Quick(er) Calculations: How to add, subtract, multiply, divide, square, and square root more swiftly

Description

Finalist of the 2022 PROSE Awards How fast can you calculate? Would you like to be faster? This book presents the time honored tricks and tips of calculation, from a fresh perspective, to boost the speed at which you can add ― whether a couple of numbers, or columns so long an accountant may faint. Find out how to subtract, multiply, divide, and find square roots more quickly. What's more, this book gives suggestions for how to find answers that are "good enough" for tricky tasks like dividing by 17. It includes brand new ways to multiply and divide irrational numbers such as pi, e, the square root of 2, and the golden ratio. It has sections devoted to ancient mathematics, and the techniques we can borrow from previous and other cultures, in order to calculate more quickly. Examples, some serious, some fun, come from everyday life or from history ― like hot dog eating competitions, the Vatican's cricket team, the molecular weight of the molecule with the world's longest name, and the amount of people taken by Henry VIII to arguably history's biggest party, the Field of the Cloth of Gold. In an age of timed multiple-choice questions, the swifter you can sum, or rule out wrong answers, the better you will do. If you love to play with numbers, this book will be recreational reading. And if you ever wonder whether simple arithmetic problems can crop up in everyday life, this book provides a fresh perspective. Cover Quick(er) Calculations: How to Add, Subtract, Multiply, Divide, Square, and Square Root More Swiftly Copyright Dedication Preface Acknowledgments Contents Introduction Challenge Chapter 1: Arithmetical Advice Take less time on your times table The case of the crooked columns Guess what? Make estimates What’s the point? Extra zeros and decimals The × factor Shunting for show How? Try these Chapter 2: Speedier Subtractions and Sums Subtract by adding Two-step subtraction Double-switch subtraction Subtraction either side of an “easy” number Two-step addition Try these Interlude I: TheMagic of 111,111 Chapter 3: Accounting for Taste: Calculating Columns Quickly Adding numbers “mystically” Adding columns without carrying Tallying in tens Circular sums Cancel as you calculate The pricing pandemic Estimating columns of numbers Try these Interlude II: Checking, Check Digits, and Casting Out Nines Chapter 4: Quicker Quotients and Pleasing Products: Multiply and Divide by Specific Numbers Multiply or divide by 4 Multiply or divide by 5 Multiplication Division Multiply or divide by 6 Multiplication Division Multiply or divide by 7 Multiplication Division How it works Multiply or divide by 8 Multiply by 9 Multiply by 11 How it works Multiply or divide by 12 Multiply by 13 Multiply by 14 Multiply or divide by 15 Multiplication Division Multiply or divide by 15, 25, 35, or numbers ending in 5 Multiplication Division Multiply by 16, 26, 36, or numbers ending in 6 Multiply by 18, 27, 36, ormultiples of 9 Multiply by 19, 29, 39, or numbers ending in 9 Try these Multiply by 21, 31, 41, or numbers ending in 1 Multiply by 32, 42, 52, or numbers ending in a 2 Multiply or divide by 75 Multiplication Division Try these Multiply by 111 How it works Multiply or divide by 125 Multiplication Division Multiply by 31623, 63313, and 950 Multiply by 999 or 1,001 Try these Interlude III: Doomsday Chapter 5: Calculations with Constraints: Multiply and Divide by Numbers with Specific Properties Multiply two numbers, 10 apart, ending in 5 How it works Multiply two numbers, 20 apart, ending in 5 How it works Multiply a one- or two-digit number, less than 50, by 98 How it works Multiply a one- or two-digit number by 99 How it works Multiply a one- or two-digit number by 101 Multiply a one- or two-digit number, less than 50, by 102 Try these Multiply two numbers that differ by 2, 4, 6, or 20 How it works Multiply two “kindred” numbers How it works Multiply by 23, 34, 45, or numbers “remainder 1” when divided by 11 Multiply by 24, 36, 42, 48, or numbers where one digit is twice the other Multiply two numbers (or square a number) just under 100 How it works Multiply two numbers (or square a number) just over 100 How it works Multiply two numbers, either side of 100 How it works Multiply together two two-digit numbers How it works Try these Interlude IV: Multicultural Multiplication Indian multiplication Egyptian multiplication How it works “Russian peasant” math Chapter 6: Super Powers: Calculate Squares, Square Roots, Cube Roots, and More Square any two-digit number ending in 1 or 9 How it works Square any number ending in 5 How it works Square any number ending in 6 or 4 How it works Square any two-digit number How it works Square any three-digit number with middle digit 0 or 9 How it works Square any three-digit number with middle digit 4 or 5 Squaring, sort of. . . How it works Try these Square roots, Babylonian style How it works Square roots, Chinese style Square roots, Indian style How it works Square roots, French style Find the square root of amystery perfect square How it works Find the cube root of amystery perfect cube How it works Find the root of amystery fifth power Try these Chapter 7: Close-Enough Calculations: Quick and Accurate Approximations Divide by 9 How it works Divide by 11 How it works Divide by 13 How it works Divide by 14 Multiply or divide by 17 Divide by 19 or 21 How it works Divide by 24 or 26 Try these Multiply or divide by 32, 33, or 34 How it works Multiply or divide by 49 or 51 Multiply or divide by 66 or 67, 666 or 667, Newton’s Universal Constant of Gravitation or Planck’s constant Divide by 91 Divide by 111 Divide by 198, 202, and other multiples of 99 and 101 Try these Interlude V: Approximating the Number of Space Aliens Chapter 8: Multiplying and Dividing Irrationally Multiply or divide by√2 Multiply or divide by√3 Multiply or divide by the Golden Ratio Multiply or divide by e Multiply or divide by π A slice of Babylonian π Similar, but different Also similar, but far more accurate An almost-precise method How it works Divide by π Try these The Grand Finale Further Reading Other works on rapid mathematics Numbers History of mathematics Appendix i: Calculating Doomsday Appendix ii: The Squares from 1 to 100 Index