Integrated Arithmetic and Basic Algebra
Pearson (Verlag)
978-0-321-13226-0 (ISBN)
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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.
(Each Chapter concludes with a Summary, Review Exercises and Test.)
0. 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.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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).
8. 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.
9. Rates, Percents, and Applications.
Ratios and Rates
Proportions
Percent
Applications of Percent
Further Applications of Percent
10. 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
11. Solving Quadratic Equations.
Solving Incomplete Quadratic Equations.
Solving Quadratic Equations by Completing the Square.
Solving Quadratic Equations by the Quadratic Formula.
Solving Mixed Equations.
Applications Involving Quadratic Equations.
Table 1. Powers and Roots.
Answers for Odd Numbered Exercises.
| Erscheint lt. Verlag | 2.9.2004 |
|---|---|
| Sprache | englisch |
| Maße | 215 x 278 mm |
| Gewicht | 1878 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 0-321-13226-2 / 0321132262 |
| ISBN-13 | 978-0-321-13226-0 / 9780321132260 |
| Zustand | Neuware |
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