Integrated Arithmetic and Basic Algebra

by Jordan, Bill E.; Palow, William P.

• ISBN13: 9780201642032
• ISBN10: 0201642034
• Edition: 2nd
• Format: Paperback
• Copyright: 2001-01-01
• Publisher: Addison Wesley

Summary

A combination of a basic mathematics or prealgebra text with an introductory algebra text, Integrated Arithmetic and Basic Algebra provides a unique, integrated presentation of the material for these courses that is extremely beneficial to students. As opposed to traditional texts that present arithmetic at the beginning and algebra at the end, this text integrates the two whenever possible, so that students see how concepts are interrelated rather than learning them in isolation and missing the big picture. The ideas and algorithms shared by arithmetic and algebra are introduced in an arithmetic context and then developed through the corresponding algebraic concept. For example, operations with rational numbers and rational expressions are discussed together, whereas most texts discuss operations with rational numbers early on and operations with rational expressions much later. The Jordan/Palow text helps students recognize algebra as a natural extension of arithmetic using variables. This approach aligns directly with NCTM and AMATYC standards, which suggest playing upon students' previous knowledge to teach new concepts.

Table of Contents

Preface	vii
Basic Ideas
Reading and Writing Numerals	2	(5)
Addition of Whole Numbers	7	(6)
Subtraction of Whole Numbers	13	(7)
Multiplication of Whole Numbers	20	(5)
Division of Whole Numbers	25	(8)
A Brief Introduction to Fractions	33	(9)
Addition and Subtraction of Decimal Numerals	42	(10)
Multiplication and Division of Decimal Numerals	52	(9)
Linear Measurement in the American and Metric Systems	61	(13)
Summary	67	(2)
Review Exercises	69	(2)
Test	71	(3)
Adding and Subtracting Integers and Polynomials
Variables, Exponents, and Order of Operations	74	(10)
Perimeters of Geometric Figures	84	(9)
Areas of Geometric Figures	93	(8)
Volumes and Surface Areas of Geometric Figures	101	(8)
Introduction to Integers	109	(6)
Addition of Integers	115	(11)
Subtraction of Integers and Combining Like Terms	126	(10)
Polynomial Definitions and Combining Polynomials	136	(22)
Summary	149	(2)
Review Exercises	151	(3)
Test	154	(4)
Laws of Exponents, Products and Quotients of Integers and Polynomials
Multiplication of Integers	158	(9)
Multiplication Laws of Exponents	167	(8)
Products of Polynomials	175	(7)
Special Products	182	(8)
Division of and Order of Operations with Integers	190	(9)
Quotient Rule and Integer Exponents	199	(9)
Power Rule for Quotients and Using Combined Laws of Exponents	208	(6)
Division of Polynomials by Monomials	214	(5)
An Application of Exponents: Scientific Notation	219	(15)
Summary	227	(2)
Review Exercises	229	(2)
Test	231	(3)
Linear Equations and Inequalities
Addition Property of Equality	234	(10)
Multiplication Property of Equality	244	(9)
Combining Properties in Solving Linear Equations	253	(10)
Solving Linear Inequalities	263	(13)
Traditional Application Problems	276	(10)
Other Types of Traditional Application Problems	286	(11)
Geometric Application Problems	297	(7)
Using and Solving Formulas	304	(12)
Summary	308	(2)
Review Exercises	310	(3)
Test	313	(3)
Graphing Linear Equations and Inequalities
Ordered Pairs and Solutions of Linear Equations with Two Variables	316	(11)
Graphing Linear Equations with Two Variables	327	(8)
Graphing Linear Equations Using Intercepts	335	(7)
Slope of a Line	342	(13)
Slope-Intercept Form of a Line	355	(8)
Point-Slope Form of a Line	363	(11)
Graphing Linear Inequalities with Two Variables	374	(9)
Relations and Functions	383	(19)
Summary	391	(2)
Review Exercises	393	(5)
Test	398	(4)
Factors, Divisors, and Factoring
Prime Factorization and Greatest Common Factor	402	(10)
Factoring Polynomials with Common Factors and by Grouping	412	(7)
Factoring General Trinomials with Leading Coefficient of One	419	(9)
Factoring General Trinomials with First Coefficient other than One	428	(5)
Factoring Binomials	433	(6)
Factoring Perfect Square Trinomials	439	(4)
Mixed Factoring	443	(3)
Solving Quadratic Equations by Factoring	446	(14)
Summary	454	(2)
Review Exercises	456	(1)
Test	457	(3)
Multiplication and Division of Rational Numbers and Expressions
Fractions and Rational Numbers	460	(12)
Reducing Rational Numbers and Rational Expressions	472	(5)
Further Reduction of Rational Expressions	477	(8)
Multiplication of Rational Numbers and Expressions	485	(8)
Further Multiplication of Rational Expressions	493	(4)
Division of Rational Numbers and Expressions	497	(6)
Division of Polynomials (Long Division)	503	(13)
Summary	508	(2)
Review Exercises	510	(3)
Test	513	(3)
Addition and Subtraction of Rational Numbers and Expressions
Addition and Subtraction of Rational Numbers and Expressions with Like Denominators	516	(10)
Least Common Multiple and Equivalent Rational Expressions	526	(11)
The Least Common Denominator of Fractions and Rational Expressions	537	(6)
Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators	543	(6)
Complex Fractions	549	(6)
Solving Equations Containing Rational Numbers and Expressions	555	(5)
Applications with Rational Expressions	560	(16)
Summary	569	(2)
Review Exercises	571	(2)
Test	573	(3)
Ratios, Percents, and Applications
Ratios and Rates	576	(7)
Proportions	583	(7)
Percent	590	(8)
Applications of Percent	598	(7)
Further Applications of Percent	605	(21)
Summary	619	(2)
Review Exercises	621	(2)
Test	623	(3)
Systems of Linear Equations
Defining Linear Systems and Solving by Graphing	626	(10)
Solving Systems of Linear Equations Using Elimination by Addition	636	(10)
Solving Systems of Linear Equations Using Substitution	646	(8)
Solving Application Problems Using Systems of Linear Equations	654	(9)
Systems of Linear Inequalities	663	(13)
Summary	670	(1)
Review Exercises	671	(2)
Test	673	(3)
Roots and Radicals
Defining and Finding Roots	676	(6)
Simplifying Radicals	682	(7)
Products and Quotients of Radicals	689	(7)
Addition, Subtraction, and Mixed Operations with Radicals	696	(10)
Rationalizing the Denominator	706	(8)
Solving Equations with Radicals	714	(7)
Pythagorean Theorem	721	(13)
Summary	729	(2)
Review Exercises	731	(1)
Test	732	(2)
Solving Quadratic Equations
Solving Incomplete Quadratic Equations	734	(6)
Solving Quadratic Equations by Completing the Square	740	(8)
Solving Quadratic Equations by the Quadratic Formula	748	(5)
Solving Mixed Equations	753	(7)
Applications Involving Quadratic Equations	760	(11)
Summary	767	(2)
Review Exercises	769	(1)
Test	770	(1)
Answers for Odd-Numbered Exercises	771	(26)
Index	797	(10)
Table 1: Powers and Roots	807