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Table of Contents
Introduction - So you’re frustrated with math and numbers too? Well, come and take this journey with me and be frustrated no longer. Find out what Arithmetic Magic is and how it can help you with math
Chapter 1 - Addition: The First Pillar to Arithmetic Magic
* The magic of 10-Complements
* Columns of numbers and the Columns Chart
* The Quick-Add Chart and Procedure
* The Commutative and Associative Properties of Addition
* Carrying numbers and the Carry-Over Principle
* The Next Challenge: Adding 2-digit numbers and beyond using the Split Technique
* Practice Exercises for Chapter 1
Chapter 2 - Subtraction: The Second Pillar to Arithmetic Magic
* Subtraction from a different perspective: The Subtraction Step-Up Procedure
* Inverse operations, borrows, and exchanges
* Algebra helps define a new subtraction method
* Beyond 10comps to 100 comps
* Stepping up and going to bat to solve subtraction problems
* Practice Exercises for Chapter 2
Chapter 3 - Multiplication: The Third Pillar to Arithmetic Magic
* The Fundamental Multiplication Table
* Learning the table through repeated additions and Quick-Adds
* Upward and Onward: Beyond the Fundamental Table
* Two Key Ingredients: The Split-Technique and the Distributive Property
* 2-digit and 3-digit multiplications
* Percents: What they are and how to work with them
* A simple discussion on ratios, decimals, and fractions
* Tenths, hundredths, and thousandths
* Solving percent problems using the Method of Decimal Shifting
* Finding discounted prices using both estimation and the exact method
* Special Multiplication Techniques: The Difference of 2 Perfect Squares Technique, the Teenage Number Trick, and the Nifty-Five Square Technique
* Practice Exercises for Chapter 3
Chapter 4 - Division: The Fourth Pillar to Arithmetic Magic
* Division from the perspective of both subtraction and multiplication
* Dividends, divisors, and quotients
* Algebra helps define division in terms of multiplication
* The Method of 10-Multiples: a new approach to division
* Practice Exercises for Chapter 4
Conclusion - Your journey has just begun; some final words
* Answers to Practice Exercises
CHAPTER 1
ADDITION: THE FIRST PILLAR TO ARITHMETIC MAGIC
ADDITION AND THE MAGIC OF 10-COMPLEMENTS
So how do we get started? Well, we begin with the simple idea of addition. A simple operation yet important one at that. In fact, addition can be thought of as the mother of arithmetic, as once we learn this operation well, we get all the others practically free. Now what do I mean by this? Well, let’s look at it this way: subtraction is the opposite of addition, so that once we know addition we can perform subtraction in terms of this operation (more on this later when we discuss subtraction). Multiplication is repeated addition, so once again we have another operation expressed in terms of addition. Division is the opposite, or inverse, operation of multiplication. Since multiplication is repeated addition, we have an indirect route to division through addition. So basically, once we master addition, the other three arithmetic operations come practically free.
I would like to say something very important here and I really want to get this point across, for it well help you out tremendously. What I want you to understand is that part of mastering mathematics is learning how to look at a problem. Many people get intimidated by the math problem and give up hope before they even give some serious thought as to how they might solve the problem at hand. This attitude of defeat penetrates their existence and affects their whole being. One of my goals here will be to fix this problem and get you on the road to full math recovery. So where do we begin. Well let’s look at this thing I call 10-Complements. Just what is a 10-Complement? If you look below, I have listed the numbers 1 through 9 with their respective 10-Complements.
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