Integrated Arithmetic and Basic Algebra

<p><strong>R. Basic Ideas</strong></p> <p>R.1 Reading and Writing Numerals</p> <p>R.2 Addition and Subtraction of Whole Numbers</p> <p>R.3 Multiplication and Division of Whole Numbers</p> <p>R.4 A Brief Introduction to Fractions</p> <p>R.5 Addition and Subtraction of Decimal Numerals</p> <p>R.6 Multiplication and Division of Decimal Numerals</p> <p>R.7 Linear Measurement in the American and Metric Systems</p> <p><strong>1. Adding and Subtracting Integers and Polynomials</strong></p> <p>1.1 Variables, Exponents, and Order of Operations</p> <p>1.2 Perimeters of Geometric Figures</p> <p>1.3 Areas of Geometric Figures</p> <p>1.4 Volumes and Surface Areas of Geometric Figures</p> <p>1.5 Introduction to Integers</p> <p>1.6 Addition of Integers</p> <p>1.7 Subtraction of Integers and Combining Like Terms</p> <p>1.8 Polynomial Definitions and Combining Polynomials</p> <p><strong>2. Laws of Exponents, Products and Quotients of Integers and Polynomials</strong></p> <p>2.1 Multiplication of Integers</p> <p>2.2 Multiplication Laws of Exponents</p> <p>2.3 Products of Polynomials</p> <p>2.4 Special Products</p> <p>2.5 Division of Integers and Order of Operations with Integers</p> <p>2.6 Quotient Rule and Integer Exponents</p> <p>2.7 Power Rule for Quotients and Using Combined Laws of Exponents</p> <p>2.8 Division of Polynomials by Monomials</p> <p>2.9 An Application of Exponents: Scientific Notation</p> <p><strong>3. Linear Equations and Inequalities</strong></p> <p>3.1 Addition Property of Equality</p> <p>3.2 Multiplication Property of Equality</p> <p>3.3 Combining Properties in Solving Linear Equations</p> <p>3.4 Using and Solving Formulas</p> <p>3.5 General, Consecutive Integer, and Distance Application Problems</p> <p>3.6 Money, Investment, and Mixture Application Problems</p> <p>3.7 Geometric Application Problems</p> <p>3.8 Solving Linear Inequalities</p> <p><strong>4. Graphing Linear Equations and Inequalities</strong></p> <p>4.1 Reading Graphs and the Cartesian Coordinate System</p> <p>4.2 Graphing Linear Equations with Two Variables</p> <p>4.5 Graphing Linear Equations by Using Intercepts</p> <p>4.4 Slope of a Line</p> <p>4.5 Slope-Intercept Form of a Line</p> <p>4.6 Point-Slope Form of a Line</p> <p>4.7 Graphing Linear Inequalities with Two Variables</p> <p>4.8 Relations and Functions</p> <p><strong>5. Factors, Divisors, and Factoring</strong></p> <p>5.1 Prime Factorization and Greatest Common Factor</p> <p>5.2 Factoring Polynomials with Common Factors and by Grouping</p> <p>5.3 Factoring General Trinomials with Leading Coefficients of One</p> <p>5.4 Factoring General Trinomials with Leading Coefficients Other than One</p> <p>5.5 Factoring Binomials</p> <p>5.6 Factoring Perfect Square Trinomials</p> <p>5.7 Mixed Factoring</p> <p>5.8 Solving Quadratic Equations by Factoring</p> <p><strong>6. Multiplication and Division of Rational Numbers and Expressions</strong></p> <p>6.1 Reducing Rational Numbers and Rational Expressions</p> <p>6.2 Further Reduction of Rational Expressions</p> <p>6.3 Multiplication of Rational Numbers and Expressions</p> <p>6.4 Further Multiplication of Rational Expressions</p> <p>6.5 Division of Rational Numbers and Expressions</p> <p>6.6 Division of Polynomials (Long Division)</p> <p><strong>7. Addition and Subtraction of Rational Numbers and Expressions</strong></p> <p>7.1 Addition and Subtraction of Rational Numbers and Expressions with Like Denominators</p> <p>7.2 Least Common Multiple and Equivalent Rational Expressions</p> <p>7.3 The Least Common Denominator of Fractions and Rational Expressions</p> <p>7.4 Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators</p> <p>7.5 Complex Fractions</p> <p>7.6 Solving Equations Containing Rational Numbers and Expressions</p> <p>7.7 Applications with Rational Expressions</p> <p><strong>8. Ratios, Percents, and Applications</strong></p> <p>8.1 Ratios and Rates</p> <p>8.2 Proportions</p> <p>8.3 Percent</p> <p>8.4 Applications of Percent</p> <p>8.5 Further Applications of Percent</p> <p><strong>9. Systems of Linear Equations</strong></p> <p>9.1 Defining Linear Systems and Solving by Graphing</p> <p>9.2 Solving Systems of Linear Equations by Using Elimination by Addition</p> <p>9.3 Solving Systems of Linear Equations by Using Substitution</p> <p>9.4 Solving Application Problems by Using Systems of Equations</p> <p>9.5 Systems of Linear Inequalities</p> <p><strong>10. Roots and Radicals</strong></p> <p>10.1 Defining and Finding Roots</p> <p>10.2 Simplifying Radicals</p> <p>10.3 Products and Quotients of Radicals</p> <p>10.4 Addition, Subtraction, and Mixed Operations with Radicals</p> <p>10.5 Rationalizing the Denominator</p> <p>10.6 Solving Equations with Radicals</p> <p>10.7 Pythagorean Theorem</p> <p><strong>11. Solving Quadratic Equations</strong></p> <p>11.1 Solving Incomplete Quadratic Equations</p> <p>11.2 Solving Quadratic Equations by Completing the Square</p> <p>11.3 Solving Quadratic Equations by the Quadratic Formula</p> <p>11.4 Quadratic Equations with Complex Solutions</p> <p>11.5 Applications Involving Quadratic Equations</p>