# Integrated Arithmetic and Basic Algebra

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• ISBN10:

## 0201642034

• Edition: 2nd
• Format: Paperback
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### 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.

Preface vii
 Basic Ideas
2(5)
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)
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
234(10)
 Multiplication Property of Equality
244(9)
 Combining Properties in Solving Linear Equations
253(10)
 Solving Linear Inequalities
263(13)
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)
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)
 Defining and Finding Roots
676(6)
682(7)
689(7)
696(10)
 Rationalizing the Denominator
706(8)
714(7)
 Pythagorean Theorem
721(13)
 Summary
729(2)
 Review Exercises
731(1)
 Test
732(2)
734(6)
 Solving Quadratic Equations by Completing the Square
740(8)
748(5)
 Solving Mixed Equations
753(7)
760(11)
 Summary
767(2)
 Review Exercises
769(1)
 Test
770(1)