tract, multiply and divide numbers so that routine calculations were no longer a bother. Numbers are now no longer your enemies but your friends. A very likely consequence would then be that the word math no longer triggers a bunch of negative impressions but rather positive ones. You now consider yourself good at a very tough subject and therefore consider yourself a “cut above the rest.” The implications of this new self-appraisal are enormous.

Furthermore, imagine having a simple method which allowed you to figure percents easily. Then you could figure discounts in a store and know exactly how much less you would pay for items that go on

So you think you’re not good with math. Hmmm. Well that’s something I hear all the time so you shouldn’t feel too bad. The truth is, many, many people, at one time or another, have felt the same way, and have experienced something which has made them feel bad about math and numbers in general. So the common complaint, “I was never good at math,” or “I hate numbers and math,” is as common as the common cold and sometimes just as annoying. Interestingly, what I have discovered from working with students through the years is that this feeling of inadequacy often stems from some negative experiences with the subject. This might very well be the case with you. Perhaps you had a hard time in one of your math classes and felt very frustrated by it. Perhaps you struggled year after year because you could’nt understand the material being taught, or because the pace was too fast. Perhaps you didn’t understand because the subject matter was presented in a way that did not get across to you. Sound familiar?

My concern with the above scenario is that, uncorrected, this problem usually leads to feelings of frustration and inadequacy toward math in general. A likely—yet very undesirable—end result would be the drawing of incorrect conclusions about yourself and your abilities. Do these sound familiar?: “I’m just not good at math and never will be,” or “I’m just not smart enough to do math,” or more general and even more crippling, “I’m just not that smart.” I cannot count how many times I have heard such statements, the like of which only serve to drain the energy and stunt the educational gains of even the best of us. Unfortunately, these statements crystallize into attitudes and beliefs which become difficult to shake off. However mistaken these beliefs might be, their burdensome influence remains for a very long time— sometimes even for life. The end result—math illiteracy.

This is very unfortunate—even tragic—since the ability to work with numbers and do math are skills that have countless benefits. After all, no one should be doomed to mathematical illiteracy, especially when the alternative is so near within reach. Let’s consider the importance of basic math skills in everyday life. For one, you couldn’t count without math, pay bills and then balance a checkbook, understand basic financial matters, such as by how much money will grow at different interest rates, or even figure how much change you should get after a simple purchase transaction. What a sorry state we would all be in if we couldn’t do these simple things! Now think for a second. Suppose you could add, subtract, multiply and divide numbers so that routine calculations were no longer a bother. Numbers are now no longer your enemies but your friends. A very likely consequence would then be that the word math no longer triggers a bunch of negative impressions but rather positive ones. You now consider yourself good at a very tough subject and therefore consider yourself a “cut above the rest.” The implications of this new self-appraisal are enormous.

Furthermore, imagine having a simple method which allowed you to figure percents easily. Then you could figure discounts in a store and know exactly how much less you would pay for items that go on s

ith you. Perhaps you had a hard time in one of your math classes and felt very frustrated by it. Perhaps you struggled year after year because you could’nt understand the material being taught, or because the pace was too fast. Perhaps you didn’t understand because the subject matter was presented in a way that did not get across to you. Sound familiar?

My concern with the above scenario is that, uncorrected, this problem usually leads to feelings of frustration and inadequacy toward math in general. A likely—yet very undesirable—end result would be the drawing of incorrect conclusions about yourself and your abilities. Do these sound familiar?: “I’m just not good at math and never will be,” or “I’m just not smart enough to do math,” or more general and even more crippling, “I’m just not that smart.” I cannot count how many times I have heard such statements, the like of which only serve to drain the energy and stunt the educational gains of even the best of us. Unfortunately, these statements crystallize into attitudes and beliefs which become difficult to shake off. However mistaken these beliefs might be, their burdensome influence remains for a very long time— sometimes even for life. The end result—math illiteracy.

This is very unfortunate—even tragic—since the ability to work with numbers and do math are skills that have countless benefits. After all, no one should be doomed to mathematical illiteracy, especially when the alternative is so near within reach. Let’s consider the importance of basic math skills in everyday life. For one, you couldn’t count without math, pay bills and then balance a checkbook, understand basic financial matters, such as by how much money will grow at different interest rates, or even figure how much change you should get after a simple purchase transaction. What a sorry state we would all be in if we couldn’t do these simple things! Now think for a second. Suppose you could add, subtract, multiply and divide numbers so that routine calculations were no longer a bother. Numbers are now no longer your enemies but your friends. A very likely consequence would then be that the word math no longer triggers a bunch of negative impressions but rather positive ones. You now consider yourself good at a very tough subject and therefore consider yourself a “cut above the rest.” The implications of this new self-appraisal are enormous.

Furthermore, imagine having a simple method which allowed you to figure percents easily. Then you could figure discounts in a store and know exactly how much less you would pay for items that go on

r?: “I’m just not good at math and never will be,” or “I’m just not smart enough to do math,” or more general and even more crippling, “I’m just not that smart.” I cannot count how many times I have heard such statements, the like of which only serve to drain the energy and stunt the educational gains of even the best of us. Unfortunately, these statements crystallize into attitudes and beliefs which become difficult to shake off. However mistaken these beliefs might be, their burdensome influence remains for a very long time— sometimes even for life. The end result—math illiteracy.

This is very unfortunate—even tragic—since the ability to work with numbers and do math are skills that have countless benefits. After all, no one should be doomed to mathematical illiteracy, especially when the alternative is so near within reach. Let’s consider the importance of basic math skills in everyday life. For one, you couldn’t count without math, pay bills and then balance a checkbook, understand basic financial matters, such as by how much money will grow at different interest rates, or even figure how much change you should get after a simple purchase transaction. What a sorry state we would all be in if we couldn’t do these simple things! Now think for a second. Suppose you could add, subtract, multiply and divide numbers so that routine calculations were no longer a bother. Numbers are now no longer your enemies but your friends. A very likely consequence would then be that the word math no longer triggers a bunch of negative impressions but rather positive ones. You now consider yourself good at a very tough subject and therefore consider yourself a “cut above the rest.” The implications of this new self-appraisal are enormous.

Furthermore, imagine having a simple method which allowed you to figure percents easily. Then you could figure discounts in a store and know exactly how much less you would pay for items that go on

to work with numbers and do math are skills that have countless benefits. After all, no one should be doomed to mathematical illiteracy, especially when the alternative is so near within reach. Let’s consider the importance of basic math skills in everyday life. For one, you couldn’t count without math, pay bills and then balance a checkbook, understand basic financial matters, such as by how much money will grow at different interest rates, or even figure how much change you should get after a simple purchase transaction. What a sorry state we would all be in if we couldn’t do these simple things! Now think for a second. Suppose you could add, subtract, multiply and divide numbers so that routine calculations were no longer a bother. Numbers are now no longer your enemies but your friends. A very likely consequence would then be that the word math no longer triggers a bunch of negative impressions but rather positive ones. You now consider yourself good at a very tough subject and therefore consider yourself a “cut above the rest.” The implications of this new self-appraisal are enormous.

Furthermore, imagine having a simple method which allowed you to figure percents easily. Then you could figure discounts in a store and know exactly how much less you would pay for items that go on

tract, multiply and divide numbers so that routine calculations were no longer a bother. Numbers are now no longer your enemies but your friends. A very likely consequence would then be that the word math no longer triggers a bunch of negative impressions but rather positive ones. You now consider yourself good at a very tough subject and therefore consider yourself a “cut above the rest.” The implications of this new self-appraisal are enormous.

Furthermore, imagine having a simple method which allowed you to figure percents easily. Then you could figure discounts in a store and know exactly how much less you would pay for items that go on sale. As you will soon see, working with calculations involving percents is nothing more than understanding decimals and how to multiply numbers. Of course, rather than figure the discounts yourself you could wait until you got to the cash register to pay for the items. This would always be a possibility, but once again these methods do not only have one practical use. If they did, their value would be that much less. Percents figure in many other areas of the real world, not just in purchase transactions. In short, these newly acquired skills, whether they be in the area of multiplication and addition, or in the area of percent problems, will certainly open up all sorts of possibilities within the mathematical realm and unleash capabilities within you that you never thought you possessed. In short, this is the aim of Arithmetic Magic: to foster an appreciation of mathematics through the study of the basic arithmetical operations.

With this goal in mind, many positive things are achieved. Specifically, as you learn the techniques in this book, your new ability to work with numbers will definitely give you an advantage—an edge, sharp and cutting—to whatever you do. Aside from giving you a command over numbers, which will come in handy in daily life and serve you countless times in your days going forward, the techniques will pave the road toward new-found confidence and a boost in attitude towards your mental abilities. This—more than the computational ability—is the key payoff. Personally, it would be difficult for me to estimate the number of times I have used these techniques or the number of ways in which they serve me. In fact, I am constantly coming up with new combinations of the techniques and teaching both myself and my students new methods based on existing ones. You will find yourself doing the same as you read this book with an open and hungry mind.

For those of you who think the ability to work easily with numbers is beyond them, think again. From my experience, I am convinced that the ability to work well with numbers is not solely a byproduct of inborn talent. This is in spite of what many might think. Barring any severe mental abnormalities, an individual can improve his ability at math. Even the so-called “classified” individuals, whether they be considered “learning disabled” or afflicted with ADD (Attention Deficit Disorder)—whatever such classifications might mean—have benefitted from these techniques. Part of the inability to do math seems to be simply that, when it comes to math and working with numbers, many individuals concede defeat before