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# Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks (English Edition) Kindle电子书

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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.

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.

## 商品描述

### 媒体推荐

“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 --此文字指其他 kindle_edition 版本。

—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 --此文字指其他 kindle_edition 版本。

### 文摘

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:

35}2

What could be easier? Now you try:

53 3 11

Since 5 1 3 5 8, your answer is simply

583

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:

93}5

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 to remember only two things.

1.The answer begins by multiplying the first digit by the next higher digit.

2.The answer ends in 25.

For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 3 4 5 12, the answer is 1225. Therefore, 35 3 35 5 1225. Our steps can be illustrated this way:

How about the square of 85? Since 8 3 9 5 72, we immediately get 85 3 85 5 7225.

We can use a similar trick when multiplying two-digit numbers with the same first digit, and second digits that sum to 10. The answer begins the same way that it did before (the first digit multiplied by the next higher digit), followed by the product of the second digits. For example, let’s try 83 3 87. (Both numbers begin with 8, and the last digits sum to 3 1 7 5 10.) Since 8 3 9 5 72, and 3 3 7 5 21, the answer is 7221.

Similarly, 84 3 86 5 7224.

Now it’s your turn. Try

26 3 24

How does the answer begin? With 2 3 3 5 6. How does it end? With 6 3 4 5 24. Thus 26 3 24 5 624.

Remember that to use this method, the first digits have to be the same, and the last digits must sum to 10. Thus, we can use this method to instantly determine that

31 3 39 5 1209

32 3 38 5 1216

33 3 37 5 1221

34 3 36 5 1224

35 3 35 5 1225

You may ask,

“What if the last digits do not sum to ten? Can we use this method to multiply twenty-two and twenty-three?”

Well, not yet. But in Chapter 8, I will show you an easy way to do problems like this using the close-together method. (For 22 3 23, you would do 20 3 25 plus 2 3 3, to get 500 1 6 5 506, but I’m getting ahead of myself!) Not only will you learn how to use these methods, but you will understand why these methods work, too.

“Are there any tricks for doing mental addition and subtraction?”

Definitely, and that is what the next chapter is all about. If I were forced to summarize my method in three words, I would say, “Left to right.” Here is a sneak preview.

Consider the subtraction problem

Most people would not like to do this problem in their head (or even on paper!), but let’s simplify it. Instead of subtracting 587, subtract 600. Since 1200 2 600 5 600, we have that

But we have subtracted 13 too much. (We will explain how to quickly determine the 13 in Chapter 1.) Thus, our painful-looking subtraction problem becomes the easy addition problem

which is not too hard to calculate in your head (especially from left to right). Thus, 1241 2 587 5 654.

Using a little bit of mathematical magic, described in Chapter 9, you will be able to instantly compute the sum of the ten numbers below.

Although I won’t reveal the magical secret right now, here is a hint. The answer, 935, has appeared elsewhere in this chapter. More tricks for doing math on paper will be found in Chapter 6. Furthermore, you will be able to quickly give the quotient of the last two numbers:

359 4 222 5 1.61 (first three digits)

We will have much more to say about division (including decimals and fractions) in Chapter 4.

More Practical Tips

Here’s a quick tip for calculating tips. Suppose your bill at a restaurant came to $42, and you wanted to leave a 15% tip. First we calculate 10% of $42, which is $4.20. If we cut that number in half, we get $2.10, which is 5% of the bill. Adding these numbers together gives us $6.30, which is exactly 15% of the bill. We will discuss strategies for calculating sales tax, discounts, compound interest, and other practical items in Chapter 5, along with strategies that you can use for quick mental estimation when an exact answer is not required.

Improve Your Memory

In Chapter 7, you will learn a useful technique for memorizing numbers. This will be handy in and out of the classroom. Using an easy-to-learn system for turning numbers into words, you will be able to quickly and easily memorize any numbers: dates, phone numbers, whatever you want.

Speaking of dates, how would you like to be able to figure out the day of the week of any date? You can use this to figure out birth dates, historical dates, future appointments, and so on. I will show you this in more detail later, but here is a simple way to figure out the day of January 1 for any year in the twenty-first century. First familiarize yourself with the following table.

MondayTuesdayWednesdayThursdayFridaySaturdaySunday

1234567 or 0

For instance, let’s determine the day of the week of January 1, 2030. Take the last two digits of the year, and consider it to be your bill at a restaurant. (In this case, your bill would be $30.) Now add a 25% tip, but keep the change. (You can compute this by cutting the bill in half twice, and ignoring any change. Half of $30 is $15. Then half of $15 is $7.50. Keeping the change results in a $7 tip.) Hence your bill plus tip amounts to $37. To figure out the day of the week, subtract the biggest multiple of 7 (0, 7, 14, 21, 28, 35, 42, 49, . . .) from your total, and that will tell you the day of the week. In this case, 37 2 35 5 2, and so January 1, 2030, will occur on 2’s day, namely Tuesday:

Bill:30

Tip: 1} } }7}

37

subtract 7s: 2} }3}5}

2 5 Tuesday

How about January 1, 2043:

Bill:43

Tip: 1} }1}0}

53

subtract 7s: 2} }4}9}

4 5 Thursday

Exception: If the year is a leap year, remove $1 from your tip, then proceed as before. For example, for January 1, 2032, a 25% tip of $32 would be $8. Removing one dollar gives a total of

32 1 7 5 39. Subtracting the largest multiple of 7 gives us 39 2 35 5 4. So January 1, 2032, will be on 4’s day, namely Thursday. For more details that will allow you to compute the day of the week of any date in history, see Chapter 9. (In fact, it’s perfectly okay to read that chapter first!)

I know what you are wondering now:

“Why didn’t they teach this to us in school?”

I’m afraid that there are some questions that even I cannot answer. Are you ready to learn more magical math? Well, what are we waiting for? Let’s go!

Chapter 1

A Little Give and Take:

Mental Addition and Subtraction

For as long as I can remember, I have always found it easier to add and subtract numbers from left to right instead of from right to left. By adding and subtracting numbers this way, I found that I could call out the answers to math problems in class well before my classmates put down their pencils. And I didn’t even need a pencil!

In this chapter you will learn the left-to-right method of doing mental addition and subtraction for most numbers that you encounter on a daily basis. These mental skills are not only important for doing the tricks in this book but are also indispensable in school, at work, or any time you use numbers. Soon you will be able to retire your calculator and use the full capacity of your mind as you add and subtract two-digit, three-digit, and even four-digit numbers with lightning speed.

Left-to-Right Addition

Most of us are taught to do math on paper from right to left. And that’s fine for doing math on paper. But if you want to do math in your head (even faster than you can on paper) there are many good reasons why it is better to work from left to right. After all, you read numbers from left to right, you pronounce numbers from left to right, and so it’s just more natural to think about (and calculate) numbers from left to right. When you compute the answer from right to left (as you probably do on paper), you generate the answer backward. That’s what makes it so hard to do math in your head. Also, if you want to estimate your answer, it’s more important to know that your answer is “a little over 1200” than to know that your answer “ends in 8.” Thus, by working from left to right, you begin with the most significant digits of your problem. If you are used to working from right to left on paper, it may seem unnatural to work with numbers from left to right. But with practice you will find that it is the most natural and efficient way to do mental calculations.

With the first set of problems—two-digit addition—the left-to-right method may not seem so advantageous. But be patient. If you stick with me, you will see that the only easy way to solve three-digit and larger addition problems, all subtraction problems, and most definitely all multiplication and division problems is from left to right. The sooner you get accustomed to computing this way, the better.

Two-Digit Addition

Our assumption in this chapter is that you know how to add and subtract one-digit numbers. We will begin with two-digit addition, something I suspect you can already do fairly well in your head. The following exercises are good practice, however, because the two-digit addition skills that you acquire here will be needed for larger addition problems, as well as virtually all multiplication problems in later chapters. It also illustrates a fundamental principle of mental arithmetic—namely, to simplify your problem by breaking it into smaller, more manageable parts. This is the key to virtually every method you will learn in this book. To paraphrase an old saying, there are three components to success—simplify, simplify, simplify.

The easiest two-digit addition problems are those that do not require you to carry any numbers, when the first digits sum to 9 or below and the last digits sum to 9 or below. For example:

(30 1 2)

To solve 47 1 32, first add 30, then add 2. After adding 30, you have the simpler problem 77 1 2, which equals 79. We illustrate this as follows:

47 1 32 5 77 1 2 5 79

(first add 30)(then add 2)

The above diagram is simply a way of representing the mental processes involved in arriving at an answer using our method. While you need to be able to read and understand such diagrams as you work your way through this book, our method does not require you to write down anything yourself. --此文字指其他 kindle_edition 版本。

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:

35}2

What could be easier? Now you try:

53 3 11

Since 5 1 3 5 8, your answer is simply

583

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:

93}5

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 to remember only two things.

1.The answer begins by multiplying the first digit by the next higher digit.

2.The answer ends in 25.

For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 3 4 5 12, the answer is 1225. Therefore, 35 3 35 5 1225. Our steps can be illustrated this way:

How about the square of 85? Since 8 3 9 5 72, we immediately get 85 3 85 5 7225.

We can use a similar trick when multiplying two-digit numbers with the same first digit, and second digits that sum to 10. The answer begins the same way that it did before (the first digit multiplied by the next higher digit), followed by the product of the second digits. For example, let’s try 83 3 87. (Both numbers begin with 8, and the last digits sum to 3 1 7 5 10.) Since 8 3 9 5 72, and 3 3 7 5 21, the answer is 7221.

Similarly, 84 3 86 5 7224.

Now it’s your turn. Try

26 3 24

How does the answer begin? With 2 3 3 5 6. How does it end? With 6 3 4 5 24. Thus 26 3 24 5 624.

Remember that to use this method, the first digits have to be the same, and the last digits must sum to 10. Thus, we can use this method to instantly determine that

31 3 39 5 1209

32 3 38 5 1216

33 3 37 5 1221

34 3 36 5 1224

35 3 35 5 1225

You may ask,

“What if the last digits do not sum to ten? Can we use this method to multiply twenty-two and twenty-three?”

Well, not yet. But in Chapter 8, I will show you an easy way to do problems like this using the close-together method. (For 22 3 23, you would do 20 3 25 plus 2 3 3, to get 500 1 6 5 506, but I’m getting ahead of myself!) Not only will you learn how to use these methods, but you will understand why these methods work, too.

“Are there any tricks for doing mental addition and subtraction?”

Definitely, and that is what the next chapter is all about. If I were forced to summarize my method in three words, I would say, “Left to right.” Here is a sneak preview.

Consider the subtraction problem

Most people would not like to do this problem in their head (or even on paper!), but let’s simplify it. Instead of subtracting 587, subtract 600. Since 1200 2 600 5 600, we have that

But we have subtracted 13 too much. (We will explain how to quickly determine the 13 in Chapter 1.) Thus, our painful-looking subtraction problem becomes the easy addition problem

which is not too hard to calculate in your head (especially from left to right). Thus, 1241 2 587 5 654.

Using a little bit of mathematical magic, described in Chapter 9, you will be able to instantly compute the sum of the ten numbers below.

Although I won’t reveal the magical secret right now, here is a hint. The answer, 935, has appeared elsewhere in this chapter. More tricks for doing math on paper will be found in Chapter 6. Furthermore, you will be able to quickly give the quotient of the last two numbers:

359 4 222 5 1.61 (first three digits)

We will have much more to say about division (including decimals and fractions) in Chapter 4.

More Practical Tips

Here’s a quick tip for calculating tips. Suppose your bill at a restaurant came to $42, and you wanted to leave a 15% tip. First we calculate 10% of $42, which is $4.20. If we cut that number in half, we get $2.10, which is 5% of the bill. Adding these numbers together gives us $6.30, which is exactly 15% of the bill. We will discuss strategies for calculating sales tax, discounts, compound interest, and other practical items in Chapter 5, along with strategies that you can use for quick mental estimation when an exact answer is not required.

Improve Your Memory

In Chapter 7, you will learn a useful technique for memorizing numbers. This will be handy in and out of the classroom. Using an easy-to-learn system for turning numbers into words, you will be able to quickly and easily memorize any numbers: dates, phone numbers, whatever you want.

Speaking of dates, how would you like to be able to figure out the day of the week of any date? You can use this to figure out birth dates, historical dates, future appointments, and so on. I will show you this in more detail later, but here is a simple way to figure out the day of January 1 for any year in the twenty-first century. First familiarize yourself with the following table.

MondayTuesdayWednesdayThursdayFridaySaturdaySunday

1234567 or 0

For instance, let’s determine the day of the week of January 1, 2030. Take the last two digits of the year, and consider it to be your bill at a restaurant. (In this case, your bill would be $30.) Now add a 25% tip, but keep the change. (You can compute this by cutting the bill in half twice, and ignoring any change. Half of $30 is $15. Then half of $15 is $7.50. Keeping the change results in a $7 tip.) Hence your bill plus tip amounts to $37. To figure out the day of the week, subtract the biggest multiple of 7 (0, 7, 14, 21, 28, 35, 42, 49, . . .) from your total, and that will tell you the day of the week. In this case, 37 2 35 5 2, and so January 1, 2030, will occur on 2’s day, namely Tuesday:

Bill:30

Tip: 1} } }7}

37

subtract 7s: 2} }3}5}

2 5 Tuesday

How about January 1, 2043:

Bill:43

Tip: 1} }1}0}

53

subtract 7s: 2} }4}9}

4 5 Thursday

Exception: If the year is a leap year, remove $1 from your tip, then proceed as before. For example, for January 1, 2032, a 25% tip of $32 would be $8. Removing one dollar gives a total of

32 1 7 5 39. Subtracting the largest multiple of 7 gives us 39 2 35 5 4. So January 1, 2032, will be on 4’s day, namely Thursday. For more details that will allow you to compute the day of the week of any date in history, see Chapter 9. (In fact, it’s perfectly okay to read that chapter first!)

I know what you are wondering now:

“Why didn’t they teach this to us in school?”

I’m afraid that there are some questions that even I cannot answer. Are you ready to learn more magical math? Well, what are we waiting for? Let’s go!

Chapter 1

A Little Give and Take:

Mental Addition and Subtraction

For as long as I can remember, I have always found it easier to add and subtract numbers from left to right instead of from right to left. By adding and subtracting numbers this way, I found that I could call out the answers to math problems in class well before my classmates put down their pencils. And I didn’t even need a pencil!

In this chapter you will learn the left-to-right method of doing mental addition and subtraction for most numbers that you encounter on a daily basis. These mental skills are not only important for doing the tricks in this book but are also indispensable in school, at work, or any time you use numbers. Soon you will be able to retire your calculator and use the full capacity of your mind as you add and subtract two-digit, three-digit, and even four-digit numbers with lightning speed.

Left-to-Right Addition

Most of us are taught to do math on paper from right to left. And that’s fine for doing math on paper. But if you want to do math in your head (even faster than you can on paper) there are many good reasons why it is better to work from left to right. After all, you read numbers from left to right, you pronounce numbers from left to right, and so it’s just more natural to think about (and calculate) numbers from left to right. When you compute the answer from right to left (as you probably do on paper), you generate the answer backward. That’s what makes it so hard to do math in your head. Also, if you want to estimate your answer, it’s more important to know that your answer is “a little over 1200” than to know that your answer “ends in 8.” Thus, by working from left to right, you begin with the most significant digits of your problem. If you are used to working from right to left on paper, it may seem unnatural to work with numbers from left to right. But with practice you will find that it is the most natural and efficient way to do mental calculations.

With the first set of problems—two-digit addition—the left-to-right method may not seem so advantageous. But be patient. If you stick with me, you will see that the only easy way to solve three-digit and larger addition problems, all subtraction problems, and most definitely all multiplication and division problems is from left to right. The sooner you get accustomed to computing this way, the better.

Two-Digit Addition

Our assumption in this chapter is that you know how to add and subtract one-digit numbers. We will begin with two-digit addition, something I suspect you can already do fairly well in your head. The following exercises are good practice, however, because the two-digit addition skills that you acquire here will be needed for larger addition problems, as well as virtually all multiplication problems in later chapters. It also illustrates a fundamental principle of mental arithmetic—namely, to simplify your problem by breaking it into smaller, more manageable parts. This is the key to virtually every method you will learn in this book. To paraphrase an old saying, there are three components to success—simplify, simplify, simplify.

The easiest two-digit addition problems are those that do not require you to carry any numbers, when the first digits sum to 9 or below and the last digits sum to 9 or below. For example:

(30 1 2)

To solve 47 1 32, first add 30, then add 2. After adding 30, you have the simpler problem 77 1 2, which equals 79. We illustrate this as follows:

47 1 32 5 77 1 2 5 79

(first add 30)(then add 2)

The above diagram is simply a way of representing the mental processes involved in arriving at an answer using our method. While you need to be able to read and understand such diagrams as you work your way through this book, our method does not require you to write down anything yourself. --此文字指其他 kindle_edition 版本。

### 作者简介

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. --此文字指其他 kindle_edition 版本。

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. --此文字指其他 kindle_edition 版本。

## 基本信息

- ASIN : B000Q80SM6
- 出版社 : Crown (2008年6月3日)
- 出版日期 : 2008年6月3日
- 语言 : 英语
- 文件大小 : 126730 KB
- 标准语音朗读 : 已启用
- X-Ray : 已启用
- 生词提示功能 : 已启用
- 纸书页数 : 296页

- 亚马逊热销商品排名: 商品里排第198,858名Kindle商店 (查看商品销售排行榜Kindle商店)
- 商品里排第84名Teaching Methods & Materials（教学方法与素材）
- 商品里排第137名Mathematics（数学）
- 商品里排第164名Test Preparation & Workbooks（备考与练习册）

- 用户评分:

## 买家评论

*5.0 颗星，最多 5 颗星*

5星，共 5 星

1
买家评价

评分是如何计算的？

在计算总星级评分以及按星级确定的百分比时，我们不使用简单的平均值。相反，我们的系统会考虑评论的最新程度以及评论者是否在亚马逊上购买了该商品。系统还会分析评论，验证评论的可信度。

### 此商品在美国亚马逊上最有用的商品评论

美国亚马逊：

*4.5 颗星，最多 5 颗星*459 条评论S.D.

*2.0 颗星，最多 5 颗星*Mixed Bag

已确认购买

More than a book of numerical parlour tricks, but less than a satisfying immersion into the world of numbers. Having watched videos of his work, I was very impressed with Benjamin's speed and fluidity with numbers, as most people are. He certainly knows his subject and clearly enjoys it. But I feel he has yet to write a good investigation on the subject. I don't know how Michael Shermer's, whom I respect, added to this, but it certainly wasn't in bringing focus to the work. The first third of this book is gold. Sure, you can find much of it online for free, but it's presented here clearly and in an organized fashion. You'll notice that in a lot of the rave reviews, however, the reviewers mention that they "haven't finished the book, but can't wait to do so." I doubt many of them have, and it's not their faults. The book becomes a slog half way through, especially if, like me, you tend to take copious notes and try to really tackle the book like a course in mental mathematics, which it really isn't but on the surface presents itself as the sort of practical tome that will guide you through a better understanding of number theory and computation. The problem is that the authors get a bit carried away. You expect methods that will simplify mathematics or lay the complex groundwork for mentally calculating numbers with minimal effort in the long run. Or maybe just learn some neat tricks. But Benjamin is the type of mountain guide who gets sidetracked at every bush, shrub, running squirrel, bird sound, river and cave he encounters. For every easy road you set out on, Benjamin exclaims, "but you can also do this!" and dedicates a long chapter to various methods that are simply "the long way around". Yes, it's fascinating how casting out nines and elevens works, but do you really need a long explanation of how it works, mapped out diagrams and exercises, etc? The criss-cross method of multiplication works whether you're doing three, four, five, or ten digits. It's actually convoluted and doesn't exactly fit the title of the book. Imagine a book called "The Secrets of Reading", written ostensibly for the layman who may or may not love reading, devoting an entire chapter to decoding and memorizing backwards acrostics and anagrams in epic poetry written in obscure meters. I said that it's a slog for the serious student, but it must seem interminable for the person with only a light interest in what Benjamin is doing. The fact of the matter is, most of this isn't what Benjamin uses for his "lightning calculation" - it's stuff he happens to find interesting. In fact, I myself found better, simpler, more intuitive methods freely distributed online for many of these operations. Some that surprised me Benjamin didn't touch on. Ultimately his digressions are too much for the casual reader and lack enough real theoretical depth that would satisfy a devout student of mathematics. Imagine a carpenter who could hammer 100 nails in under a minute who then proceeded to show you 20 different methods for hammering in a nail or two at a time while throwing in tidbits about the lives of famous carpenters and carpentry styles throughout history. You'll either want to skip the hundred methods and concentrate on two or three that get the job done, or you'll ask to hear more about the history of carpentry but skip the 100 (often redundant or similar) methods for hammering with household objects. This is definitely a book you'll want to skip around in. Too bad the table of contents isn't obliging.

169 个人发现此评论有用

Jim Romo

*5.0 颗星，最多 5 颗星*Who Knew Math Could Be FUN?

已确认购买

I'm retired and having loads of fun with this book on math. The painful paradox is that I have always liked math but it didn't like me; I struggled with math all my life.

I am quintessentially stubborn. Never give up. (Pain is temporary, quitting is forever. ) I have purchased books on Algebra and Geometry; I won't lie to you, my struggle continues. The "Secrets of Mental Math" however is fun AND practical. It should be this much fun for everyone.

I read it over once without actually practicing any of the tricks having purchased it on Amazon for my Kindle library. I liked it so much I went to used book stores to find a hard copy. If math and magic intrigues you, you should get this book.

I am quintessentially stubborn. Never give up. (Pain is temporary, quitting is forever. ) I have purchased books on Algebra and Geometry; I won't lie to you, my struggle continues. The "Secrets of Mental Math" however is fun AND practical. It should be this much fun for everyone.

I read it over once without actually practicing any of the tricks having purchased it on Amazon for my Kindle library. I liked it so much I went to used book stores to find a hard copy. If math and magic intrigues you, you should get this book.

32 个人发现此评论有用

Aaron Ziegler

*4.0 颗星，最多 5 颗星*Should be given to all elementary school students.

已确认购买

I'm about half way through the book and can say I've definitely picked up some useful tricks. Be warned, this isn't a passive read where everything will suddenly click and you will be a math whiz. I recommend taking the chapters slowly and making your own exercises to really drive the concepts home. The first few chapters are cumulative, but eventually you are able to jump around and learn what tricks sound most appealing to you. My personal favorite is the ability to memorize strings of numbers. Has a ton of practical use in everyday life. I love being good at arithmetic and this book gives you the tools to get there.

42 个人发现此评论有用

darkguardian2

*5.0 颗星，最多 5 颗星*Good Book...Bad Kindle Format

已确认购买

This is a good math book that easy to read and very motivating.

It's similar to other books about math like "Math Magic" by Scott Flansburg (The Human Calculator).

I issue is the Kindle format having the examples set to small print.

Enlarging the letters doesn't help and disrupts the flow of reading the material. (Pictured)

Since, it's a math book the examples are critical to understanding the concepts.

I highly recommend it and no in-place advertisements in the texts hawking up training packages.

It's similar to other books about math like "Math Magic" by Scott Flansburg (The Human Calculator).

I issue is the Kindle format having the examples set to small print.

Enlarging the letters doesn't help and disrupts the flow of reading the material. (Pictured)

Since, it's a math book the examples are critical to understanding the concepts.

I highly recommend it and no in-place advertisements in the texts hawking up training packages.

*5.0 颗星，最多 5 颗星*Good Book...Bad Kindle Format

2019年6月4日 在美国审核

It's similar to other books about math like "Math Magic" by Scott Flansburg (The Human Calculator).

I issue is the Kindle format having the examples set to small print.

Enlarging the letters doesn't help and disrupts the flow of reading the material. (Pictured)

Since, it's a math book the examples are critical to understanding the concepts.

I highly recommend it and no in-place advertisements in the texts hawking up training packages.

该评价的图片

7 个人发现此评论有用

Tom Steele

*5.0 颗星，最多 5 颗星*Awesome book that shows the beauty of math...

已确认购买

OMG, my son is the math hero in his third grade class. Full of tricks like multiply times eleven - any number. Simply do this... 11 x 35: Take the 3 and the 5 and separate them, add 3+5=8 Put the 8 in between the 3 and 5. 11x35 is 385. Another example 11 x 72, separate the 7 and 2. 7+2 = 9. Put the 9 between the 7 and 2 and 11 x 72 = 792. Presto. Your kid is a math genius. The book is full of these.

77 个人发现此评论有用