Integrated Arithmetic and Basic Algebra

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

• ISBN13: 9780321132260
• ISBN10: 0321132262
• Edition: 3rd
• Format: Paperback
• Copyright: 2005-01-01
• Publisher: Addison Wesley

Summary

A combination of a basic mathematics or prealgebra text and an introductory algebra text, Integrated Arithmetic and Basic Algebra, Third Edition, provides a uniquely integrated presentation of the material for these courses in a way 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

Basic Ideas

Reading and Writing Numerals

Addition and Subtraction of Whole Numbers

Multiplication of Whole Numbers

Division of Whole Numbers

A Brief Introduction to Fractions

Addition and Subtraction of Decimal Numerals

Multiplication and Division of Decimal Numerals

Addition and Subtraction of Integers and Polynomials

Variables, Exponents and Order of Operations

Unit Conversions and Perimeters of Geometric Figures

Areas of Geometric Figures

Volumes and Surface Area of Geometric Figures

Introduction to Integers

Addition of Integers

Subtraction of Integers and Combining Like Terms

Polynomial Definitions and Combining Polynomials

Laws of Exponents, Products and Quotients of Polynomials

Multiplication of Integers

Multiplication Laws of Exponents

Products of Polynomials

Special Products

Division of and Order of Operations with Integers

Quotient Rule and Integer Exponents

Power Rule for Quotients and Using Combined Laws of Exponents

Division of Polynomials by Monomials

An Application of Exponents: Scientific Notation

Linear Equations and Inequalities

Addition Property of Equality

Multiplication Property of Equality

Combining Properties in Solving Linear Equations

Using and Solving Formulas

Solving Linear Inequalities

Traditional Applications Problems

More Traditional Applications Problems

Geometric Applications Problems

Using and Solving Formulas

Graphing Linear Equations and Inequalities

Ordered Pairs and Solutions of Linear Equations with Two Variables

Graphing Linear Equations with Two Variables

Graphing Linear Equations using Intercepts

Slope - Intercept Form of a Line

Point - Slope Form of a Line

Graphing Linear Inequalities with Two Variables

Relations and Functions

Systems of Linear Equations

Defining Linear Systems and Solving by Graphing

Solving Linear Systems of Equations Using Elimination by Addition

Solving Systems of Linear Equations Using Substitution

Applications Using Systems of Linear Equations

Systems of Linear Inequalities

Factors, Divisors, and Factoring

Introduction

Prime Factorization and Greatest Common Factor

Factoring Polynomials with Common Factors and by Grouping

Factoring General Trinomials with Leading Coefficient of One

Factoring General Trinomials with First Coefficient Other Than One

Factoring Binomials

Factoring Perfect Square Trinomials

Mixed Factoring

Solving Quadratic Equations by Factoring

Multiplication and Division of Rational Numbers and Expressions

Fractions and Rational Numbers

Reducing Rational Numbers and Rational Expressions

Further Reduction of Rational Expressions

Multiplication of Rational Numbers and Expressions

Further Multiplication of Rational Expressions

Division of Rational Numbers and Expressions

Division of Polynomials (Long Division)

Addition and Subtraction of Rational Numbers and Expressions

Addition and Subtraction of Rational Numbers and Expressions with Like Denominators

Least Common Multiple and Equivalent Rational Expressions

The Least Common Denominator of Fractions and Rational Expressions

Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators

Complex Fractions

Solving Equations Containing Rational Numbers and Expressions

Rates, Percents, and Applications Ratios and Rates

Proportions Percent Applications of Percent

Further Applications of Percent

Roots and Radicals

Defining and Finding Roots

Simplifying Radicals

Products and Quotients of Radicals

Addition, Subtraction, and Mixed Operations with Radicals

Rationalizing the Denominator

Solving Equations with Radicals

Pythagorean Theorem

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