Like it or not, math is here to stay. We live in a world of percentages, statistics, interest rates, and taxes. The Dow goes up 3 percent, the NASDAQ drops 5 percent. The inflation rate is such-and-such a percent, the trade deficit is so many billions, and the national debt is so many trillions. And how big of a tip should you leave? You just can't get away from numbers. My aim in writing this book is to give you an easy-to-follow guide to the math you encounter in your everyday life. I hope this single volume will become the first resource you turn to for all your mathematical or numerical questions. The topics range from the simple-how to solve a percentage problem, how to figure a tip, how to balance your checkbook-to the complex-the formula for the present value of an annuity, an installment loan formula, and believe it or not, a simple explanation of Einstein's famous formula, E = mc2. You will also find here important numerical facts and definitions: everything from the definitions of gross domestic product and the federal deficit to windchill and heat index tables and the meaning of barometric pressure. Regardless of the complexity of the topic, all explanations are in plain English with a minimum of technical jargon. The first part of the book is a review of all the math topics you need in your day-to-day life. This is not a review of high school mathematics. High school math teachers often try to persuade students that what they're studying will prove useful, but let's face it, students are generally on the mark when they ask rhetorically, "When are we ever going to use this?" Few adults will ever need to use geometry proofs, trigonometry, advanced algebra, pre-calculus, or calculus. In fact, although simple algebra can come in handy, you can really get by without it. Here are topics you do need. Basic arithmetic is useful for doing things like balancing your checkbook and dealing with big numbers in the millions and billions. Fractions, decimals, and percents have endless applications: cooking, tipping, discounts, markups, mortgage rates, investments, etc. You use ratios and proportions whenever you change the scale of something, like with a scale drawing or a map, or when you adjust a recipe for different numbers of people. You will want to have a basic understanding of powers and roots to be able to work with financial formulas, among other things. Another fundamental is basic geometry -shapes are all around us, and every adult should understand the few simple formulas for perimeter, area, and volume, and the various units of measure for these quantities: inches, feet, miles, square feet, square yards, acres, cubic feet, gallons, etc. Sample problems include estimating how many square yards of carpeting you'll need to buy, and figuring the amount of fertilizer you need for your lawn. You need to have a basic understanding of probability and odds for gambling, dice games, card games, and the lottery, and to grasp the meaning of statements like "there's a 25 percent chance of rain tomorrow," or the often-quoted probability that a woman has a one-in-nine chance of contracting breast cancer sometime in her life. The media inundates us with medical studies, opinion polls, political polls, etc., and thus we need a basic understanding of statistics to separate the wheat from the chaff. If you read part I carefully, I'm confident that you will come away with the feeling that you can handle most, if not all, of the math problems you encounter in your day-to-day life. Those of you who do not need this mathematics refresher course can skip part I or read only the chapters you need. Parts II, III, and IV contain straightforward explanations of a hundred or so frequently encountered practical math problems. Simply look up your math question in the table of contents or the index. You'll find here explanations of things like converting between U.S. dollars and foreign currency, tips for helping your children with math, explanations of casino games, calculating mortgage payments, understanding credit card rates, and how to compute a pitcher's earned run average. DO THE MATH One of my objectives is to give you the tools you need to become mathematically self-reliant, so that as you go about your day-to-day affairs, you'll consider the math when making your decisions. You should know, for example, that flying from Chicago to Miami is much safer than driving. You may decide to drive anyway, for any number of reasons-the scenery, you enjoy driving, etc.-but you should know the relative accident statistics. You should be aware that if you carry a large credit card debt (at, say, a 19.8 percent APR) month after month without paying down the debt, you are throwing money down the drain at a truly alarming rate. When you do the math, you'll see that it rarely makes sense to take advantage of the "convenience" of a credit card unless you know that you'll be able to pay the balance down to zero in the near future. You may decide to buy that new computer or big-screen TV anyway, but you should be aware of the financial implications. Before you decide to buy a low-deductible health insurance plan-so that you'll "never have to worry about medical bills again"-you should know that you'll probably come out ahead if you buy a high-deductible plan. Before you go to the casino, you should know that roulette and craps are games of luck, not skill, and that the odds are against you. When it comes to math, ignorance is not bliss. THEN IGNORE THE MATH You should do the math, but the math won't always give you the answer you seek. Say you're buying a house and you've narrowed your choices down to two homes. The most important factors to you are location, price, the neighborhood, and the quality of the schools. You rate each of these two homes on each of the four factors, on a scale from 1 to 10, and house A comes out ahead of house B on three of the four factors, or even on all four factors, yet for some unexplained reason you still prefer house B. What should you do? Go with the math or your gut? Go with your gut . Why ignore your careful analysis? I suspect that what happens in situations like this is that we're subconsciously considering more factors or assigning them different weights than we are aware of or are able to articulate. Let's say house B came out on top only on the schools issue and only by a little. If you nevertheless prefer house B, it may be because you are aware subconsciously that the schools factor is more important than the other three combined. What if you prefer house B even when house A comes out ahead on all four factors? The likely explanation is that one or more factors that you weren't aware of or had decided weren't important or "shouldn't" be important-like a beautiful porch or the number of trees on the property-really are important to you. Now, does this mean that your analysis was a waste of time? Not at all. If you had not done any analysis and had made your decision only on instinct, you might end up in the wrong house. Let's say you don't have any children yet but are planning to raise a family, and thus you absentmindedly neglect to consider the schools issue. If you buy the house you like and then later learn that the schools are the worst in the country, you will wish you had done a thorough analysis before buying. The moral of the story is that in complex situations like this, you should do the math and listen to your gut instincts. Both are important. You can't make an informed decision unless you do the math. And you should also listen to your instincts because, in the words of mathematician and philosopher Blaise Pascal, "The heart has its reasons." A NOTE ON CALCULATOR USE, MENTAL COMPUTATION, AND ESTIMATION Calculators are great. I have several, I use them often, and couldn't get along without them. Everyone should know how to use them. They're fast, they never make mistakes-assuming, of course, that you punch the right buttons-and there are many math problems that are either too difficult or too time-consuming to do by hand. Throughout this book, I'll go through the calculator steps needed for solving various problems. But , I think it's unwise to use a calculator for every computation you do. When you use calculators for even the simplest of computations, your math muscles atrophy and you are more likely to view mathematics as a foreign, mysterious language that you will never really understand, an esoteric code that only a calculator can "understand." In contrast, when you work with numbers mentally or with pencil and paper, you strengthen your facility for math, and math will gradually come to make more and more sense to you. You will learn that you can do math with your common sense. If you have forgotten the times table up to 9 times 9-perhaps because you have been using a calculator even for problems like 9 times 4 or 8 times 6-you owe it to yourself to relearn it. You should also be able to multiply numbers like 40 times 25 in your head. Four quarters make a dollar, right? So, of course, 4 times 25 is 100, and since 40 is 10 times as big as 4, the answer is 10 times as big as 100, or 1000. And 30 times 120 should be easy to do mentally: multiply 3 by 12 to get 36 and then add two zeros to get 3600. What about 1.4 of 120?-half of 120 is 60, and half of that is 30. When you take a few seconds to think about how problems like this work rather than just pushing buttons on your calculator, your confidence in your math abilities will grow. In the final analysis, you should do what's comfortable for you. It won't be the end of the world if you decide to use a calculator even for 2 times 3 or 5 times 4. It certainly is reassuring to know that the calculator can't err. And if you're working on an important project where accuracy is absolutely critical, it may make sense to use the calculator, or at least to use it to check your answers. But your confidence and competence in mathematics will likely increase if, at least for the easy stuff, you do the math. Whether you do a problem in your head, on paper, or with a calculator, it's a good idea to also estimate a rough answer to the problem. Estimating builds confidence in math because when you estimate, you have to rely on your own grasp of a problem rather than just following memorized rules and formulas. Estimating is also a good way to catch errors. You shouldn't just blindly accept the answer you get with pencil and paper or with a calculator. Make sure that the answer agrees with your estimate and that it doesn't fly in the face of common sense. If you don't have a rough idea of what kind of answer to expect, you might push the wrong button on your calculator, get a ridiculous answer, and not realize that it's wrong. A FEW SUGGESTIONS TO THOSE WHO NEVER LIKED MATH OR WHOSE MATH IS RUSTY Whether you have never liked math or feel that you've forgotten most of the math you learned in high school, I'm confident that if you work through part I of this book patiently and thoroughly, you'll come away with a solid grasp of all the mathematics you need for practical math problems. Even if you've always hated math, you'll find that the math presented in part I is manageable. You may find that my explanations bring math down to earth and make it easier to grasp than you experienced in school. There are many reasons for not liking math-for feeling like a fish out of water whenever you deal with numbers. You may have had a bad experience in school that made you feel that you weren't good at math. You may have found math boring, meaningless, or irrelevant-and it's difficult to learn anything we believe is unimportant to us-or your teachers or parents may not have pushed you to succeed in math. And, for girls and women, although things are getting better all the time, there still remains in our culture a gender bias that expects more of boys than girls when it comes to math, science, and technology. The good news is that once you have a real desire to learn mathematics, none of the above will matter much. Everyone can learn math, we're hardwired for it. When the right approach is taken, math is something we can grasp with our common sense; it need not seem strange or esoteric. Two strategies that make math easier, for example, are to make math concrete and to learn why things are true . Math concepts make more sense to us when we see the connection between what may seem like a foreign or abstract rule or formula and the concrete reality of the world around us. For example, adding, subtracting, multiplying, and dividing negative numbers confuse some people. This is understandable because negative numbers can seem abstract-we can't have -5 apples, for example. Some people might be confused about how to add -8 and -5. For example, they might mistakenly use the multiplication rule that two negatives make a positive for this addition problem. But this problem needn't involve learning or remembering any abstract rules. You can think of negative numbers like debt. Two negatives add up to a bigger negative in precisely the same way that two debts add up to a bigger debt. That's all there is to it. When you make connections like this between seemingly strange math concepts and the familiar things from your day-to-day life, math gets so much easier. We can see that the area of the triangle is half of the area of the rectangle because triangle ABF (shaded black) is half of the rectangle on the left (rectangle ADBF), and triangle FBC (shaded gray) is half of the rectangle on the right (rectangle FBEC). Therefore, since the area of a rectangle equals base times height (which means the same thing as length times width ), the area of a triangle must be half of that, or half of base times height. In short, the formula for the area of a triangle is based on the simple fact that a triangle takes up half the area of a rectangle. When you learn the logic underlying mathematical ideas like these, math becomes far less intimidating. (Continues...) Excerpted from Everyday Math for Everyday Life by Mark Ryan Copyright © 2002 by The Math Center, Inc. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.