Preface  (Page 3/3)

We have taken great care to present concepts and techniques so they are under­standable and easily remembered. After concepts have been developed, students are warned about common pitfalls. We have tried to make the text an information source accessible to prealgebra students.

Addition and subtraction of whole numbers

This chapter in­cludes the study of whole numbers, including a discussion of the Hindu-Arabic numeration and the base ten number systems. Rounding whole numbers is also presented, as are the commutative and associative properties of addition.

Multiplication and division of whole numbers

The operations of multiplication and division of whole numbers are explained in this chapter. Multi­plication is described as repeated addition. Viewing multiplication in this way may provide students with a visualization of the meaning of algebraic terms such as $8x$ when they start learning algebra. The chapter also includes the commutative and associative properties of multiplication.

Exponents, roots, and factorizations of whole numbers

The concept and meaning of the word root is introduced in this chapter. A method of reading root notation and a method of determining some common roots, both mentally and by calculator, is then presented. We also present grouping symbols and the order of operations, prime factorization of whole numbers, and the greatest common factor and least common multiple of a collection of whole numbers.

Introduction to fractions and multiplication and division of frac­tions

We recognize that fractions constitute one of the foundations of problem solving. We have, therefore, given a detailed treatment of the operations of multi­plication and division of fractions and the logic behind these operations. We believe that the logical treatment and many practice exercises will help students retain the information presented in this chapter and enable them to use it as a foundation for the study of rational expressions in an algebra course.

Addition and subtraction of fractions, comparing fractions, and complex fractions

A detailed treatment of the operations of addition and sub­traction of fractions and the logic behind these operations is given in this chapter. Again, we believe that the logical treatment and many practice exercises will help students retain the information, thus enabling them to use it in the study of rational expressions in an algebra course. We have tried to make explanations dynamic. A method for comparing fractions is introduced, which gives the student another way of understanding the relationship between the words denominator and denomination . This method serves to show the student that it is sometimes possible to compare two different types of quantities. We also study a method of simplifying complex fractions and of combining operations with fractions.

Decimals

The student is introduced to decimals in terms of the base ten number system, fractions, and digits occurring to the right of the units position. A method of converting a fraction to a decimal is discussed. The logic behind the standard methods of operating on decimals is presented and many examples of how to apply the methods are given. The word of as related to the operation of multipli­cation is discussed. Nonterminating divisions are examined, as are combinations of operations with decimals and fractions.

Ratios and rates

We begin by defining and distinguishing the terms ratio and rate . The meaning of proportion and some applications of propor­tion problems are described. Proportion problems are solved using the "Five-Step Method." We hope that by using this method the student will discover the value of introducing a variable as a first step in problem solving and the power of organiza­tion. The chapter concludes with discussions of percent, fractions of one percent, and some applications of percent.

Techniques of estimation

One of the most powerful problem-solv­ing tools is a knowledge of estimation techniques. We feel that estimation is so important that we devote an entire chapter to its study. We examine three estima­tion techniques: estimation by rounding, estimation by clustering, and estimation by rounding fractions. We also include a section on the distributive property, an important algebraic property.

Measurement and geometry

This chapter presents some of the techniques of measurement in both the United States system and the metric sys­tem. Conversion from one unit to another (in a system) is examined in terms of unit fractions. A discussion of the simplification of denominate numbers is also in­cluded. This discussion helps the student understand more clearly the association between pure numbers and dimensions. The chapter concludes with a study of perimeter and circumference of geometric figures and area and volume of geometric figures and objects.

Signed numbers

A look at algebraic concepts and techniques is begun in this chapter. Basic to the study of algebra is a working knowledge of signed numbers. Definitions of variables, constants, and real numbers are introduced. We then distinguish between positive and negative numbers, learn how to read signed numbers, and examine the origin and use of the double-negative property of real numbers. The concept of absolute value is presented both geometrically (using the number line) and algebraically. The algebraic definition is followed by an interpre­tation of its meaning and several detailed examples of its use. Addition, subtrac­tion, multiplication, and division of signed numbers are presented first using the number line, then with absolute value.

Algebraic expressions and equations

The student is introduced to some elementary algebraic concepts and techniques in this final chapter. Alge­braic expressions and the process of combining like terms are discussed in [link] and [link] . The method of combining like terms in an algebraic expression is explained by using the interpretation of multiplication as a description of repeated addition (as in [link] ).