 0 is 4, which is the difference in the thousands column. You are done.

This is the same step as subtracting 0 from 4 in our speed method.

If you didn’t write the numbers down in order to follow the explanation, or didn't at least look at the numbers in the numbers above, it would seem difficult. It isn’t, though. You already know how to do it. It is normal subtraction, like you learned in the first or second grade. The speed-subtraction method mearly does the same things without the crutch of re-writing the numbers in two rows.

Look at the example again, represented below. This will show you where we get the "imaginary zeros" for our speed method. The imaginary zeros are highlighted in red. See, speed-math is not fundamentally different from the math you learned in school. You actually have been using the imaginary zeros all along. Now you are more aware of how they work, and can use them in a more streamlined way, with Math Mojo.

Remember - nothing I will teach you is "hard." It is all fairly easy. But "easy" doesn’t mean it requires no effort. It is easy if you put the effort in. Keep that in mind as we continue.
Normally, when you write the numbers down, each time you borrow, you put a slash through a digit, and write the number minus the carry above it, and then write a little "one" to the top left of the number you are carrying it to.

Why?

You do it because you learned that in first or second grade. And you still do it! You learned to crawl before you learned to walk, and you don’t crawl whenever you want to get someplace now, do you? Why still use the crutches they gave you in first grade? Don’t write your borrows or carries anymore. Not in real life. Don’t use a pencil to do things your brain can do better, if you trust it.

They may make you "write your work" on tests in school. OK, do it for them, because they are grading you. But when you do it, think about the two farmers in the story in the Math Mojo Monthly, Issue #1.

If you or someone you know would like to learn an even easier alternative to the "times-tables," click here to check out "Numbers Juggling - Basic Multiplication of One-Digit-Numbers." It also contains an amazing speed-math method for instantly multiplying any number by 5, from left-to-right! That method is even easier than this method of multiplication by 9!

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