Foundations of Mathematics for Virginia
0.1 Reading and Writing Whole Numbers
0.2 Addition and Subtraction with Whole Numbers
- Examples
- Example 1: Adding Whole Numbers
- Example 2: Adding Whole Numbers
- Example 4: Adding Whole Numbers
- Example 5: The Properties of Addition
- Example 6: Finding the Perimeter of a Triangle
- Example 7: Finding the Perimeter of a Geometric Figure
- Example 8: Subtracting Whole Numbers
- Example 9: Subtracting Whole Numbers
- Example 10: Subtracting Whole Numbers
- Example 11: Subtracting Whole Numbers
- Example 12: Subtracting Whole Numbers
- Example 13: Subtracting Whole Numbers
0.3 Multiplication with Whole Numbers
0.4 Division with Whole Numbers
- Examples
- Example 1: Division using Repeated Subtraction
- Example 2: Division with Whole Numbers
- Example 3: Division Involving 0
- Example 4: Using Long Division
- Example 5: Using Long Division
- Example 6: Using Long Division
- Example 7: Using Long Division
- Example 10: Using Long Division
- Example 11: Using Long Division
- Example 12: Using Long Division
- Example 13: Using Long Division
0.5 Rounding and Estimating with Whole Numbers
- Examples
- Example 1: Rounding Whole Numbers
- Example 2: Rounding Whole Numbers
- Example 3: Rounding Whole Numbers
- Example 4: Estimating a Sum of Whole Numbers
- Example 6: Estimating a Difference of Whole Numbers
- Example 7: Estimating a Difference of Whole Numbers
- Example 8: Estimating Products of Whole Numbers
- Example 9: Estimating Products of Whole Numbers
- Example 10: Estimating Quotients of Whole Numbers
- Example 11: Estimating Quotients of Whole Numbers
- Example 13: Estimating Quotients of Whole Numbers
0.6 Exponents and Order of Operations
- Examples
- Example 1: Understanding the Terms Base and Exponent
- Example 2: Reading Equations Containing Exponential Expressions
- Example 3: Writing and Evaluating Exponential Expressions
- Example 4: Evaluating Exponential Expressions
- Example 5: Order of Operations
- Example 6: Order of Operations
- Example 7: Order of Operations
- Example 8: Order of Operations
- Example 9: Order of Operations
0.7 Problem Solving with Whole Numbers
1.1 Exponents and Prime Numbers
1.2 Introduction to Fractions and Mixed Numbers
- Examples
- Example 1: Understanding Fractions
- Example 2: Proper Fractions
- Example 3: Improper Fractions
- Example 4: The Number 0 in Fractions
- Example 5: Reducing Fractions to Lowest Terms
- Example 6: Reducing Fractions to Lowest Terms
- Example 8: Changing a Mixed Number to an Improper Fraction
- Example 10: Changing an Improper Fraction to a Mixed Number
1.3 Ratios and Rates
1.4 Multiplication and Division with Fractions and Mixed Numbers
- Examples
- Example 1: Multiplication with Fractions
- Example 2: Multiplication with Fractions
- Example 3: Multiplication with Mixed Numbers
- Example 4: Multiplication with Fractions and Mixed Numbers
- Example 5: Multiplying and Reducing with Fractions
- Example 6: Multiplying and Reducing with Fractions
- Example 8: Multiplying and Reducing with Mixed Numbers
- Example 9: Multiplying and Reducing with Fractions
- Example 10: Multiplying and Reducing with Fractions
- Example 11: Application of Multiplying and Reducing with Fractions
- Example 12: Reciprocals
- Example 13: Reciprocals
- Example 14: Dividing with Fractions
- Example 15: Dividing and Reducing Fractions
- Example 16: Dividing and Reducing with Fractions and Mixed Numbers
- Example 18: Multiplying and Dividing with Fractions and Mixed Numbers
- Example 19: Multiplying and Dividing with Fractions and Mixed Numbers
1.5 Least Common Multiple
- Examples
- Example 1: Finding the Least Common Multiple (LCM)
- Example 2: Finding the Least Common Multiple (LCM)
- Example 4: Finding the Least Common Multiple (LCM)
- Example 5: Finding the Least Common Multiple (LCM)
- Example 6: Understanding Least Common Multiple (LCM)
- Example 7: Understanding Least Common Multiple (LCM)
- Example 8: Application: Finding the LCM
- Example 9: Finding Equivalent Fractions
- Example 10: Finding Equivalent Fractions
1.6 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Fractions with the Same Denominator
- Example 2: Adding Fractions with the Same Denominator
- Example 3: Adding Fractions with the Same Denominator
- Example 4: Adding Fractions with Different Denominators
- Example 5: Adding Fractions with Different Denominators
- Example 6: Adding Three Fractions with Different Denominators
- Example 7: Application of Adding Fractions with Different Denominators
- Example 8: Application of Adding Fractions with Different Denominators
- Example 9: Subtracting Fractions with the Same Denominator
- Example 10: Subtracting Fractions with the Same Denominator
- Example 11: Subtracting Fractions with Different Denominators
- Example 12: Subtracting Fractions with Different Denominators
- Example 14: Application of Subtracting Fractions with Different Denominators
1.7 Addition and Subtraction with Mixed Numbers
- Examples
- Example 1: Adding Mixed Numbers
- Example 2: Adding Mixed Numbers
- Example 3: Adding Mixed Numbers
- Example 4: Subtracting Mixed Numbers
- Example 5: Subtracting Mixed Numbers
- Example 6: Subtracting Mixed Numbers with Borrowing
- Example 7: Subtracting Mixed Numbers with Borrowing
- Example 8: Subtracting Mixed Numbers with Borrowing
1.8 Order of Operations with Fractions and Mixed Numbers
- Examples
- Example 1: Comparing Fractions
- Example 2: Comparing Fractions
- Example 3: Comparing Fractions
- Example 4: Order of Operations with Fractions
- Example 5: Order of Operations with Fractions
- Example 6: Order of Operations with Fractions
- Example 8: Order of Operations with Mixed Numbers
- Example 9: Order of Operations with Mixed Numbers
- Example 10: Order of Operations with Mixed Numbers
- Example 11: Average of Mixed Numbers
2.1 Introduction to Decimal Numbers
- Examples
- Example 1: Reading and Writing Decimal Numbers
- Example 2: Reading and Writing Decimal Numbers
- Example 3: Reading and Writing Decimal Numbers
- Example 4: Reading and Writing Decimal Numbers
- Example 5: Comparing Decimal Numbers
- Example 6: Comparing Decimal Numbers
- Example 7: Comparing Decimal Numbers
- Example 8: Rounding Decimal Numbers
- Example 9: Rounding Decimal Numbers
2.2 Addition and Subtraction with Decimal Numbers
2.3 Multiplication with Decimal Numbers
2.4 Division with Decimal Numbers
- Examples
- Example 1: Division with Decimal Numbers
- Example 3: Division with Decimal Numbers
- Example 4: Division with Decimal Numbers
- Example 5: Division by Powers of 10
- Example 6: Division with Decimal Numbers
- Example 7: Order of Operations with Decimal Numbers
- Example 8: Order of Operations with Decimal Numbers
- Example 9: Gas Mileage
- Example 10: Bicycle Speed
- Example 11: Gasoline Prices
2.5 Decimal Numbers and Fractions
- Examples
- Example 1: Changing Decimal Numbers to Fractions
- Example 2: Changing Decimal Numbers to Fractions
- Example 3: Changing Decimal Numbers to Fractions
- Example 4: Changing Decimal Numbers to Fractions
- Example 5: Changing Decimal Numbers to Fractions
- Example 6: Changing Decimal Numbers to Fractions
- Example 7: Changing Fractions to Decimal Numbers
- Example 8: Changing Fractions to Decimal Numbers
- Example 9: Changing Fractions to Decimal Numbers
- Example 10: Changing Fractions to Decimal Numbers
- Example 11: Operating with Both Fractions and Decimal Numbers
- Example 12: Operating with Both Fractions and Decimal Numbers
2.9 U.S. Measurements
- Examples
- Example 1: Basic Conversions
- Example 2: Using Multiplication/Division to Convert Measures
- Example 3: Using Unit Fractions to Convert Measures
- Example 4: Using Unit Fractions to Convert Measures in Two Steps
- Example 5: Converting Measures with a Remainder
- Example 6: Adding and Subtracting Measures
2.10 The Metric System
- Examples
- Example 1: Converting Metric Units of Length
- Example 2: Converting Metric Units of Length
- Example 3: Converting Metric Units of Length
- Example 4: Converting Metric Units of Length
- Example 5: Equivalent Measures of Mass
- Example 6: Equivalent Measures of Mass
- Example 7: Equivalent Measures of Volume
- Example 8: Equivalent Measures of Volume
- Example 9: Equivalent Measures of Liquid Volume
- Example 10: Equivalent Measures of Liquid Volume
- Example 11: Operation with Metric Units
2.11 U.S. to Metric Conversions
- Examples
- Example 1: Equivalent Measures of Temperature
- Example 2: Converting Measures of Temperature
- Example 3: Converting Measures of Temperature
- Example 4: Converting Measures of Length
- Example 5: Converting Measures of Length
- Example 6: Converting Measures of Length
- Example 7: Converting Measures of Length
- Example 8: Converting Measures of Area
- Example 9: Converting Measures of Area
- Example 10: Converting Measures of Area
- Example 11: Converting Measures of Area
- Example 12: Converting Measures of Liquid Volume
- Example 13: Converting Measures of Liquid Volume
- Example 14: Converting Measures of Liquid Volume
- Example 15: Converting Measures of Volume
- Example 16: Converting Measures of Mass
- Example 17: Converting Measures of Mass
2.12 Reading Graphs
3.1a The Real Number Line and Inequalities
3.1b Introduction to Absolute Value
3.2 Introduction to Exponents
- Examples
- Example 1: Understanding the Terms Base and Exponent
- Example 2: Reading Equations Containing Exponential Expressions
- Example 3: Writing and Evaluating Exponential Expressions
- Example 5: Order of Operations
- Example 6: Order of Operations
- Example 7: Order of Operations
- Example 8: Order of Operations
- Example 9: Order of Operations
3.3 Square Roots
3.4 Addition with Real Numbers
3.5 Subtraction with Real Numbers
3.6 Multiplication and Division with Real Numbers
3.7 Order of Operations with Real Numbers
3.8 Introduction to Scientific Notation
3.9 Properties of Real Numbers
3.10 Simplifying and Evaluating Algebraic Expressions
3.11a Solving Linear Equations: x + b = c
3.11b Solving Linear Equations: ax = c
3.12 Solving Percent Problems Using the Equation: R * B = A
3.13 Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease
3.14 Applications: Simple Interest
3.15 Perimeter
3.16 Area
3.17 Circles
3.18 Volume
- Examples
- Example 1: Finding the Volume of a Rectangular Solid
- Example 2: Finding the Volume of a Sphere
- Example 3: Finding the Volume of a Cylinder
- Example 4: Finding the Volume of a Solid
- Example 5: Finding the Volume of a Cube
- Example 6: Finding the Surface Area of a Rectangular Solid
- Example 7: Finding the Surface Area of a Right Circular Cylinder
4.1a Solving Linear Equations: x + b = c
4.1b Solving Linear Equations: ax = c
4.2 Solving Linear Equations: ax + b = c
- Examples
- Example 1: Solving Linear Equations of the Form ax + b = c
- Example 2: Solving Linear Equations of the Form ax + b = c
- Example 3: Solving Linear Equations of the Form ax + b = c
- Example 4: Solving Linear Equations Involving Decimals
- Example 5: Solving Linear Equations Involving Decimals
- Example 6: Solving Linear Equations with Fractional Coefficients
- Example 7: Solving Linear Equations with Fractional Coefficients
4.3 Solving Linear Equations: ax + b = cx + d
- Examples
- Example 1: Solving Equations of the Form ax + b = cx + d
- Example 2: Solving Equations of the Form ax + b = cx + d
- Example 3: Solving Linear Equations Involving Decimals
- Example 4: Solving Linear Equations with Fractional Coefficients
- Example 5: Solving Equations with Parentheses
- Example 6: Solving Equations with Parentheses
- Example 8: Solutions of Equations
- Example 9: Solutions of Equations
- Example 10: Solutions of Equations
4.4 Working with Formulas
4.5 Translating English Phrases and Algebraic Expressions
4.6 Applications: Number Problems and Consecutive Integers
4.7 Applications: Distance-Rate-Time, Interest, Average
4.8 Solving Absolute Value Equations
4.9 Linear Inequalities
- Examples
- Example 1: Graphing Intervals
- Example 2: Graphing Intervals
- Example 3: Graphing Intervals
- Example 4: Graphing Intervals
- Example 5: Sets of Real Numbers Illustrating Union
- Example 6: Sets of Real Numbers Illustrating Intersection
- Example 7: Solving Linear Inequalities
- Example 8: Solving Linear Inequalities
- Example 9: Solving Linear Inequalities
- Example 11: Solving Compound Inequalities
- Example 12: Solving Compound Inequalities
- Example 13: Solving Compound Inequalities
- Example 14: Application with an Inequality
- Example 15: Application with an Inequality
5.1 The Cartesian Coordinate System
5.2 Graphing Linear Equations in Two Variables
5.3a Slope
5.3b Slope-Intercept Form
5.4a Point-Slope Form
5.4b Parallel and Perpendicular Lines
5.5 Graphing Linear Inequalities in Two Variables
5.6 Introduction to Functions and Function Notation
6.1a Exponents
6.1b Negative Exponents
6.2a Power Rules for Exponents
6.2b Scientific Notation
6.3 Introduction to Polynomials
6.4 Addition and Subtraction with Polynomials
6.5 Multiplication with Polynomials
6.6a The FOIL Method
- Examples
- Example 1: FOIL Method
6.6b Special Products of Binomials
6.7 Division by a Monomial
6.8a Greatest Common Factor of Two or More Terms
- Examples
- Example 1: Finding the GCF
6.8b Greatest Common Factor of a Polynomial
6.8c Factoring Expressions by Grouping
6.9 Factoring Trinomials with Leading Coefficient 1
6.10a Factoring Trinomials by the ac-Method
- Examples
- Example 1: Using the ac-Method
6.10b Factoring Trinomials by Trial and Error
6.11a Special Factorizations - Squares
6.11b Special Factorizations - Cubes
6.12 Additional Factoring Practice
6.13 Solving Quadratic Equations by Factoring
6.14 Applications of Quadratic Equations
7.1a Introduction to Rational Expressions
7.1b Multiplication and Division with Rational Expressions
7.2 Addition and Subtraction with Rational Expressions
- Examples
- Example 1: Adding Rational Expressions with a Common Denominator
- Example 2: Finding the LCD of Two Rational Expressions
- Example 3: Building Rational Expressions to Higher Terms
- Example 4: Adding Rational Expressions with Different Denominators
- Example 6: Subtracting Rational Expressions with a Common Denominator
- Example 7: Subtracting Rational Expressions with Different Denominators
7.3 Complex Fractions
7.4a Division by a Monomial
7.4b The Division Algorithm
7.5 Solving Equations with Rational Expressions
7.6 Applications: Rational Expressions
8.1 Evaluating Radicals
8.2 Rational Exponents
8.3 Simplifying Radicals
8.4a Addition and Subtraction with Radicals
8.4b Multiplication with Radicals
8.5 Rationalizing Denominators
8.6 Equations with Radicals
8.7 Complex Numbers
8.8a Applications: The Pythagorean Theorem
8.8b Applications: Distance Formula and Midpoint Formula
9.1 Functions and Function Notation
- Examples
- Example 1: Finding the Domain and Range
- Example 2: Reading the Domain and Range from the Graph of a Relation
- Example 3: Functions
- Example 4: Vertical Line Test
- Example 5: Domain
- Example 6: Finding the Domain of a Radical Function
- Example 7: Function Evaluation
- Example 8: Nonlinear Function Evaluation
- Example 9: Evaluating Radical Functions