Contents

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

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