MATH EE MAGICS Workbook
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CHAPTER 1 MENTAL ADDITION
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I remember the day in third grade when I discovered that it was easier to add and subtract from left to right than from right to left, which was the way we had all been taught. Suddenly I was able to blurt out the answers to math problems in class well before my classmates put down their pencils. And I didn't even need a pencil! The method was so simple that I performed most calculations in my head. Looking back, I admit I did so as much tc show off as for any mathematical reason. Most kids outgrow such behavior. Those who don't probably become either teachers or magicians. In this chapter you will learn the left-to-right method of doing mental addition for numbers that range in size from two to four digits. These mental skills are not only important for doing the tricks in this book but are also indispensable in school or at work, or any time you use numbers. Soon you will be able to retire your calculator and use the full capacity of your mind as you add, subtract, multiply, and divide 2-digit, 3-digit, and even 4-digit numbers.
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LEFT-TO-RIGHT ADDITION There are many good reasons why adding left to right is a superior method for mental calculation. For one thing, you do not have to reverse the numbers (as you do when adding right to left). And if you want to estimate your answer, then adding only the leading digits will get you pretty close. If you are used to working from right to left on paper, it may seem unnatural to add and multiply from left to right. But with practice you will find that it is the most natural and efficient way to do mental calculations. With the first set of problems—2 digit addition—the left to right method may not seem so advantageous. But be patient. If you stick with me, you will see that the only easy way to solve 3-digit and larger addition problems, all subtraction problems, and most definitely all multiplication and division problems, is from left to right. The sooner you get accustomed to computing this way, the better. 2-DIGIT ADDITION Our assumption in this chapter is that you know how to add and subtract 1-digit numbers. We will begin with 2-digit addition, something I suspect you can already do fairly well in your head. The following exercises are good practice, however, because you will use the 2-digit addition skills you polish here for larger addition problems, as well as virtually all multiplication problems in later chapters. It also illustrates a fundamental
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principle of mental arithmetic—namely, to simplify your problem by breaking it into smaller, more manageable components to success—simplify, simplify, simplify. The easiest 2-digit addition problems, of course, are those that do not require you to cany any numbers. For example:
To add 32 to 47, you can simplify by treating 32 as 30 + 2, add 30 to 47 and then add 2. In this way the problem becomes 77 + 2, which equals 79.
Keep in mind that the above diagram is simply a way of representing the mental processes involved in arriving at an answer using one method. While you need to be able to read and understand such diagrams as you work your way through this book, our method does not require you to write down anything yourself. Now let's try a calculation that requires you to carry a number:
Adding from left to right, you can simplify the problem by adding 67 + 20 = 87; then 87 + 8 = 95.