Foundational Mathematics

Foundational Mathematics is a textbook for our Basic Skills Mathematics courses, including our Emporium mode of offering. Foundational Mathematics contains Prealgebra, Elementary Algebra and Intermediate Algebra content to support our students throughout their beginning mathematics journey.

Mathematics

Author: Ashley McHale
Publisher: Las Positas College
Source: LibreTexts
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 415 sections

01: The Whole Numbers
1.01: An Introduction to the Whole Numbers
1.02: Adding and Subtracting Whole Numbers
1.03: Multiplication and Division of Whole Numbers
1.04: Prime Factorization
1.05: Order of Operations
1.06: Solving Equations by Addition and Subtraction
1.07: Solving Equations by Multiplication and Division
1.08: Use the Language of Algebra (Part 1)
1.09: Use the Language of Algebra (Part 2)
1.10: Evaluate Simplify and Translate Expressions (Part 1)
1.11: Evaluate Simplify and Translate Expressions (Part 2)
1.12: Solving Equations Using the Subtraction and Addition Properties of Equality (Part 1)
1.13: Solving Equations Using the Subtraction and Addition Properties of Equality (Part 2)
1.E: Introduction to the Language of Algebra (Exercises)
1.E: Whole Numbers (Exercises)
1.S: Introduction to the Language of Algebra (Summary)
1.S: Whole Numbers (Summary)
02: Integers
2.01: Introduction to Integers (Part 1)
2.02: Introduction to Integers (Part 2)
2.03: Add Integers (Part 1)
2.04: Add Integers (Part 2)
2.05: Subtract Integers (Part 1)
2.06: Subtract Integers (Part 2)
2.07: Multiply and Divide Integers (Part 1)
2.08: Multiply and Divide Integers (Part 2)
2.09: Square Roots
2.10: What to Combine Order of Operations with Integers
2.11: Mathematical Expressions (NOT Equations)
2.12: Evaluating (NOT Solving) Algebraic Expressions
2.13: Simplifying (Still Not Solving) Algebraic Expressions)
2.13.01: Simplifying Algebraic Expressions
2.13.02: Combining Like Terms
2.14: Mean
2.15: Solve Equations Using Integers The Division Property of Equality (Part 1)
2.16: Solve Equations Using Integers The Division Property of Equality (Part 2)
2.E: Integers (Exercises)
2.S: Integers (Summary)
03: Algebraic Expressions
3.01: Use the Language of Algebra (Part 1)
3.02: Use the Language of Algebra (Part 2)
3.03: Evaluate Simplify and Translate Expressions (Part 1)
3.04: Evaluate Simplify and Translate Expressions (Part 2)
3.05: Solving Equations Using the Subtraction and Addition Properties of Equality (Part 1)
3.06: Solving Equations Using the Subtraction and Addition Properties of Equality (Part 2)
3.E: Introduction to the Language of Algebra (Exercises)
3.S: Introduction to the Language of Algebra (Summary)
04: Fractions
4.01: Visualize Fractions (Part 1)
4.02: Visualize Fractions (Part 2)
4.03: Rational Expressions (INTRO)
4.04: Multiply and Divide Fractions (Part 1)
4.05: Multiply and Divide Fractions (Part 2)
4.06: Find Multiples and Factors (Part 1)
4.07: Find Multiples and Factors (Part 2)
4.08: Prime Factorization and the Least Common Multiple (Part 1)
4.09: Prime Factorization and the Least Common Multiple (Part 2)
4.10: Multiply and Divide Mixed Numbers and Complex Fractions (Part 1)
4.11: Multiply and Divide Mixed Numbers and Complex Fractions (Part 2)
4.12: Add and Subtract Fractions with Common Denominators
4.13: Add and Subtract Fractions with Different Denominators (Part 1)
4.14: Add and Subtract Fractions with Different Denominators (Part 2)
4.15: Add and Subtract Mixed Numbers (Part 1)
4.16: Add and Subtract Mixed Numbers (Part 2)
4.17: Complex Rational Expressions
4.18: Solve Equations with Fractions (Part 1)
4.19: Solve Equations with Fractions (Part 2)
4.E: Fractions (Exercises)
4.S: Fractions (Summary)
05: Decimals
5.01: Decimals (Part 1)
5.02: Decimals (Part 2)
5.03: Decimal Operations (Part 1)
5.04: Decimal Operations (Part 2)
5.05: Decimals and Fractions (Part 1)
5.06: Decimals and Fractions (Part 2)
5.07: Rational and Irrational Numbers
5.08: Averages and Probability (Part 1)
5.09: Averages and Probability (Part 2)
5.10: Ratios and Rate (Part 1)
5.11: Ratios and Rate (Part 2)
5.12: Simplify and Use Square Roots (Part 1)
5.13: Simplify and Use Square Roots (Part 2)
5.14: Commutative and Associative Properties (Part 1)
5.15: Commutative and Associative Properties (Part 2)
5.16: Distributive Property
5.17: Properties of Identity Inverses and Zero
5.18: Solve Equations with Decimals
5.E: Decimals (Exercises)
5.E: The Properties of Real Numbers (Exercises)
5.S: Decimals (Summary)
5.S: The Properties of Real Numbers (Summary)
06: Ratio Proportion and Measurement
6.01: Ratio and Proportion
6.02: Introduction to Ratios and Rates
6.03: Introduction to Proportion
6.04: Unit Conversion - American System
6.05: Unit Conversion- Metric System
6.06: American Units to Metric Units and Vice-Versa
6.07: Use a Problem Solving Strategy (Part 1)
6.08: Use a Problem Solving Strategy (Part 2)
6.09: Solve a Formula for a Specific Variable
6.E: Math Models and Geometry (Exercises)
6.S: Math Models and Geometry (Summary)
07: Percents
7.01: Understand Percent
7.02: Solve General Applications of Percent
7.03: Solve Sales Tax Commission and Discount Applications
7.04: Solve Simple Interest Applications
7.05: Percent Increase or Decrease
7.06: Pie Charts
7.07: Solve Proportions and their Applications (Part 1)
7.08: Solve Proportions and their Applications (Part 2)
7.E: Percents (Exercises)
7.S: Percents (Summary)
08: Geometry and Graphing
8.01: Solve Geometry Applications- Circles and Irregular Figures
8.02: Use the Rectangular Coordinate System (Part 1)
8.03: Solve Geometry Applications- Volume and Surface Area (Part 1)
8.04: Use the Rectangular Coordinate System (Part 2)
8.05: Graphing Linear Equations (Part 1)
8.06: Solve Geometry Applications- Volume and Surface Area (Part 2)
8.07: Graphing Linear Equations (Part 2)
8.08: Use the Rectangular Coordinate System
8.8E: Exercises
8.09: Graphing with Intercepts (Part 1)
8.10: Graph Linear Equations in Two Variables
8.10E: Exercises
8.11: Graphing with Intercepts (Part 2)
8.12: Graph with Intercepts
8.12E: Exercises
8.13: Understand Slope of a Line (Part 1)
8.14: Understand Slope of a Line (Part 2)
8.E: Graphs (Exercises)
8.E: Review Exercises
8.S: Graphs (Summary)
09: Solving Linear Equations and Inequalities
9.01: Solve Equations Using the Subtraction and Addition Properties of Equality
9.1E: Exercises
9.02: Solve Equations using the Division and Multiplication Properties of Equality
9.2E: Exercises
9.03: Solve Equations with Variables and Constants on Both Sides
9.3E: Exercises
9.04: Use a General Strategy to Solve Linear Equations
9.4E: Exercises
9.05: Solve Equations with Fractions or Decimals
9.5E: Exercises
9.06: Solve a Formula for a Specific Variable
9.6E: Exercises
9.07: Solve Linear Inequalities
9.7E: Exercises
9.08: Chapter 2 Review Exercises
10: Graphs
10.01: Understanding the Slope of a Line
10.1E: Exercises
10.02: Use the SlopeIntercept Form of an Equation of a Line
10.2E: Exercises
10.03: Find the Equation of a Line
10.3E: Exercises
11: Systems of Linear Equations
11.01: Solve Systems of Linear Equations with Two Variables
11.1E: Exercises
11.02: Solve Applications with Systems of Equations
11.2E: Exercises
11.03: Solve Mixture Applications with Systems of Equations
11.3E: Exercises
11.04: Graphs of Linear Inequalities
11.4E: Exercises
12: Polynomials
12.01: Add and Subtract Polynomials
12.02: Use Multiplication Properties of Exponents (Part 1)
12.03: Use Multiplication Properties of Exponents (Part 2)
12.04: Multiply Polynomials (Part 1)
12.05: Multiply Polynomials (Part 2)
12.06: Divide Monomials (Part 1)
12.07: Divide Monomials (Part 2)
12.08: Integer Exponents and Scientific Notation (Part 1)
12.09: Integer Exponents and Scientific Notation (Part 2)
12.10: Introduction to Factoring Polynomials
12.E: Polynomials (Exercises)
12.S: Polynomials (Summary)
13: Additional Foundational Content
13.01: Cumulative Review
13.02: Powers and Roots
13.03: Geometric Formulas
13.04: Math Models and Geometry
13.4.01: Solve Money Applications
13.4.02: Use Properties of Angles Triangles and the Pythagorean Theorem (Part 1)
13.4.03: Use Properties of Angles Triangles and the Pythagorean Theorem (Part 2)
13.4.04: Use Properties of Rectangles Triangles and Trapezoids (Part 1)
13.4.05: Use Properties of Rectangles Triangles and Trapezoids (Part 2)
13.05: Foundations
13.5.01: Prelude to Foundations of Algebra
13.5.02: Introduction to Whole Numbers
13.5.2E: Exercises
13.5.03: Use the Language of Algebra
13.5.3E: Exercises
13.5.04: Add and Subtract Integers
13.5.4E: Exercises
13.5.05: Multiply and Divide Integers
13.5.5E: Exercises
13.5.06: Visualize Fractions
13.5.6E: Exercises
13.5.07: Add and Subtract Fractions
13.5.7E: Exercises
13.5.08: Decimals
13.5.8E: Exercises
13.5.09: The Real Numbers
13.5.9E: Exercises
13.5.10: Properties of Real Numbers
13.5.10E: Exercises
13.5.11: Systems of Measurement
13.5.11E: Exercises
13.5.12: Chapter 1 Review Exercises
13.06: Math Models
13.6.01: Use a Problem-Solving Strategy
13.6.1E: Exercises
13.6.02: Solve Percent Applications
13.6.2E: Exercises
13.6.03: Solve Mixture Applications
13.6.3E: Exercises
13.6.04: Triangles Rectangles and the Pythagorean Theorem
13.6.4E: Exercises
13.6.05: Solve Uniform Motion Applications
13.6.5E: Exercises
13.6.06: Solve Applications with Linear Inequalities
13.6.6E: Exercises
13.6.07: Chapter 3 Review Exercises
13.07: Foundations
13.7.01: Prelude to the Foundations of Algebra
13.7.02: Use the Language of Algebra
13.7.2E: Exercises
13.7.03: Integers
13.7.3E: Exercises
13.7.04: Fractions
13.7.4E: Exercises
13.7.05: Decimals
13.7.5E: Exercises
13.7.06: Properties of Real Numbers
13.7.6E: Exercises
13.7.07: Chapter 1 Review Exercises
13.08: Roots and Radicals
13.8.01: Simplify and Use Square Roots
13.8.1E: Exercises
13.8.02: Simplify Square Roots
13.8.2E: Exercises
13.8.03: Add and Subtract Square Roots
13.8.3E: Exercises
13.8.04: Multiply Square Roots
13.8.4E: Exercises
13.8.05: Divide Square Roots
13.8.06: Solve Equations with Square Roots
13.8.6E: Exercises
13.8.07: Higher Roots
13.8.08: Rational Exponents
13.8.8E: Exercises
13.8.09: Chapter 9 Review Exercises
13.09: Rational Expressions and Equations
13.9.01: Simplify Rational Expressions
13.9.1E: Exercises
13.9.02: Multiply and Divide Rational Expressions
13.9.2E: Exersices
13.9.03: Add and Subtract Rational Expressions with a Common Denominator
13.9.3E: Exersices
13.9.04: Add and Subtract Rational Expressions with Unlike Denominators
13.9.4E: Exercises
13.9.05: Simplify Complex Rational Expressions
13.9.5E: Exercises
13.9.06: Solve Rational Equations
13.9.6E: Exercises
13.9.07: Solve Proportion and Similar Figure Applications
13.9.7E: Exercises
13.9.08: Solve Uniform Motion and Work Applications
13.9.8E: Exercises
13.9.09: Use Direct and Inverse Variation
13.9.9E: Exercises
13.9.10: Chapter 8 Review Exercises
13.E: Review Exercises 2
14: Factoring
14.01: Prelude to Factoring
14.02: Greatest Common Factor and Factor by Grouping
14.2E: Exercises
14.03: Factor Trinomials
14.3E: Exercises
14.04: Factor Special Products
14.4E: Exercises
14.05: General Strategy for Factoring Polynomials
14.5E: Exercises
14.06: Polynomial Equations
14.6E: Exercises
14.E: Chapter 6 Review Exercises
15: Rational Expressions
15.01: Rational Expressions and Functions
15.02: Multiply and Divide Rational Expressions
15.2E: Exercises
15.03: Add and Subtract Rational Expressions
15.3E: Exercises
15.04: Simplify Complex Rational Expressions
15.4E: Exercises
15.05: Solve Rational Equations
15.5E: Exercises
15.06: Solve Applications with Rational Equations
15.6.01: More Examples of Applications
15.6E: Exercises
15.E: Review Exercises
16: Introduction to Functions
16.01: Relations and Functions
16.1E: Exercises
16.02: Basic Classes of Functions
16.2.01: Linear Functions and Slope
16.2.02: Equations of Lines
16.2.03: Rational Functions
16.2.04: Power Functions and Polynomial Functions
16.2E: Exercises
16.03: Graphs of Functions
16.3.01: Domain and Range
16.3E: Exercises
16.04: Graph Quadratic Functions Using Properties
16.4E: Exercises
16.05: Transformation of Functions
16.5.01: Vertical Transformations
16.5.02: Horizontal Transformations
16.5.03: Graph Quadratic Functions Using Transformations
16.5.3E: Exercises
16.5E: Exercises
16.06: The Algebra of Functions
16.E: Review Exercises 1
16.E: Review Exercises 2
17: Radical Expressions and Functions
17.01: Prelude to Roots and Radicals
17.02: Simplify Expressions with Roots
17.2E: Exercises
17.03: Simplify Radical Expressions
17.3E: Exercises
17.04: Simplify Rational Exponents
17.4E: Exercises
17.05: Add Subtract and Multiply Radical Expressions
17.5E: Exercises
17.06: Divide Radical Expressions
17.6E: Exercises
17.07: Solve Radical Equations
17.7E: Exercises
17.08: Use Radicals in Functions
17.8E: Exercises
17.09: Use the Complex Number System
17.9E: Exercises
17.10: Review Exercises
18: Quadratic Equations and Functions
18.01: Prelude to Quadratic Equations and Functions
18.02: Solve Quadratic Equations Using the Square Root Property
18.2E: Exercises
18.03: Solve Quadratic Equations by Completing the Square
18.3E: Exercises
18.04: Solve Quadratic Equations Using the Quadratic Formula
18.4E: Exercises
18.05: Solve Quadratic Equations in Quadratic Form
18.5E: Exercises
18.06: Solve Applications of Quadratic Equations
18.6E: Exercises
18.07: Review Exercises
19: Equations and Inequalities
19.01: Review- Solve Linear Inequalities
19.1E: Exercises
19.02: Solve Compound Inequalities
19.2E: Exercises
19.03: Solve Absolute Value Equations and Inequalities
19.3E: Exercises
19.04: Solve Rational Inequalities
19.4E: Exercises
19.05: Solve Quadratic Inequalities
19.5E: Exercises
19.E: Review Exercises 1
19.E: Review Exercises 2
20: Exponential and Logarithmic Functions
20.01: Prelude to Exponential and Logarithmic Functions
20.02: Finding Composite and Inverse Functions
20.2E: Exercises
20.03: Evaluate and Graph Exponential Functions
20.3E: Exercises
20.04: Evaluate and Graph Logarithmic Functions
20.4E: Exercises
20.05: Use the Properties of Logarithms
20.5E: Exercises
20.06: Solve Exponential and Logarithmic Equations
20.6E: Exercises
20.07: Review Exercises
21: Systems of Linear Equations
21.01: Introduction
21.02: Solve Systems of Linear Equations with Two Variables
21.2E: Exercises
21.03: Solve Applications with Systems of Equations
21.3E: Exercises
21.04: Solve Mixture Applications with Systems of Equations
21.4E: Exercises
21.05: Solve Systems of Equations with Three Variables
21.5E: Exercises
21.06: Solve Systems of Equations Using Matrices
21.6E: Exercises
21.07: Solve Systems of Equations Using Determinants
21.7E: Exercises
21.08: Review Exercises
22: Conics
22.01: Prelude to Conics
22.02: Distance and Midpoint Formulas and Circles
22.2E: Exercises
22.03: Parabolas
22.3E: Exercises
22.04: Ellipses
22.4E: Exercises
22.05: Hyperbolas
22.5E: Exercises
22.06: Solving Systems of Nonlinear Equations
22.6E: Exercises
22.07: Review Exercises