Secrets of Mental Math - Arthur Benjamin (bill gates best books .TXT) 📗

× 12) = 1680 + 48 = 1728

2. 173 = (14 × 17 × 20) + (32 × 17) = 4760 + 153 = 4913

3. 213 = (20 × 21 × 22) + (12 × 21) = 9240 + 21 = 9261

4. 283 = (26 × 28 × 30) + (22 × 28) = 21,840 + 112 = 21,952 5 . 333 = (30 × 33 × 36) + (32 × 33) = 35,640 + 297 = 35,93 7

6. 393 = (38 × 39 × 40) + (12 × 39) = 59,280 + 39 = 59,319

7. 403 = 40 × 40 × 40 = 64,000

8. 443 = (40 × 44 × 48) + (42 × 44) = 84,480 + 704 = 85,184

9. 523 = (50 × 52 × 54) + (22 × 52) = 140,400 + 208 = 140,608

10. 563 = (52 × 56 × 60) + (42 × 56) = 174,720 + 896 = 175,616

11. 653 = (60 × 65 × 70) + (52 × 65) = 273,000 + 1,625 = 274,625

12. 713 = (70 × 71 × 72) + (12 × 71) = 357,840 + 71 = 357,911

13. 783 = (76 × 78 × 80) + (22 × 78) = 474,240 + 312 = 474,552

14. 853 = (80 × 85 × 90) + (52 × 85) = 612,000 + 2,125 = 614,125

15. 873 = (84 × 87 × 90) + (32 × 87) = 657,720 + 783 = 658,503

16. 993 = (98 × 99 × 100) + (12 × 99) = 970,200 + 99 = 970,299

CHAPTER 4: DIVIDE AND CONQUER

One-Digit Division (this page)

Two-Digit Division (this page)

Decimalization (this page)

Testing for Divisibility (this page)

Multiplying Fractions (this page)

Dividing Fractions (this page)

Simplifying Fractions (this page)

Adding Fractions (Equal Denominators) (this page)

Adding Fractions (Unequal Denominators) (this page)

Subtracting Fractions (this page)

CHAPTER 5: GOOD ENOUGH

Addition Guesstimation (this page)

Subtraction Guesstimation (this page)

Division Guesstimation (this page)

Multiplication Guesstimation (this page)

Square Root Guesstimation (this page)

Everyday Math (this page)

1. $8.80 + $4.40 = $13.20

2. $5.30 + $2.65 = $7.95

3. $74 ÷ 2 ÷ 2 = $37 ÷ 2 = $18.50

4. Since 70 ÷ 10 = 7, seven years

5. Since 70 ÷ 6 = 11 .67, it will take twelve years to double

6. Since 110 ÷ 7= 15.714, it will take sixteen years to triple

7. Since 70 ÷ 7 = 10, it will take ten years to double, then another ten years to double again. Thus it will take twenty years to quadruple.

CHAPTER 6: MATH FOR THE BOARD

Columns of Numbers (this page)

Subtracting on Paper (this page)

Square Root Guesstimation (this page)

Pencil-and-Paper Multiplication (this page)

CHAPTER 8: THE TOUGH STUFF MADE EASY

Four-Digit Squares (this page)

3-by-2 Exercises Using Factoring, Addition, and Subtraction Methods (this page)

Five-Digit Squares (this page)

3-by-3 Multiplication (this page)

5-by-5 Multiplication (this page)

A Day for Any Date (this page)

1. January 19, 2007, is Friday: 6 + 19 + 1 = 26;26 − 21 = 5

2. February 14, 2012, is Tuesday: 1 + 14 + 1 = 16; 16 − 14 = 2

3. June 20, 1993, is Sunday: 3 + S + 20 = 28; 28 − 28 = 0

4. September 1, 1983, is Thursday: 4 + 1 + 6=11;11−7 = 4

5. September 8, 1954, is Wednesday: 4 + 8 + 5= 17; 17 − 14=3

6. November 19, 1863, is Thursday: 2 + 19 + 4 = 25; 25 − 21 =4

7. July 4, 1776, is Thursday: 5 + 4 + 2= 11I;11 − 7 = 4

8. February 22,2222, is Friday: 2 + 22 + 2 = 26; 26 − 21 =5

9. June 3 1,2468, doesn’t exist (only 30 days in June)! But June 30, 2468, is Saturday, so the next day would be Sunday.

10. January 1, 2358, is Wednesday: 6 + 1 + 3= 10; 10−7=3

Bibliography

Bibliography

RAPID CALCULATION

Cutler, Ann, and Rudolph McShane. The Trachtenberg Speed System of Basic Mathematics. New York: Doubleday, 1960.

Devi, Shakuntala. Figuring: The Joys of Numbers. New York: Basic Books, 1964.

Doerfler, Ronald W. Dead Reckoning: Calculating Without Instruments. Houston: Gulf Publishing Company, 1993.

Flansburg, Scott, and Victoria Hay. Math Magic. New York: William Morrow and Co., 1993.

Handley, Bill. Speed Mathematics: Secrets of Lightning Mental Calculation. Queensland, Australia: Wrightbooks, 2003.

Julius, Edward H. Rapid Math Tricks and Tips: 30 Days to Number Power. New York: John Wiley & Sons, 1992.

Lucas, Jerry. Becoming a Mental Math Wizard. Crozet, Virginia: Shoe Tree Press, 1991.

Menninger, K. Calculator’s Cunning. New York: Basic Books, 1964.

Smith, Steven B. The Great Mental Calculators: The Psychology, Methods, and Lives of Calculating Prodigies, Past and Present. New York: Columbia University Press, 1983.

Sticker, Henry. How to Calculate Quickly. New York: Dover, 1955.

Stoddard, Edward. Speed Mathematics Simplified. New York: Dover, 1994.

Tirtha, Jagadguru Swami Bharati Krishna, Shankaracharya of Govardhana Pitha. Vedic Mathematics or “Sixteen Simple Mathematical Formulae from the Vedas.” Banaras, India: Hindu University Press, 1965.

MEMORY

Lorayne, Harry, and Jerry Lucas. The Memory Book. New York: Ballantine Books, 1974.

Sanstrom, Robert. The Ultimate Memory Book. Los Angeles: Stepping Stone Books, 1990.

RECREATIONAL MATHEMATICS

Gardner, Martin. Magic and Mystery. New York: Random House, 1956.

———. Mathematical Carnival. Washington, D.C.: Mathematical Association of America, 1965.

———. Mathematical Magic Show. New York: Random House, 1977.

———. The Unexpected Hanging and Other Mathematical Diversions. New York: Simon & Schuster, 1969.

Huff, Darrell. How to Lie with Statistics. New York: Norton, 1954.

Paulos, John Allen. Innumeracy: Mathematical Illiteracy and Its Consequences. New York: Hill and Wang, 1988.

Stewart, Ian. Game, Set, and Math: Enigmas and Conundrums. New York: Penguin Books, 1989.

ADVANCED MATHEMATICS (BY ARTHUR BENJAMIN)

Benjamin, Arthur T., and Jennifer J. Quinn. Proofs That Really Count: The Art of Combinatorial Proof. Washington: Mathematical Association of America, 2003.

Benjamin, Arthur T., and Kan Yasuda. “Magic ‘Squares’ Indeed!,” The American Mathematical Monthly 106, no. 2 (February 1999): 152−56.

About the Author

About the Authors

DR. ARTHUR BENJAMIN is a professor of mathematics at Harvey Mudd College in Claremont, California, having received his PhD in mathematical sciences from Johns Hopkins University in 1989. In 2000, the Mathematical Association of America awarded him the Haimo Prize for Distinguished College Teaching. He is also a professional magician and frequently performs at the Magic Castle in Hollywood. He has demonstrated and explained his calculating talents to audiences all over the world. In 2005, Reader’s Digest called him “America’s Best Math Whiz.”

DR. MICHAEL SHERMER is a contributing editor to and monthly columnist for Scientific American, the publisher of Skeptic magazine (www.skeptic.com), the executive director of the Skeptics Society, and the host of the Caltech public science lecture series. He is the author of numerous science books, including Why People Believe Weird Things, How We Believe, The Science of Good and Evil, The Borderlands of Science, and Science Friction.

Imprint

Publication Date: 09-20-2016

All Rights Reserved

Dedication:
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 effortlessl