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Idiot’s Guides®: Speed Math
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Idiot’s Guides®: Speed Math
by Gaurav Tekriwal
Speed Math
Cover
Title Page
Copyright Page
Introduction
Part 1: High-Speed Operations
1 Multiplication
Finger Multiplication
The 2 Times Table
The 3 Times Table
The 4 Times Table
The Universal Times Tables
The 9 Times Table
Special Multiplication by 11
Multiplication of Two-Digit Numbers with 11
Multiplication of Larger Numbers with 11
Below the Base Method
Below Base 10
Below Base 100
Above the Base Method
Above Base 10
Above Base 100
Above and Below the Base Method
Above and Below Base 10
Above and Below Base 100
Multiples and Submultiples
Combined Problems
General Multiplication Using the Vertically and Crosswise Method
Two-Digit by Two-Digit Multiplication
Three-Digit by Three-Digit Multiplication
2 Addition
Left-to-Right Addition
Two-Digit Numbers
Three-Digit Numbers
Rapid Left-to-Right Columnar Addition
Addition with Numbers Near 10 or a Multiple of 10
Number Splitting
3 Subtraction
Left-to-Right Subtraction
Subtraction with Numbers Near 10 or a Multiple of 10
Number Splitting
Subtraction with the All from 9 and Last from 10 Method
Subtracting from a Power of 10
Subtracting a Number Ending in Zero from a Power of 10
Subtracting When Neither Number is a Power of 10
Starting the Method Later in the Problem
Ending the Method Earlier in the Problem
4 Division
Division with the Flag Method
Two-Digit Divisors
Three-Digit Divisors
Four-Digit Divisors
Altered Remainders
Auxiliary Fractions
Type 1: Fractions with a Denominator Ending in 9 or a Series of 9s
Type 2: Fractions with a Denominator Ending in 1 or a Series of 1s
5 Checking Your Answers with Digit Sums
What Are Digit Sums?
Casting Out Nines
The Nine-Point Circle
Using Digit Sums to Check Your Answers
Checking Addition Answers
Checking Subtraction Answers
Checking Multiplication Answers
Checking Division Answers
Part 2: High-Speed Math Applications
6 Fractions
Adding Fractions
Fractions with the Same Denominator
Fractions Where One Denominator Is a Factor of the Other
Addition with the Vertically and Crosswise Method
Subtracting Fractions
Fractions with the Same Denominator
Fractions Where One Denominator Is a Factor of the Other
Subtraction with the Vertically and Crosswise Method
Multiplying Fractions
Dividing Fractions
7 Decimals
The Decimal System and Place Value
Adding Decimal Numbers
Subtracting Decimal Numbers
Multiplying Decimal Numbers
Multiplying by Powers of 10
Multiplying Vertically and Crosswise
Dividing Decimal Numbers
Dividing by Powers of 10
Dividing a Decimal Number by a Whole Number
Dividing a Decimal Number by Another Decimal Number
8 Percentages
Converting Percentages into Fractions
Converting Fractions into Percentages
Converting Percentages into Decimals
Finding the Percentage of a Given Quantity
Two-Digit Numbers
Three-Digit Numbers
Expressing One Quantity as a Percentage of Another
Approximating Percentages
Percentage Increase or Decrease
Percentage Increase
Percentage Decrease
9 Divisibility
Divisibility Rules
The Osculation Method
Positive Osculation
Negative Osculation
10 Squared Numbers
Finding Squares of Numbers Ending in 5
Finding Squares of Numbers Near 50
Numbers Above 50
Numbers Below 50
Using the Duplex to Find the Value of a Squared Number
Two-Digit Squares
Three-Digit Squares
Four-Digit Squares
Combined Operations: Sums of Squares
11 Cubed Numbers
Finding the Cubes of Two-Digit Numbers
Calculating Cubes Near a Base
When the Number Is Above the Base
When the Number Is Below the Base
12 Numbers to the Fourth and Fifth Powers
Calculating a Number to the Fourth Power
Calculating a Number to the Fifth Power
13 Square and Cube Roots
Square Roots of Perfect Squares
Using Duplexes to Find Square Roots
Cube Roots of Perfect Cubes
Appendixes
A Practice Problems
Chapter 1: Multiplication
Chapter 2: Addition
Chapter 3: Subtraction
Chapter 4: Division
Chapter 5: Checking Your Answers with Digit Sums
Chapter 6: Fractions
Chapter 7: Decimals
Chapter 8: Percentages
Chapter 9: Divisibility
Chapter 10: Squared Numbers
Chapter 11: Cubed Numbers
Chapter 12: Numbers to the Fourth and Fifth Powers
Chapter 13: Square and Cube Roots
B Answer Key
Chapter 1: Multiplication
Chapter 2: Addition
Chapter 3: Subtraction
Chapter 4: Division
Chapter 5: Checking Your Answers with Digit Sums
Chapter 6: Fractions
Chapter 7: Decimals
Chapter 8: Percentages
Chapter 9: Divisibility
Chapter 10: Squared Numbers
Chapter 11: Cubed Numbers
Chapter 12: Numbers to the Fourth and Fifth Powers
Chapter 13: Square and Cube Roots
Index
About the Author
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