2009-06-24

The Secrets of Mental Math

"What will you learn from this book? You will learn to do math in your head faster than you ever thought possible..." -- Dr. Arthur Benjamin, "Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks"

Let's take the simple 1-10 multiplication table for example. You can do it in your head:


However, can you do it further across and down the table? Can you multiply 64 x 78 mentally?

You can't and this is why you always need your calculator. (But a calculator isn't always at hand when you need it. Looking for pencil and paper...)

In fact not just mental multiplication trips you, but also addition, subtraction and division - simple arithmetic that kids learn in kindergartens.

You can now blame your math teachers for not teaching you the secrets of mental math. (But you insisted on using the calculator, didn't you?)

Let Dr. Benjamin's book come to your rescue - there are mental math techniques, and a lot of them. Each technique helps you do mental math in a certain scenario, and they all together contribute to your mind's number crunching power.

For example, the first technique introduced by Dr. Benjamin is to multiply any two-digit number by 11, e.g. 32 x 11. It does quick math magic - you need only to place the digit sum of the two-digit number between the two digits:

Digit sum of 32 = 3 + 2 = 5

Place the 5 in the middle of 32 = 352

That is, 32 x 11 = 352 (Ans.)

This "eleventh magic" technique also works on numbers of three or more digits. For example:

314 x 11 = [3][3+1][1+4][4] = [3][4][5][4] = 3454 (Ans.)

I've drawn the following mind map to illustrate how your mind should be crunching the numbers:


This mental math technique is simple. However, its simplicity doesn't mean you'll always remember to apply it. You don't do multiplication by 11 very often, do you?

If you do, congratulations. In any case I hope the above mind map will help recall.

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