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192 Secrets of Mental Math (e.g., 447 our rug) and put the hundreds digit (1) on my fingers: 851 527 5 851 4,255 8 27 “Our rug” 216 4,471 100 447,100 51 27 1,377 448,477 Let’s do another example, but this time I’ll break up the first number. (I usually break up the larger one so that the addition problem is easier.) 923 673 9 673 6,057 6 23 “Shut up” 138 6,195 100 619,500 73 23 1,679 621,179 EXERCISE: 3-BY-3 MULTIPLICATION 644 286 596 167 853 325 343 226 1. 2. 3. 4. 5. 809 527 942 879 692 644 446 176 658 468 6. 7. 8. 9. 10. 273 138
The Tough Stuff Made Easy: Advanced Multiplication 193 824 206 642 249 783 589 871 926 11. 12. 13. 14. 15. 341 715 417 298 557 756 976 878 16. 17. 18. 19. 765 350 The following problems are embedded in the 5-by-5 multiplication problems in the next section: 154 423 545 834 216 653 20. 21. 22. 23. 393 822 5-BY-5 MULTIPLICATION The largest problem we will attempt is the mental multiplication of two five-digit numbers. To do a 5-by-5, you need to have mastered 2-by-2s, 2-by-3s, and 3-by-3s, as well as the phonetic code. Now it is just a matter of putting it all together. As you did in the five-digit square problems, you will use the distributive law to break down the numbers. For example: 27,639 (27,000 639) 52,196 (52,000 196) Based on this you can break down the problem into four easier multiplication problems, which I illustrate below in crisscross fashion as a 2-by-2, two 3-by-2s, and finally a 3-by-3, summing the results for a grand total. That is, (27 52) million [(27 196) (52 639)] thousand (639 196)
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This book has been optimized for vi
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SECRE+S OF MEN+AL MA+H The Mathemag
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I dedicate this book to my wife, De
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Contents Foreword by Bill Nye (the
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Foreword by Bill Nye (the Science G
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Foreword xiii Well, actually, I hop
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Foreword xv there are also an infin
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xviii Foreword math nut. Immunizati
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xx Prologue in on his secrets of
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xxii Prologue where he learned thes
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xxiv Introduction Too often, math i
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2 Secrets of Mental Math 35 2 What
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4 Secrets of Mental Math Absolutely
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6 Secrets of Mental Math Similarly,
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8 Secrets of Mental Math Although I
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10 Secrets of Mental Math Exception
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12 Secrets of Mental Math math in y
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16 Secrets of Mental Math 858 7 re
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18 Secrets of Mental Math lot easie
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20 Secrets of Mental Math Carl Frie
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22 Secrets of Mental Math Of course
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24 Secrets of Mental Math 958 417
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26 Secrets of Mental Math to 10. We
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28 Secrets of Mental Math By roundi
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30 Secrets of Mental Math mentally,
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32 Secrets of Mental Math 48 40 8
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34 Secrets of Mental Math problems
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36 Secrets of Mental Math 3-BY-1 MU
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38 Secrets of Mental Math sometimes
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40 Secrets of Mental Math 376 (300
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42 Secrets of Mental Math 925 (900
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44 Secrets of Mental Math BE THERE
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48 Secrets of Mental Math other squ
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50 Secrets of Mental Math WHY THESE
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52 Secrets of Mental Math Similarly
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54 Secrets of Mental Math Gardner o
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56 Secrets of Mental Math same digi
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New and Improved Products: Intermed
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64 Secrets of Mental Math To see ho
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66 Secrets of Mental Math Remember
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68 Secrets of Mental Math 67: 67 3
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70 Secrets of Mental Math EXERCISE:
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72 Secrets of Mental Math Rounding
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76 Secrets of Mental Math 13 1,000
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78 Secrets of Mental Math Chapter 8
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Chapter 4 Divide and Conquer: Menta
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82 Secrets of Mental Math Let’s t
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86 Secrets of Mental Math In using
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88 Secrets of Mental Math 682 23 I
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94 Secrets of Mental Math way is to
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98 Secrets of Mental Math You can e
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100 Secrets of Mental Math A number
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102 Secrets of Mental Math Divisibi
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104 Secrets of Mental Math It is al
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106 Secrets of Mental Math So, To a
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Chapter 5 Good Enough: The Art of
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110 Secrets of Mental Math Notice t
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112 Secrets of Mental Math 8,367 5
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114 Secrets of Mental Math onds doe
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116 Secrets of Mental Math We obser
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118 Secrets of Mental Math Divide:
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120 Secrets of Mental Math roots. I
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122 Secrets of Mental Math MORE TIP
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124 Secrets of Mental Math I will s
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126 Secrets of Mental Math number o
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128 Secrets of Mental Math and sinc
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130 Secrets of Mental Math EXERCISE
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132 Secrets of Mental Math COLUMNS
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134 Secrets of Mental Math As illus
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136 Secrets of Mental Math 4. 3 5 8
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138 Secrets of Mental Math Next, we
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140 Secrets of Mental Math You have
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Page 259 and 260: Answers CHAPTER 1: A LITTLE GIVE AN
Page 261 and 262: Answers 235 Three-Digit Subtraction
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2-by-2 Factoring-Method Multiplicat
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Answers 245 13. 38 63 (9 7) 15.
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Answers 247 234 17 3. 217 2 46,800
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Answers 249 CHAPTER 4: DIVIDE AND C
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Answers 251 23. 4,425,575 No: 4 4
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Answers 253 7. 7 8 1 1 4 1
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Answers 255 9. 104,972 10. 5,462,74
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Square Root Guesstimation (page 150
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3-by-2 Exercises Using Factoring, A
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21. 281 or 281 (280 1) 44 (11 4
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Answers 263 3. 58,324 2 “Liver”
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3-by-3 Multiplication (page 192) 1.
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Answers 267 13. 783 (87 9) 589 1
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Answers 269 5-by-5 Multiplication (
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Bibliography RAPID CALCULATION Cutl
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Index addition: an “amazing” su
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Index 275 factoring a number: in th
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Index 277 three-by-two problems, 16
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About the Authors DR. ARTHUR BENJAM
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