Algebra father may answer that if the boy added six years to his mother's age the result would be equal to the father's age The father has thus found an excellent opportunity to help his son understand how an algebraic equation may be made up and solved The father writes the mother's age on a slip of paper and turns the slip over so the boy cannot see the numeral He then lays the slip blank side up on a tablet Next to the slip he writes the symbols that will help solve the problem D 6 38 The son takes only a moment to guess that his mother is 32 years old When the father turns the slip of paper over they see this answer is correct 32 6 38 This will have been the boy s first lesson in algebra because he essentially solved the equa tion x 6
INTRODUCTION The father did not say anything about a mys terious letter x that can stand for any number Nor did he tell the boy about any rule such as changing the sign of the six and writing it on the other side of the equation Instead the boy s first lesson in algebra evolved in a natural way from a problem in arithmetic When you study algebra in school you will learn more about the relationship between algebra and arithmetic Some of the fundar mental concepts of algebra that are taught in school are explained in the following chap ters You will learn why algebra was developed basic principles of algebra such as variables generalizations and patterns and everything you need to know about real numbers More important you will learn how to apply alge bra's fundamental concepts In no time at all algebra will cease to be a mystery A R a costs
WHAT IS ALGEBRA lgebra has often been described as arith metic with letters Unlike arithmetic which deals with specific numbers algebra introduces variables that greatly extend the generality and scope of arithmetic This book will focus on the algebra taught in middle schools and high schools often referred to as elementary algebra which deals with the gen eral properties of numbers and the relations between them sin ALGEBRAIC QUANTITIES The principal distinguishing characteristic of algebra is the use of letters to represent numeri cal quantities and simple symbols to represent 10 Sin
WHAT IS ALGEBRA mathematical operations Following a system that originated with the 17th century French thinker René Descartes letters especially x y and 2 represent unknown quantities or vari ables The and signs indicate addition and subtraction of these quantities but multipli cation is simply indicated by adjacent letters Thus ax represents the product of a by x This simple expression can be interpreted for example as the interest earned in one year by a sum of a dollars invested at an annual rate of x It can also be interpreted as the distance traveled in a hours by a car moving at x miles per hour Such flexibility of representation is what gives algebra its great utility THE BEGINNINGS OF ALGEBRA More than 3 500 years ago an Egyptian named Ahmes collected a set of mathematical prob lems and their solutions About 2 500 years ago the Greek mathematician Pythagoras started a religious mathematical brother hood Intensely interested in geometry they classified numbers according to geometri cal properties The famous Greek geometer 11 R a costs
