Secrets Of Mental Math

Secrets Of Mental Math

The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks, Ausgezeichnet: New York Public Library Books for the Teen Age, 2007

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These simple math secrets and tricks will forever change how you look at the world of numbers.

Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends and yourself with incredible calculations you never thought you could master, as renowned mathemagician Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and maybe for the first time make mathematics fun.

Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.

A great introduction to the wonder of numbers, from two superb teachers.
Brian Greene, author of The Elegant Universe

A magical mystery tour of mental mathematics! Fascinating and fun.
Joseph Gallian, president of the Mathematical Association of America

The clearest, simplest, most entertaining, and best book yet on the art of calculating in your head.
Martin Gardner, author of Mathematical Magic Show and Mathematical Carnival

This book can teach you mental math skills that will surprise you and your friends. Better, you will have fun and have valuable practical tools inside your head.
Dr. Edward O. Thorp, mathematician and author of Beat the Dealer and Beat the Market

Arthur Benjamin is a professor of mathematics at Harvey Mudd College in Claremont, California. He is also a professional magician and performs his mixture of math and magic all over the world.

Michael Shermer is host of the Caltech public lecture series, a contributing editor to and monthly columnist of
Scientific American, the publisher of
Skeptic magazine, and the author of several science books. He lives in Altadena, California.







Penguin Random House










Penguin Random House



Maße (L/B/H)

20,4/13,3/1,7 cm


240 g


Deutsch, Englisch



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Chapter 0

Quick Tricks: Easy (and Impressive) Calculations

In the pages that follow, you will learn to do math in your head faster than you ever thought possible. After practicing the methods in this book for just a little while, your ability to work with numbers will increase dramatically. With even more practice, you will be able to perform many calculations faster than someone using a calculator. But in this chapter, my goal is to teach you some easy yet impressive calculations you can learn to do immediately. We ll save some of the more serious stuff for later.

Instant Multiplication

Let s begin with one of my favorite feats of mental math how to multiply, in your head, any two-digit number by eleven. It s very easy once you know the secret. Consider the problem:

32 3 11

To solve this problem, simply add the digits, 3 1 2 5 5}, put the 5 between the 3 and the 2, and there is your answer:


What could be easier? Now you try:

53 3 11

Since 5 1 3 5 8, your answer is simply


One more. Without looking at the answer or writing anything down, what is

81 3 11?

Did you get 891? Congratulations!

Now before you get too excited, I have shown you only half of what you need to know. Suppose the problem is

85 3 11

Although 8 1 5 5 1}3}, the answer is NOT 81}3}5!

As before, the 3} goes in between the numbers, but the 1} needs to be added to the 8 to get the correct answer:


Think of the problem this way:

Here is another example. Try 57 3 11.

Since 5 1 7 5 12, the answer is

Okay, now it s your turn. As fast as you can, what is

77 3 11?

If you got the answer 847, then give yourself a pat on the back. You are on your way to becoming a mathemagician.

Now, I know from experience that if you tell a friend or teacher that you can multiply, in your head, any two-digit number by eleven, it won t be long before they ask you to do 99 3 11. Let s do that one now, so we are ready for it.

Since 9 1 9 5 18, the answer is:

Okay, take a moment to practice your new skill a few times, then start showing off. You will be amazed at the reaction you get. (Whether or not you decide to reveal the secret is up to you!)

Welcome back. At this point, you probably have a few questions, such as:

Can we use this method for multiplying three-digit numbers (or larger) by eleven?

Absolutely. For instance, for the problem 314 3 11, the answer still begins with 3 and ends with 4. Since 3 1 1 5 4}, and 1 1 4 5 5}, the answer is 34}5}4. But we ll save larger problems like this for later.

More practically, you are probably saying to yourself,

Well, this is fine for multiplying by elevens, but what about larger numbers? How do I multiply numbers by twelve, or thirteen, or thirty-six?

My answer to that is, Patience! That s what the rest of the book is all about. In Chapters 2, 3, 6, and 8, you will learn methods for multiplying together just about any two numbers. Better still, you don t have to memorize special rules for every number. Just a handful of techniques is all that it takes to multiply numbers in your head, quickly and easily.

Squaring and More

Here is another quick trick.

As you probably know, the square of a number is a number multiplied by itself. For example, the square of 7 is 7 3 7 5 49. Later, I will teach you a simple method that will enable you to easily calculate the square of any two-digit or three-digit (or higher) number. That method is especially simple when the number ends in 5, so let s do that trick now.

To square a two-digit number that ends in 5, you need
  • Secrets Of Mental Math